MethodsBench.md

v4.1 Branch

1000 random votes different for each test, variable number of candidates (look at column "set")

• AMD Ryzen 9 5900X

PHPBench (1.2.5) with PHP version 8.1.7, xdebug ❌, opcache ✔ (with JIT Tracing)

    #[Bench\Warmup(1)]
    #[Bench\Iterations(3)]
    #[Bench\Revs(1)]

Non-Proportional

Same as 4.0

Proportional

Subjects: 1, Assertions: 0, Failures: 0, Errors: 0 +--------------------------+-------------------+-----------------------+------+-----+-----------+-------------+---------+ | benchmark | subject | set | revs | its | mem_peak | mode | rstdev | +--------------------------+-------------------+-----------------------+------+-----+-----------+-------------+---------+ | MethodsProportionalBench | benchByCandidates | STV,3 | 1 | 3 | 6.140mb | 0.002796s | ±18.88% | | MethodsProportionalBench | benchByCandidates | CPO STV,3 | 1 | 3 | 6.150mb | 0.013553s | ±46.44% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,3 | 1 | 3 | 3.963mb | 0.001552s | ±7.83% | | MethodsProportionalBench | benchByCandidates | Jefferson,3 | 1 | 3 | 3.963mb | 0.001470s | ±2.80% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,3 | 1 | 3 | 3.963mb | 0.001400s | ±6.81% | | MethodsProportionalBench | benchByCandidates | STV,4 | 1 | 3 | 6.649mb | 0.003776s | ±5.99% | | MethodsProportionalBench | benchByCandidates | CPO STV,4 | 1 | 3 | 6.770mb | 0.020136s | ±28.89% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,4 | 1 | 3 | 4.407mb | 0.001897s | ±2.65% | | MethodsProportionalBench | benchByCandidates | Jefferson,4 | 1 | 3 | 4.407mb | 0.001770s | ±5.52% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,4 | 1 | 3 | 4.407mb | 0.001668s | ±11.97% | | MethodsProportionalBench | benchByCandidates | STV,5 | 1 | 3 | 7.470mb | 0.004705s | ±1.49% | | MethodsProportionalBench | benchByCandidates | CPO STV,5 | 1 | 3 | 7.669mb | 0.023462s | ±15.21% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,5 | 1 | 3 | 4.851mb | 0.002089s | ±8.17% | | MethodsProportionalBench | benchByCandidates | Jefferson,5 | 1 | 3 | 4.851mb | 0.001867s | ±2.44% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,5 | 1 | 3 | 4.851mb | 0.001759s | ±7.13% | | MethodsProportionalBench | benchByCandidates | STV,6 | 1 | 3 | 8.292mb | 0.005555s | ±8.11% | | MethodsProportionalBench | benchByCandidates | CPO STV,6 | 1 | 3 | 10.407mb | 0.169012s | ±2.73% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,6 | 1 | 3 | 5.295mb | 0.002087s | ±0.79% | | MethodsProportionalBench | benchByCandidates | Jefferson,6 | 1 | 3 | 5.295mb | 0.001869s | ±0.41% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,6 | 1 | 3 | 5.295mb | 0.001886s | ±1.77% | | MethodsProportionalBench | benchByCandidates | STV,7 | 1 | 3 | 9.113mb | 0.008930s | ±7.93% | | MethodsProportionalBench | benchByCandidates | CPO STV,7 | 1 | 3 | 13.333mb | 0.344687s | ±0.74% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,7 | 1 | 3 | 5.739mb | 0.002214s | ±4.71% | | MethodsProportionalBench | benchByCandidates | Jefferson,7 | 1 | 3 | 5.739mb | 0.002079s | ±1.59% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,7 | 1 | 3 | 5.739mb | 0.002031s | ±8.01% | | MethodsProportionalBench | benchByCandidates | STV,8 | 1 | 3 | 10.609mb | 0.009126s | ±0.97% | | MethodsProportionalBench | benchByCandidates | CPO STV,8 | 1 | 3 | 18.034mb | 0.641492s | ±0.78% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,8 | 1 | 3 | 6.503mb | 0.002300s | ±22.88% | | MethodsProportionalBench | benchByCandidates | Jefferson,8 | 1 | 3 | 6.503mb | 0.002214s | ±3.09% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,8 | 1 | 3 | 6.503mb | 0.002173s | ±2.41% | | MethodsProportionalBench | benchByCandidates | STV,9 | 1 | 3 | 11.447mb | 0.007795s | ±6.70% | | MethodsProportionalBench | benchByCandidates | CPO STV,9 | 1 | 3 | 83.423mb | 5.907340s | ±0.54% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,9 | 1 | 3 | 6.961mb | 0.002415s | ±2.68% | | MethodsProportionalBench | benchByCandidates | Jefferson,9 | 1 | 3 | 6.961mb | 0.002306s | ±4.59% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,9 | 1 | 3 | 6.961mb | 0.002176s | ±2.10% | | MethodsProportionalBench | benchByCandidates | STV,10 | 1 | 3 | 12.233mb | 0.008335s | ±12.54% | | MethodsProportionalBench | benchByCandidates | CPO STV,10 | 1 | 3 | 155.669mb | 13.365452s | ±1.92% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,10 | 1 | 3 | 7.408mb | 0.004098s | ±15.02% | | MethodsProportionalBench | benchByCandidates | Jefferson,10 | 1 | 3 | 7.408mb | 0.003836s | ±19.18% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,10 | 1 | 3 | 7.408mb | 0.003827s | ±17.49% | | MethodsProportionalBench | benchByCandidates | STV,11 | 1 | 3 | 13.091mb | 0.010444s | ±6.50% | | MethodsProportionalBench | benchByCandidates | CPO STV,11 | 1 | 3 | 286.707mb | 25.839933s | ±1.15% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,11 | 1 | 3 | 7.854mb | 0.002936s | ±1.94% | | MethodsProportionalBench | benchByCandidates | Jefferson,11 | 1 | 3 | 7.854mb | 0.002715s | ±4.13% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,11 | 1 | 3 | 7.854mb | 0.002782s | ±0.63% | | MethodsProportionalBench | benchByCandidates | STV,12 | 1 | 3 | 13.879mb | 0.010493s | ±1.24% | | MethodsProportionalBench | benchByCandidates | CPO STV,12 | 1 | 3 | 2.417gb | 310.681427s | ±0.34% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,12 | 1 | 3 | 8.300mb | 0.003592s | ±51.21% | | MethodsProportionalBench | benchByCandidates | Jefferson,12 | 1 | 3 | 8.299mb | 0.003187s | ±34.53% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,12 | 1 | 3 | 8.300mb | 0.003387s | ±32.42% | | MethodsProportionalBench | benchByCandidates | STV,13 | 1 | 3 | 14.701mb | 0.012803s | ±1.34% | | MethodsProportionalBench | benchByCandidates | CPO STV,13 | 1 | 3 | 14.732mb | 0.004578s | ±0.85% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,13 | 1 | 3 | 8.745mb | 0.003384s | ±4.92% | | MethodsProportionalBench | benchByCandidates | Jefferson,13 | 1 | 3 | 8.745mb | 0.003551s | ±4.73% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,13 | 1 | 3 | 8.745mb | 0.003303s | ±4.17% | | MethodsProportionalBench | benchByCandidates | STV,14 | 1 | 3 | 15.522mb | 0.013331s | ±4.09% | | MethodsProportionalBench | benchByCandidates | CPO STV,14 | 1 | 3 | 15.487mb | 0.005143s | ±14.17% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,14 | 1 | 3 | 9.191mb | 0.003328s | ±0.64% | | MethodsProportionalBench | benchByCandidates | Jefferson,14 | 1 | 3 | 9.191mb | 0.003417s | ±3.84% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,14 | 1 | 3 | 9.191mb | 0.003650s | ±14.27% | | MethodsProportionalBench | benchByCandidates | STV,15 | 1 | 3 | 16.346mb | 0.014077s | ±4.13% | | MethodsProportionalBench | benchByCandidates | CPO STV,15 | 1 | 3 | 16.309mb | 0.004995s | ±4.99% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,15 | 1 | 3 | 9.640mb | 0.005224s | ±31.24% | | MethodsProportionalBench | benchByCandidates | Jefferson,15 | 1 | 3 | 9.639mb | 0.003729s | ±16.58% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,15 | 1 | 3 | 9.640mb | 0.003584s | ±0.64% | | MethodsProportionalBench | benchByCandidates | STV,16 | 1 | 3 | 18.446mb | 0.015429s | ±8.53% | | MethodsProportionalBench | benchByCandidates | CPO STV,16 | 1 | 3 | 18.411mb | 0.004596s | ±7.59% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,16 | 1 | 3 | 10.728mb | 0.004133s | ±0.77% | | MethodsProportionalBench | benchByCandidates | Jefferson,16 | 1 | 3 | 10.727mb | 0.003669s | ±4.98% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,16 | 1 | 3 | 10.728mb | 0.004017s | ±4.55% | | MethodsProportionalBench | benchByCandidates | STV,17 | 1 | 3 | 19.326mb | 0.016124s | ±2.04% | | MethodsProportionalBench | benchByCandidates | CPO STV,17 | 1 | 3 | 19.287mb | 0.005705s | ±1.88% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,17 | 1 | 3 | 11.237mb | 0.004140s | ±1.00% | | MethodsProportionalBench | benchByCandidates | Jefferson,17 | 1 | 3 | 11.236mb | 0.003962s | ±4.62% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,17 | 1 | 3 | 11.237mb | 0.003954s | ±4.42% | | MethodsProportionalBench | benchByCandidates | STV,18 | 1 | 3 | 20.157mb | 0.016955s | ±4.44% | | MethodsProportionalBench | benchByCandidates | CPO STV,18 | 1 | 3 | 20.115mb | 0.005920s | ±1.38% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,18 | 1 | 3 | 11.700mb | 0.004243s | ±11.95% | | MethodsProportionalBench | benchByCandidates | Jefferson,18 | 1 | 3 | 11.699mb | 0.004167s | ±5.96% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,18 | 1 | 3 | 11.700mb | 0.004331s | ±10.30% | | MethodsProportionalBench | benchByCandidates | STV,19 | 1 | 3 | 20.984mb | 0.017616s | ±1.99% | | MethodsProportionalBench | benchByCandidates | CPO STV,19 | 1 | 3 | 20.940mb | 0.005932s | ±7.57% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,19 | 1 | 3 | 12.151mb | 0.004609s | ±3.18% | | MethodsProportionalBench | benchByCandidates | Jefferson,19 | 1 | 3 | 12.151mb | 0.004244s | ±4.38% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,19 | 1 | 3 | 12.151mb | 0.004391s | ±3.48% | | MethodsProportionalBench | benchByCandidates | STV,20 | 1 | 3 | 21.808mb | 0.019353s | ±6.03% | | MethodsProportionalBench | benchByCandidates | CPO STV,20 | 1 | 3 | 21.765mb | 0.006336s | ±0.70% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,20 | 1 | 3 | 12.602mb | 0.004655s | ±2.31% | | MethodsProportionalBench | benchByCandidates | Jefferson,20 | 1 | 3 | 12.602mb | 0.004561s | ±0.98% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,20 | 1 | 3 | 12.602mb | 0.004507s | ±0.33% | | MethodsProportionalBench | benchByCandidates | STV,30 | 1 | 3 | 30.114mb | 0.027635s | ±2.53% | | MethodsProportionalBench | benchByCandidates | CPO STV,30 | 1 | 3 | 30.138mb | 0.010538s | ±12.38% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,30 | 1 | 3 | 17.213mb | 0.008364s | ±9.75% | | MethodsProportionalBench | benchByCandidates | Jefferson,30 | 1 | 3 | 17.212mb | 0.006590s | ±3.75% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,30 | 1 | 3 | 17.213mb | 0.006709s | ±1.63% | | MethodsProportionalBench | benchByCandidates | STV,40 | 1 | 3 | 41.236mb | 0.037545s | ±4.36% | | MethodsProportionalBench | benchByCandidates | CPO STV,40 | 1 | 3 | 41.193mb | 0.012487s | ±2.01% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,40 | 1 | 3 | 23.370mb | 0.009508s | ±11.16% | | MethodsProportionalBench | benchByCandidates | Jefferson,40 | 1 | 3 | 23.369mb | 0.009279s | ±1.30% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,40 | 1 | 3 | 23.370mb | 0.009423s | ±4.00% | | MethodsProportionalBench | benchByCandidates | STV,50 | 1 | 3 | 49.602mb | 0.047640s | ±1.69% | | MethodsProportionalBench | benchByCandidates | CPO STV,50 | 1 | 3 | 49.443mb | 0.014999s | ±5.16% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,50 | 1 | 3 | 28.048mb | 0.012300s | ±1.65% | | MethodsProportionalBench | benchByCandidates | Jefferson,50 | 1 | 3 | 28.047mb | 0.011829s | ±4.08% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,50 | 1 | 3 | 28.047mb | 0.012519s | ±2.92% | | MethodsProportionalBench | benchByCandidates | STV,60 | 1 | 3 | 57.963mb | 0.060343s | ±3.62% | | MethodsProportionalBench | benchByCandidates | CPO STV,60 | 1 | 3 | 57.755mb | 0.019293s | ±5.08% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,60 | 1 | 3 | 32.772mb | 0.015561s | ±2.90% | | MethodsProportionalBench | benchByCandidates | Jefferson,60 | 1 | 3 | 32.771mb | 0.014827s | ±0.42% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,60 | 1 | 3 | 32.772mb | 0.015001s | ±1.17% | | MethodsProportionalBench | benchByCandidates | STV,70 | 1 | 3 | 79.765mb | 0.072319s | ±1.12% | | MethodsProportionalBench | benchByCandidates | CPO STV,70 | 1 | 3 | 79.335mb | 0.024373s | ±3.34% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,70 | 1 | 3 | 45.391mb | 0.019033s | ±6.86% | | MethodsProportionalBench | benchByCandidates | Jefferson,70 | 1 | 3 | 45.390mb | 0.018760s | ±5.18% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,70 | 1 | 3 | 45.391mb | 0.018700s | ±0.84% | | MethodsProportionalBench | benchByCandidates | STV,80 | 1 | 3 | 88.501mb | 0.083748s | ±6.08% | | MethodsProportionalBench | benchByCandidates | CPO STV,80 | 1 | 3 | 87.929mb | 0.027875s | ±2.13% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,80 | 1 | 3 | 50.453mb | 0.022614s | ±2.68% | | MethodsProportionalBench | benchByCandidates | Jefferson,80 | 1 | 3 | 50.451mb | 0.022171s | ±0.40% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,80 | 1 | 3 | 50.452mb | 0.022119s | ±0.68% | | MethodsProportionalBench | benchByCandidates | STV,90 | 1 | 3 | 97.257mb | 0.095371s | ±0.50% | | MethodsProportionalBench | benchByCandidates | CPO STV,90 | 1 | 3 | 96.523mb | 0.032974s | ±2.87% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,90 | 1 | 3 | 55.586mb | 0.026290s | ±1.04% | | MethodsProportionalBench | benchByCandidates | Jefferson,90 | 1 | 3 | 55.585mb | 0.026412s | ±3.99% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,90 | 1 | 3 | 55.586mb | 0.026185s | ±1.39% | | MethodsProportionalBench | benchByCandidates | STV,100 | 1 | 3 | 105.949mb | 0.119077s | ±6.04% | | MethodsProportionalBench | benchByCandidates | CPO STV,100 | 1 | 3 | 105.116mb | 0.041255s | ±5.16% | | MethodsProportionalBench | benchByCandidates | Largest Remainder,100 | 1 | 3 | 60.703mb | 0.030632s | ±4.05% | | MethodsProportionalBench | benchByCandidates | Jefferson,100 | 1 | 3 | 60.703mb | 0.030897s | ±0.77% | | MethodsProportionalBench | benchByCandidates | Sainte-Laguë,100 | 1 | 3 | 60.703mb | 0.030627s | ±2.33% | +--------------------------+-------------------+-----------------------+------+-----+-----------+-------------+---------+

v4.0-beta1 Branch

1000 random votes different for each test, variable number of candidates (look at column "set")

• AMD Ryzen 9 5900X

PHPBench (1.2.5) with PHP version 8.1.6, xdebug ❌, opcache ✔ (with JIT Tracing)

    #[Bench\Warmup(1)]
    #[Bench\Iterations(3)]
    #[Bench\Revs(1)]

Non-Proportional

Subjects: 1, Assertions: 0, Failures: 0, Errors: 0 +-----------------------------+-------------------+-----------------------------------+------+-----+----------+-------------+----------+ | benchmark | subject | set | revs | its | mem_peak | mode | rstdev | +-----------------------------+-------------------+-----------------------------------+------+-----+----------+-------------+----------+ | MethodsNonProportionalBench | benchByCandidates | BordaCount,3 | 1 | 3 | 4.271mb | 0.002924s | ±1.54% | | MethodsNonProportionalBench | benchByCandidates | Copeland,3 | 1 | 3 | 3.935mb | 0.000023s | ±13.03% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,3 | 1 | 3 | 3.863mb | 0.000020s | ±0.00% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,3 | 1 | 3 | 3.864mb | 0.000024s | ±5.27% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,3 | 1 | 3 | 3.926mb | 0.001511s | ±1.33% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,3 | 1 | 3 | 3.932mb | 0.004448s | ±48.14% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,3 | 1 | 3 | 4.282mb | 0.000276s | ±138.24% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,3 | 1 | 3 | 3.929mb | 0.002349s | ±27.04% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,3 | 1 | 3 | 3.932mb | 0.004415s | ±1.34% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,3 | 1 | 3 | 3.864mb | 0.000024s | ±4.04% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,3 | 1 | 3 | 3.864mb | 0.000024s | ±0.00% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,3 | 1 | 3 | 3.864mb | 0.000023s | ±3.55% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,3 | 1 | 3 | 3.934mb | 0.001575s | ±77.80% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,3 | 1 | 3 | 3.932mb | 0.000203s | ±135.55% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,3 | 1 | 3 | 3.865mb | 0.000027s | ±1.72% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,3 | 1 | 3 | 3.865mb | 0.000028s | ±2.92% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,3 | 1 | 3 | 3.865mb | 0.000029s | ±1.64% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,5 | 1 | 3 | 4.815mb | 0.002170s | ±28.16% | | MethodsNonProportionalBench | benchByCandidates | Copeland,5 | 1 | 3 | 4.755mb | 0.000030s | ±3.07% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,5 | 1 | 3 | 4.753mb | 0.000024s | ±1.94% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,5 | 1 | 3 | 4.755mb | 0.000030s | ±1.55% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,5 | 1 | 3 | 4.785mb | 0.002025s | ±8.04% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,5 | 1 | 3 | 4.817mb | 0.008432s | ±30.49% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,5 | 1 | 3 | 4.835mb | 0.002584s | ±63.87% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,5 | 1 | 3 | 4.815mb | 0.001811s | ±52.88% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,5 | 1 | 3 | 4.786mb | 0.003948s | ±1.11% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,5 | 1 | 3 | 4.755mb | 0.000031s | ±23.38% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,5 | 1 | 3 | 4.755mb | 0.000032s | ±3.94% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,5 | 1 | 3 | 4.755mb | 0.000030s | ±0.00% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,5 | 1 | 3 | 4.837mb | 0.002302s | ±105.98% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,5 | 1 | 3 | 4.840mb | 0.000156s | ±123.44% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,5 | 1 | 3 | 4.816mb | 0.000036s | ±51.31% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,5 | 1 | 3 | 4.824mb | 0.000126s | ±132.19% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,5 | 1 | 3 | 4.819mb | 0.005626s | ±91.76% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,6 | 1 | 3 | 5.229mb | 0.002457s | ±5.62% | | MethodsNonProportionalBench | benchByCandidates | Copeland,6 | 1 | 3 | 5.269mb | 0.002489s | ±49.30% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,6 | 1 | 3 | 5.260mb | 0.001559s | ±78.69% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,6 | 1 | 3 | 5.264mb | 0.003050s | ±73.92% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,6 | 1 | 3 | 5.229mb | 0.002449s | ±3.15% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,6 | 1 | 3 | 5.262mb | 0.014201s | ±13.25% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,6 | 1 | 3 | 5.277mb | 0.001201s | ±1.27% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,6 | 1 | 3 | 5.229mb | 0.001869s | ±2.08% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,6 | 1 | 3 | 5.230mb | 0.004348s | ±1.65% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,6 | 1 | 3 | 5.261mb | 0.000115s | ±133.60% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,6 | 1 | 3 | 5.260mb | 0.001349s | ±68.59% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,6 | 1 | 3 | 5.201mb | 0.000027s | ±5.05% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,6 | 1 | 3 | 5.295mb | 0.002948s | ±42.04% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,6 | 1 | 3 | 5.228mb | 0.000107s | ±14.62% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,6 | 1 | 3 | 5.201mb | 0.000044s | ±18.40% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,6 | 1 | 3 | 5.201mb | 0.000046s | ±3.75% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,6 | 1 | 3 | 5.267mb | 0.009940s | ±22.86% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,7 | 1 | 3 | 5.674mb | 0.002877s | ±4.27% | | MethodsNonProportionalBench | benchByCandidates | Copeland,7 | 1 | 3 | 5.646mb | 0.000032s | ±5.10% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,7 | 1 | 3 | 5.643mb | 0.000025s | ±1.91% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,7 | 1 | 3 | 5.646mb | 0.000030s | ±7.44% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,7 | 1 | 3 | 5.674mb | 0.002809s | ±2.26% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,7 | 1 | 3 | 5.743mb | 0.014805s | ±4.45% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,7 | 1 | 3 | 5.723mb | 0.010580s | ±6.88% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,7 | 1 | 3 | 5.705mb | 0.002164s | ±48.66% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,7 | 1 | 3 | 5.674mb | 0.005069s | ±3.11% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,7 | 1 | 3 | 5.705mb | 0.001430s | ±68.26% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,7 | 1 | 3 | 5.706mb | 0.000121s | ±132.79% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,7 | 1 | 3 | 5.646mb | 0.000030s | ±4.56% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,7 | 1 | 3 | 5.726mb | 0.002715s | ±34.92% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,7 | 1 | 3 | 5.687mb | 0.000184s | ±12.97% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,7 | 1 | 3 | 5.647mb | 0.000051s | ±0.93% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,7 | 1 | 3 | 5.647mb | 0.000056s | ±4.34% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,7 | 1 | 3 | 5.716mb | 0.002377s | ±106.81% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,8 | 1 | 3 | 6.438mb | 0.003243s | ±5.05% | | MethodsNonProportionalBench | benchByCandidates | Copeland,8 | 1 | 3 | 6.470mb | 0.000122s | ±131.50% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,8 | 1 | 3 | 6.470mb | 0.001435s | ±82.71% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,8 | 1 | 3 | 6.413mb | 0.000031s | ±8.12% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,8 | 1 | 3 | 6.438mb | 0.002999s | ±3.19% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,8 | 1 | 3 | 6.474mb | 0.018136s | ±4.09% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,8 | 1 | 3 | 6.489mb | 0.104723s | ±0.40% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,8 | 1 | 3 | 6.439mb | 0.002409s | ±9.94% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,8 | 1 | 3 | 6.439mb | 0.005636s | ±2.19% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,8 | 1 | 3 | 6.411mb | 0.000034s | ±7.20% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,8 | 1 | 3 | 6.411mb | 0.000032s | ±14.19% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,8 | 1 | 3 | 6.413mb | 0.000031s | ±0.00% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,8 | 1 | 3 | 6.465mb | 0.000189s | ±16.95% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,8 | 1 | 3 | 6.463mb | 0.000203s | ±9.52% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,8 | 1 | 3 | 6.469mb | 0.000142s | ±125.75% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,8 | 1 | 3 | 6.414mb | 0.000061s | ±2.28% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,8 | 1 | 3 | 6.469mb | 0.003305s | ±101.92% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,9 | 1 | 3 | 6.897mb | 0.003411s | ±3.49% | | MethodsNonProportionalBench | benchByCandidates | Copeland,9 | 1 | 3 | 6.873mb | 0.000036s | ±4.04% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,9 | 1 | 3 | 6.872mb | 0.000029s | ±2.82% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,9 | 1 | 3 | 6.873mb | 0.000034s | ±4.04% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,9 | 1 | 3 | 6.897mb | 0.003076s | ±2.97% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,9 | 1 | 3 | 6.930mb | 0.021697s | ±5.03% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,9 | 1 | 3 | 6.950mb | 1.160851s | ±0.82% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,9 | 1 | 3 | 6.897mb | 0.002320s | ±5.76% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,9 | 1 | 3 | 6.897mb | 0.005771s | ±3.65% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,9 | 1 | 3 | 6.873mb | 0.000036s | ±8.41% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,9 | 1 | 3 | 6.930mb | 0.000122s | ±131.63% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,9 | 1 | 3 | 6.873mb | 0.000036s | ±3.50% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,9 | 1 | 3 | 6.951mb | 0.000457s | ±85.52% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,9 | 1 | 3 | 6.943mb | 0.000356s | ±12.93% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,9 | 1 | 3 | 6.876mb | 0.000076s | ±3.22% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,9 | 1 | 3 | 6.876mb | 0.000079s | ±2.59% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,9 | 1 | 3 | 6.928mb | 0.001263s | ±103.98% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,10 | 1 | 3 | 7.344mb | 0.003596s | ±2.72% | | MethodsNonProportionalBench | benchByCandidates | Copeland,10 | 1 | 3 | 7.321mb | 0.000037s | ±3.40% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,10 | 1 | 3 | 7.321mb | 0.000030s | ±3.21% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,10 | 1 | 3 | 7.322mb | 0.000039s | ±39.55% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,10 | 1 | 3 | 7.344mb | 0.003367s | ±3.86% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,10 | 1 | 3 | 7.352mb | 0.023994s | ±0.42% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,10 | 1 | 3 | 7.400mb | 14.549329s | ±0.38% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,10 | 1 | 3 | 7.344mb | 0.002413s | ±1.69% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,10 | 1 | 3 | 7.344mb | 0.006122s | ±0.24% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,10 | 1 | 3 | 7.322mb | 0.000036s | ±0.00% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,10 | 1 | 3 | 7.322mb | 0.000036s | ±3.82% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,10 | 1 | 3 | 7.322mb | 0.000040s | ±4.32% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,10 | 1 | 3 | 7.402mb | 0.000546s | ±6.04% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,10 | 1 | 3 | 7.402mb | 0.000592s | ±12.46% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,10 | 1 | 3 | 7.329mb | 0.000089s | ±10.25% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,10 | 1 | 3 | 7.329mb | 0.000089s | ±2.30% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,10 | 1 | 3 | 7.329mb | 0.000217s | ±109.63% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,11 | 1 | 3 | 7.790mb | 0.003812s | ±2.17% | | MethodsNonProportionalBench | benchByCandidates | Copeland,11 | 1 | 3 | 7.768mb | 0.000038s | ±0.00% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,11 | 1 | 3 | 7.767mb | 0.000055s | ±41.31% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,11 | 1 | 3 | 7.769mb | 0.000038s | ±2.15% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,11 | 1 | 3 | 7.790mb | 0.003964s | ±0.42% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,11 | 1 | 3 | 7.798mb | 0.028704s | ±1.44% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,11 | 1 | 3 | 7.849mb | 193.044781s | ±1.45% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,11 | 1 | 3 | 7.790mb | 0.002761s | ±3.59% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,11 | 1 | 3 | 7.790mb | 0.007038s | ±3.48% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,11 | 1 | 3 | 7.769mb | 0.000036s | ±7.44% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,11 | 1 | 3 | 7.769mb | 0.000040s | ±6.13% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,11 | 1 | 3 | 7.769mb | 0.000041s | ±6.94% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,11 | 1 | 3 | 7.866mb | 0.000817s | ±1.51% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,11 | 1 | 3 | 7.862mb | 0.000724s | ±9.95% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,11 | 1 | 3 | 7.776mb | 0.000104s | ±3.36% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,11 | 1 | 3 | 7.777mb | 0.000110s | ±7.03% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,11 | 1 | 3 | 7.777mb | 0.000160s | ±4.44% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,20 | 1 | 3 | 12.511mb | 0.007010s | ±0.76% | | MethodsNonProportionalBench | benchByCandidates | Copeland,20 | 1 | 3 | 12.503mb | 0.000066s | ±2.55% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,20 | 1 | 3 | 12.507mb | 0.000050s | ±1.63% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,20 | 1 | 3 | 12.504mb | 0.000067s | ±9.96% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,20 | 1 | 3 | 12.511mb | 0.007244s | ±1.16% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,20 | 1 | 3 | 12.533mb | 0.090596s | ±1.12% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,20 | 1 | 3 | 12.474mb | 0.000007s | ±22.17% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,20 | 1 | 3 | 12.510mb | 0.004687s | ±1.64% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,20 | 1 | 3 | 12.510mb | 0.012116s | ±0.28% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,20 | 1 | 3 | 12.503mb | 0.000067s | ±1.22% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,20 | 1 | 3 | 12.502mb | 0.000153s | ±122.93% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,20 | 1 | 3 | 12.503mb | 0.000066s | ±2.11% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,20 | 1 | 3 | 12.785mb | 0.011022s | ±11.77% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,20 | 1 | 3 | 12.802mb | 0.012487s | ±0.22% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,20 | 1 | 3 | 12.542mb | 0.000431s | ±1.23% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,20 | 1 | 3 | 12.542mb | 0.000454s | ±2.35% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,20 | 1 | 3 | 12.542mb | 0.000775s | ±2.63% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,30 | 1 | 3 | 17.044mb | 0.010831s | ±0.89% | | MethodsNonProportionalBench | benchByCandidates | Copeland,30 | 1 | 3 | 17.047mb | 0.000111s | ±22.90% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,30 | 1 | 3 | 17.054mb | 0.000072s | ±21.70% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,30 | 1 | 3 | 17.048mb | 0.000102s | ±2.01% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,30 | 1 | 3 | 17.044mb | 0.010428s | ±1.02% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,30 | 1 | 3 | 17.080mb | 0.193523s | ±4.90% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,30 | 1 | 3 | 17.007mb | 0.000009s | ±21.60% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,30 | 1 | 3 | 17.043mb | 0.006859s | ±1.91% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,30 | 1 | 3 | 17.043mb | 0.018535s | ±0.59% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,30 | 1 | 3 | 17.046mb | 0.000192s | ±114.86% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,30 | 1 | 3 | 17.045mb | 0.000108s | ±1.16% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,30 | 1 | 3 | 17.046mb | 0.000108s | ±2.32% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,30 | 1 | 3 | 17.660mb | 0.101841s | ±12.55% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,30 | 1 | 3 | 17.667mb | 0.099423s | ±5.12% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,30 | 1 | 3 | 17.219mb | 0.001361s | ±3.04% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,30 | 1 | 3 | 17.216mb | 0.001365s | ±7.51% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,30 | 1 | 3 | 17.103mb | 0.002616s | ±3.81% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,40 | 1 | 3 | 23.088mb | 0.015801s | ±0.85% | | MethodsNonProportionalBench | benchByCandidates | Copeland,40 | 1 | 3 | 23.098mb | 0.000158s | ±0.30% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,40 | 1 | 3 | 23.137mb | 0.000108s | ±0.88% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,40 | 1 | 3 | 23.100mb | 0.000165s | ±23.09% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,40 | 1 | 3 | 23.088mb | 0.014674s | ±1.13% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,40 | 1 | 3 | 23.190mb | 0.334868s | ±5.42% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,40 | 1 | 3 | 23.045mb | 0.000008s | ±16.27% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,40 | 1 | 3 | 23.075mb | 0.009288s | ±2.02% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,40 | 1 | 3 | 23.075mb | 0.025577s | ±0.95% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,40 | 1 | 3 | 23.089mb | 0.000154s | ±16.71% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,40 | 1 | 3 | 23.090mb | 0.000154s | ±1.90% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,40 | 1 | 3 | 23.089mb | 0.000152s | ±1.92% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,40 | 1 | 3 | 24.218mb | 0.440535s | ±11.54% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,40 | 1 | 3 | 24.196mb | 0.459768s | ±6.19% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,40 | 1 | 3 | 23.269mb | 0.002907s | ±1.89% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,40 | 1 | 3 | 23.272mb | 0.003054s | ±0.85% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,40 | 1 | 3 | 23.270mb | 0.005822s | ±1.07% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,50 | 1 | 3 | 27.651mb | 0.020448s | ±0.99% | | MethodsNonProportionalBench | benchByCandidates | Copeland,50 | 1 | 3 | 27.665mb | 0.000216s | ±0.88% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,50 | 1 | 3 | 27.722mb | 0.000133s | ±0.71% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,50 | 1 | 3 | 27.668mb | 0.000215s | ±2.19% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,50 | 1 | 3 | 27.652mb | 0.019335s | ±0.66% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,50 | 1 | 3 | 27.784mb | 0.470916s | ±10.21% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,50 | 1 | 3 | 27.601mb | 0.000006s | ±20.20% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,50 | 1 | 3 | 27.631mb | 0.011887s | ±1.77% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,50 | 1 | 3 | 27.631mb | 0.033005s | ±0.23% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,50 | 1 | 3 | 27.653mb | 0.000218s | ±13.74% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,50 | 1 | 3 | 27.659mb | 0.000212s | ±1.45% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,50 | 1 | 3 | 27.661mb | 0.000210s | ±1.33% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,50 | 1 | 3 | 29.349mb | 1.454932s | ±5.84% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,50 | 1 | 3 | 29.321mb | 1.577493s | ±11.78% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,50 | 1 | 3 | 27.886mb | 0.005544s | ±1.19% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,50 | 1 | 3 | 27.886mb | 0.005489s | ±3.28% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,50 | 1 | 3 | 27.887mb | 0.011167s | ±1.39% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,60 | 1 | 3 | 32.216mb | 0.025406s | ±0.36% | | MethodsNonProportionalBench | benchByCandidates | Copeland,60 | 1 | 3 | 32.229mb | 0.000284s | ±1.35% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,60 | 1 | 3 | 32.303mb | 0.000176s | ±22.99% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,60 | 1 | 3 | 32.235mb | 0.000286s | ±2.46% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,60 | 1 | 3 | 32.216mb | 0.024220s | ±1.01% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,60 | 1 | 3 | 32.383mb | 0.774454s | ±5.71% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,60 | 1 | 3 | 32.157mb | 0.000006s | ±0.00% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,60 | 1 | 3 | 32.186mb | 0.014692s | ±1.33% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,60 | 1 | 3 | 32.186mb | 0.041035s | ±0.53% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,60 | 1 | 3 | 32.223mb | 0.000283s | ±2.00% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,60 | 1 | 3 | 32.221mb | 0.000282s | ±1.02% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,60 | 1 | 3 | 32.214mb | 0.000281s | ±5.60% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,60 | 1 | 3 | 34.635mb | 3.743467s | ±5.62% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,60 | 1 | 3 | 34.706mb | 4.070218s | ±5.76% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,60 | 1 | 3 | 32.495mb | 0.009350s | ±1.08% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,60 | 1 | 3 | 32.497mb | 0.009517s | ±2.41% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,60 | 1 | 3 | 32.498mb | 0.019421s | ±0.57% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,70 | 1 | 3 | 44.439mb | 0.032305s | ±1.34% | | MethodsNonProportionalBench | benchByCandidates | Copeland,70 | 1 | 3 | 44.434mb | 0.000380s | ±0.81% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,70 | 1 | 3 | 44.720mb | 0.000224s | ±3.00% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,70 | 1 | 3 | 44.462mb | 0.000373s | ±2.55% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,70 | 1 | 3 | 44.439mb | 0.030708s | ±2.96% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,70 | 1 | 3 | 44.823mb | 1.023154s | ±6.37% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,70 | 1 | 3 | 44.361mb | 0.000008s | ±16.27% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,70 | 1 | 3 | 44.392mb | 0.019544s | ±1.65% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,70 | 1 | 3 | 44.392mb | 0.052625s | ±0.48% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,70 | 1 | 3 | 44.420mb | 0.000353s | ±1.61% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,70 | 1 | 3 | 44.423mb | 0.000370s | ±7.45% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,70 | 1 | 3 | 44.422mb | 0.000363s | ±0.67% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,70 | 1 | 3 | 47.656mb | 6.784191s | ±1.86% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,70 | 1 | 3 | 47.611mb | 6.588119s | ±6.27% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,70 | 1 | 3 | 45.530mb | 0.015970s | ±6.81% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,70 | 1 | 3 | 45.534mb | 0.016065s | ±2.66% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,70 | 1 | 3 | 45.529mb | 0.031048s | ±0.63% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,80 | 1 | 3 | 49.285mb | 0.038611s | ±0.73% | | MethodsNonProportionalBench | benchByCandidates | Copeland,80 | 1 | 3 | 49.281mb | 0.000463s | ±3.47% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,80 | 1 | 3 | 49.633mb | 0.000269s | ±14.00% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,80 | 1 | 3 | 49.311mb | 0.000468s | ±19.71% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,80 | 1 | 3 | 49.285mb | 0.038735s | ±1.24% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,80 | 1 | 3 | 49.632mb | 1.428535s | ±11.94% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,80 | 1 | 3 | 49.199mb | 0.000008s | ±23.18% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,80 | 1 | 3 | 49.233mb | 0.022248s | ±1.47% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,80 | 1 | 3 | 49.233mb | 0.063431s | ±0.89% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,80 | 1 | 3 | 49.266mb | 0.000446s | ±0.49% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,80 | 1 | 3 | 49.267mb | 0.000454s | ±2.22% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,80 | 1 | 3 | 49.264mb | 0.000452s | ±0.82% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,80 | 1 | 3 | 53.517mb | 18.839536s | ±21.46% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,80 | 1 | 3 | 53.492mb | 16.246016s | ±14.55% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,80 | 1 | 3 | 50.527mb | 0.022245s | ±0.63% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,80 | 1 | 3 | 50.532mb | 0.023183s | ±2.02% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,80 | 1 | 3 | 50.534mb | 0.046185s | ±0.61% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,90 | 1 | 3 | 54.130mb | 0.046329s | ±1.19% | | MethodsNonProportionalBench | benchByCandidates | Copeland,90 | 1 | 3 | 54.154mb | 0.000574s | ±2.18% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,90 | 1 | 3 | 54.497mb | 0.000318s | ±7.27% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,90 | 1 | 3 | 54.160mb | 0.000607s | ±3.88% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,90 | 1 | 3 | 54.130mb | 0.045796s | ±1.57% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,90 | 1 | 3 | 54.478mb | 1.483854s | ±10.63% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,90 | 1 | 3 | 54.036mb | 0.000007s | ±31.50% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,90 | 1 | 3 | 54.074mb | 0.026423s | ±1.50% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,90 | 1 | 3 | 54.074mb | 0.075511s | ±0.51% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,90 | 1 | 3 | 54.109mb | 0.000619s | ±7.23% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,90 | 1 | 3 | 54.107mb | 0.000535s | ±0.95% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,90 | 1 | 3 | 54.111mb | 0.000554s | ±0.52% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,90 | 1 | 3 | 59.327mb | 26.526442s | ±14.83% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,90 | 1 | 3 | 59.269mb | 28.957465s | ±10.13% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,90 | 1 | 3 | 55.537mb | 0.031824s | ±1.01% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,90 | 1 | 3 | 55.537mb | 0.031800s | ±3.34% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,90 | 1 | 3 | 55.536mb | 0.063706s | ±0.29% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,100 | 1 | 3 | 58.976mb | 0.054073s | ±1.33% | | MethodsNonProportionalBench | benchByCandidates | Copeland,100 | 1 | 3 | 58.999mb | 0.000670s | ±0.63% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,100 | 1 | 3 | 59.394mb | 0.000375s | ±0.65% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,100 | 1 | 3 | 59.010mb | 0.000691s | ±0.96% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,100 | 1 | 3 | 58.976mb | 0.052387s | ±1.49% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,100 | 1 | 3 | 59.436mb | 1.900686s | ±7.49% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,100 | 1 | 3 | 58.873mb | 0.000006s | ±13.61% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,100 | 1 | 3 | 58.916mb | 0.030921s | ±3.30% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,100 | 1 | 3 | 58.916mb | 0.086447s | ±0.74% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,100 | 1 | 3 | 58.953mb | 0.000642s | ±1.26% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,100 | 1 | 3 | 58.950mb | 0.000636s | ±0.52% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,100 | 1 | 3 | 58.952mb | 0.000641s | ±0.89% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,100 | 1 | 3 | 65.323mb | 49.233827s | ±3.59% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,100 | 1 | 3 | 65.547mb | 55.108877s | ±14.49% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,100 | 1 | 3 | 60.537mb | 0.043607s | ±0.64% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,100 | 1 | 3 | 60.534mb | 0.043322s | ±1.61% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,100 | 1 | 3 | 60.537mb | 0.089272s | ±6.19% | +-----------------------------+-------------------+-----------------------------------+------+-----+----------+-------------+----------+

Proportional

+--------------------------+-------------------+-------------+------+-----+-----------+-------------+---------+ | benchmark | subject | set | revs | its | mem_peak | mode | rstdev | +--------------------------+-------------------+-------------+------+-----+-----------+-------------+---------+ | MethodsProportionalBench | benchByCandidates | STV,3 | 1 | 3 | 5.829mb | 0.002659s | ±7.56% | | MethodsProportionalBench | benchByCandidates | CPO STV,3 | 1 | 3 | 5.964mb | 0.014000s | ±73.36% | | MethodsProportionalBench | benchByCandidates | STV,4 | 1 | 3 | 6.649mb | 0.003441s | ±0.53% | | MethodsProportionalBench | benchByCandidates | CPO STV,4 | 1 | 3 | 6.770mb | 0.018359s | ±41.91% | | MethodsProportionalBench | benchByCandidates | STV,5 | 1 | 3 | 7.470mb | 0.004373s | ±10.45% | | MethodsProportionalBench | benchByCandidates | CPO STV,5 | 1 | 3 | 7.669mb | 0.021245s | ±31.55% | | MethodsProportionalBench | benchByCandidates | STV,6 | 1 | 3 | 8.292mb | 0.005903s | ±11.56% | | MethodsProportionalBench | benchByCandidates | CPO STV,6 | 1 | 3 | 10.407mb | 0.166816s | ±5.62% | | MethodsProportionalBench | benchByCandidates | STV,7 | 1 | 3 | 9.143mb | 0.009377s | ±19.86% | | MethodsProportionalBench | benchByCandidates | CPO STV,7 | 1 | 3 | 13.332mb | 0.328804s | ±0.72% | | MethodsProportionalBench | benchByCandidates | STV,8 | 1 | 3 | 10.573mb | 0.007267s | ±3.74% | | MethodsProportionalBench | benchByCandidates | CPO STV,8 | 1 | 3 | 18.034mb | 0.611943s | ±1.64% | | MethodsProportionalBench | benchByCandidates | STV,9 | 1 | 3 | 11.409mb | 0.007971s | ±17.82% | | MethodsProportionalBench | benchByCandidates | CPO STV,9 | 1 | 3 | 83.441mb | 5.551505s | ±1.05% | | MethodsProportionalBench | benchByCandidates | STV,10 | 1 | 3 | 12.233mb | 0.008690s | ±3.30% | | MethodsProportionalBench | benchByCandidates | CPO STV,10 | 1 | 3 | 155.667mb | 11.802237s | ±0.17% | | MethodsProportionalBench | benchByCandidates | STV,11 | 1 | 3 | 13.056mb | 0.009754s | ±1.28% | | MethodsProportionalBench | benchByCandidates | CPO STV,11 | 1 | 3 | 286.714mb | 23.326424s | ±0.37% | | MethodsProportionalBench | benchByCandidates | STV,12 | 1 | 3 | 13.878mb | 0.010488s | ±4.76% | | MethodsProportionalBench | benchByCandidates | CPO STV,12 | 1 | 3 | 2.417gb | 287.180966s | ±13.06% | | MethodsProportionalBench | benchByCandidates | STV,13 | 1 | 3 | 14.700mb | 0.015853s | ±1.94% | | MethodsProportionalBench | benchByCandidates | CPO STV,13 | 1 | 3 | 14.666mb | 0.004435s | ±6.87% | | MethodsProportionalBench | benchByCandidates | STV,14 | 1 | 3 | 15.524mb | 0.016821s | ±2.48% | | MethodsProportionalBench | benchByCandidates | CPO STV,14 | 1 | 3 | 15.487mb | 0.005004s | ±11.10% | | MethodsProportionalBench | benchByCandidates | STV,15 | 1 | 3 | 16.345mb | 0.016804s | ±5.20% | | MethodsProportionalBench | benchByCandidates | CPO STV,15 | 1 | 3 | 16.309mb | 0.005149s | ±10.15% | | MethodsProportionalBench | benchByCandidates | STV,16 | 1 | 3 | 18.447mb | 0.017804s | ±8.62% | | MethodsProportionalBench | benchByCandidates | CPO STV,16 | 1 | 3 | 18.411mb | 0.005673s | ±11.23% | | MethodsProportionalBench | benchByCandidates | STV,17 | 1 | 3 | 19.327mb | 0.018709s | ±2.85% | | MethodsProportionalBench | benchByCandidates | CPO STV,17 | 1 | 3 | 19.287mb | 0.005789s | ±6.55% | | MethodsProportionalBench | benchByCandidates | STV,18 | 1 | 3 | 20.157mb | 0.018876s | ±2.92% | | MethodsProportionalBench | benchByCandidates | CPO STV,18 | 1 | 3 | 20.115mb | 0.006241s | ±3.11% | | MethodsProportionalBench | benchByCandidates | STV,19 | 1 | 3 | 20.982mb | 0.022289s | ±4.29% | | MethodsProportionalBench | benchByCandidates | CPO STV,19 | 1 | 3 | 20.940mb | 0.005274s | ±8.26% | | MethodsProportionalBench | benchByCandidates | STV,20 | 1 | 3 | 21.809mb | 0.022712s | ±1.60% | | MethodsProportionalBench | benchByCandidates | CPO STV,20 | 1 | 3 | 21.765mb | 0.005522s | ±8.89% | | MethodsProportionalBench | benchByCandidates | STV,30 | 1 | 3 | 30.112mb | 0.032666s | ±4.21% | | MethodsProportionalBench | benchByCandidates | CPO STV,30 | 1 | 3 | 30.054mb | 0.008870s | ±6.10% | | MethodsProportionalBench | benchByCandidates | STV,40 | 1 | 3 | 41.229mb | 0.044671s | ±1.33% | | MethodsProportionalBench | benchByCandidates | CPO STV,40 | 1 | 3 | 41.131mb | 0.011938s | ±6.82% | | MethodsProportionalBench | benchByCandidates | STV,50 | 1 | 3 | 49.601mb | 0.057759s | ±2.21% | | MethodsProportionalBench | benchByCandidates | CPO STV,50 | 1 | 3 | 49.443mb | 0.013495s | ±6.86% | | MethodsProportionalBench | benchByCandidates | STV,60 | 1 | 3 | 57.954mb | 0.068025s | ±0.86% | | MethodsProportionalBench | benchByCandidates | CPO STV,60 | 1 | 3 | 57.755mb | 0.018584s | ±4.75% | | MethodsProportionalBench | benchByCandidates | STV,70 | 1 | 3 | 79.813mb | 0.083113s | ±0.45% | | MethodsProportionalBench | benchByCandidates | CPO STV,70 | 1 | 3 | 79.335mb | 0.022136s | ±3.20% | | MethodsProportionalBench | benchByCandidates | STV,80 | 1 | 3 | 88.545mb | 0.096366s | ±1.30% | | MethodsProportionalBench | benchByCandidates | CPO STV,80 | 1 | 3 | 87.929mb | 0.026070s | ±2.65% | | MethodsProportionalBench | benchByCandidates | STV,90 | 1 | 3 | 97.297mb | 0.111921s | ±0.16% | | MethodsProportionalBench | benchByCandidates | CPO STV,90 | 1 | 3 | 96.523mb | 0.031376s | ±2.81% | | MethodsProportionalBench | benchByCandidates | STV,100 | 1 | 3 | 106.003mb | 0.127644s | ±1.99% | | MethodsProportionalBench | benchByCandidates | CPO STV,100 | 1 | 3 | 105.116mb | 0.035404s | ±1.94% | +--------------------------+-------------------+-------------+------+-----+-----------+-------------+---------+

v4.0-alpha1 Branch

1000 random votes different for each test, variable number of candidates (look at column "set")

• AMD Ryzen 9 5900X

PHPBench (1.2.5) with PHP version 8.1.6, xdebug ❌, opcache ✔ (with JIT Tracing)

    #[Bench\Warmup(1)]
    #[Bench\Iterations(10)]
    #[Bench\Revs(1)]

Non-Proportional

Subjects: 1, Assertions: 0, Failures: 0, Errors: 0 +-----------------------------+-------------------+-----------------------------------+------+-----+-----------+------------+----------+ | benchmark | subject | set | revs | its | mem_peak | mode | rstdev | +-----------------------------+-------------------+-----------------------------------+------+-----+-----------+------------+----------+ | MethodsNonProportionalBench | benchByCandidates | BordaCount,3 | 1 | 10 | 4.267mb | 0.001576s | ±28.18% | | MethodsNonProportionalBench | benchByCandidates | Copeland,3 | 1 | 10 | 3.934mb | 0.000024s | ±11.86% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,3 | 1 | 10 | 3.861mb | 0.000020s | ±5.84% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,3 | 1 | 10 | 3.863mb | 0.000024s | ±3.35% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,3 | 1 | 10 | 3.925mb | 0.001621s | ±12.99% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,3 | 1 | 10 | 3.931mb | 0.003948s | ±43.00% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,3 | 1 | 10 | 3.937mb | 0.000084s | ±177.58% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,3 | 1 | 10 | 3.928mb | 0.001411s | ±3.14% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,3 | 1 | 10 | 3.931mb | 0.003039s | ±17.49% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,3 | 1 | 10 | 3.863mb | 0.000024s | ±3.95% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,3 | 1 | 10 | 3.863mb | 0.000023s | ±3.92% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,3 | 1 | 10 | 3.863mb | 0.000025s | ±2.72% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,3 | 1 | 10 | 3.932mb | 0.000036s | ±186.95% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,3 | 1 | 10 | 3.868mb | 0.000037s | ±8.30% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,3 | 1 | 10 | 3.863mb | 0.000028s | ±3.09% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,3 | 1 | 10 | 3.863mb | 0.000030s | ±24.61% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,3 | 1 | 10 | 3.863mb | 0.000030s | ±1.54% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,5 | 1 | 10 | 4.814mb | 0.002172s | ±18.53% | | MethodsNonProportionalBench | benchByCandidates | Copeland,5 | 1 | 10 | 4.754mb | 0.000030s | ±6.13% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,5 | 1 | 10 | 4.814mb | 0.000025s | ±190.78% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,5 | 1 | 10 | 4.754mb | 0.000030s | ±16.08% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,5 | 1 | 10 | 4.784mb | 0.002020s | ±2.71% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,5 | 1 | 10 | 4.818mb | 0.008122s | ±30.49% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,5 | 1 | 10 | 4.946mb | 0.000265s | ±2.46% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,5 | 1 | 10 | 4.815mb | 0.001705s | ±45.21% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,5 | 1 | 10 | 4.816mb | 0.003976s | ±9.82% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,5 | 1 | 10 | 4.754mb | 0.000032s | ±3.82% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,5 | 1 | 10 | 4.754mb | 0.000030s | ±3.82% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,5 | 1 | 10 | 4.754mb | 0.000030s | ±2.54% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,5 | 1 | 10 | 4.836mb | 0.000607s | ±200.45% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,5 | 1 | 10 | 4.774mb | 0.000071s | ±4.95% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,5 | 1 | 10 | 4.824mb | 0.000788s | ±133.97% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,5 | 1 | 10 | 4.754mb | 0.000043s | ±22.29% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,5 | 1 | 10 | 4.817mb | 0.002600s | ±107.48% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,6 | 1 | 10 | 5.228mb | 0.002455s | ±3.85% | | MethodsNonProportionalBench | benchByCandidates | Copeland,6 | 1 | 10 | 5.267mb | 0.000087s | ±126.33% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,6 | 1 | 10 | 5.197mb | 0.000026s | ±7.69% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,6 | 1 | 10 | 5.200mb | 0.000030s | ±3.57% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,6 | 1 | 10 | 5.228mb | 0.002404s | ±3.31% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,6 | 1 | 10 | 5.297mb | 0.010311s | ±0.64% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,6 | 1 | 10 | 5.981mb | 0.001599s | ±14.74% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,6 | 1 | 10 | 5.228mb | 0.001897s | ±2.98% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,6 | 1 | 10 | 5.229mb | 0.004465s | ±2.30% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,6 | 1 | 10 | 5.200mb | 0.000030s | ±6.99% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,6 | 1 | 10 | 5.200mb | 0.000030s | ±7.99% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,6 | 1 | 10 | 5.200mb | 0.000031s | ±5.87% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,6 | 1 | 10 | 5.292mb | 0.000143s | ±194.55% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,6 | 1 | 10 | 5.229mb | 0.000097s | ±10.28% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,6 | 1 | 10 | 5.267mb | 0.000367s | ±164.46% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,6 | 1 | 10 | 5.262mb | 0.000041s | ±258.69% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,6 | 1 | 10 | 5.259mb | 0.001026s | ±120.33% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,7 | 1 | 10 | 5.672mb | 0.002705s | ±4.59% | | MethodsNonProportionalBench | benchByCandidates | Copeland,7 | 1 | 10 | 5.708mb | 0.000048s | ±95.75% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,7 | 1 | 10 | 5.712mb | 0.000031s | ±246.98% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,7 | 1 | 10 | 5.705mb | 0.000032s | ±180.86% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,7 | 1 | 10 | 5.673mb | 0.002667s | ±2.17% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,7 | 1 | 10 | 5.712mb | 0.013131s | ±4.15% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,7 | 1 | 10 | 11.331mb | 0.013923s | ±5.26% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,7 | 1 | 10 | 5.673mb | 0.002031s | ±2.42% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,7 | 1 | 10 | 5.673mb | 0.004654s | ±1.60% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,7 | 1 | 10 | 5.704mb | 0.000036s | ±142.26% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,7 | 1 | 10 | 5.645mb | 0.000032s | ±3.34% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,7 | 1 | 10 | 5.645mb | 0.000033s | ±4.84% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,7 | 1 | 10 | 5.749mb | 0.000365s | ±128.92% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,7 | 1 | 10 | 5.688mb | 0.000138s | ±9.68% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,7 | 1 | 10 | 5.703mb | 0.000051s | ±169.59% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,7 | 1 | 10 | 5.703mb | 0.000052s | ±219.33% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,7 | 1 | 10 | 5.703mb | 0.000408s | ±146.29% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,8 | 1 | 10 | 6.437mb | 0.002997s | ±12.75% | | MethodsNonProportionalBench | benchByCandidates | Copeland,8 | 1 | 10 | 6.412mb | 0.000034s | ±4.63% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,8 | 1 | 10 | 6.468mb | 0.000031s | ±144.07% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,8 | 1 | 10 | 6.412mb | 0.000034s | ±4.84% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,8 | 1 | 10 | 6.437mb | 0.002964s | ±2.69% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,8 | 1 | 10 | 6.475mb | 0.016236s | ±6.00% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,8 | 1 | 10 | 83.245mb | 0.150337s | ±1.54% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,8 | 1 | 10 | 6.475mb | 0.002121s | ±19.90% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,8 | 1 | 10 | 6.437mb | 0.005121s | ±12.26% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,8 | 1 | 10 | 6.412mb | 0.000034s | ±12.26% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,8 | 1 | 10 | 6.412mb | 0.000036s | ±4.23% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,8 | 1 | 10 | 6.412mb | 0.000036s | ±4.70% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,8 | 1 | 10 | 6.467mb | 0.000255s | ±11.85% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,8 | 1 | 10 | 6.468mb | 0.000245s | ±9.11% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,8 | 1 | 10 | 6.466mb | 0.000063s | ±207.41% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,8 | 1 | 10 | 6.412mb | 0.000065s | ±3.48% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,8 | 1 | 10 | 6.467mb | 0.001233s | ±129.54% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,9 | 1 | 10 | 6.896mb | 0.003210s | ±2.84% | | MethodsNonProportionalBench | benchByCandidates | Copeland,9 | 1 | 10 | 6.926mb | 0.000036s | ±238.83% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,9 | 1 | 10 | 6.870mb | 0.000030s | ±5.64% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,9 | 1 | 10 | 6.872mb | 0.000036s | ±1.86% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,9 | 1 | 10 | 6.896mb | 0.003026s | ±2.54% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,9 | 1 | 10 | 6.926mb | 0.019699s | ±2.99% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,9 | 1 | 10 | 672.151mb | 1.652125s | ±0.27% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,9 | 1 | 10 | 6.895mb | 0.002209s | ±3.77% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,9 | 1 | 10 | 6.895mb | 0.005537s | ±1.11% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,9 | 1 | 10 | 6.872mb | 0.000037s | ±14.11% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,9 | 1 | 10 | 6.872mb | 0.000036s | ±4.33% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,9 | 1 | 10 | 6.872mb | 0.000036s | ±5.63% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,9 | 1 | 10 | 6.952mb | 0.000362s | ±91.18% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,9 | 1 | 10 | 6.938mb | 0.000309s | ±14.39% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,9 | 1 | 10 | 6.931mb | 0.000078s | ±157.32% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,9 | 1 | 10 | 6.875mb | 0.000081s | ±26.92% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,9 | 1 | 10 | 6.928mb | 0.000917s | ±105.36% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,10 | 1 | 10 | 7.343mb | 0.003537s | ±3.00% | | MethodsNonProportionalBench | benchByCandidates | Copeland,10 | 1 | 10 | 7.385mb | 0.000046s | ±194.34% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,10 | 1 | 10 | 7.319mb | 0.000034s | ±4.46% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,10 | 1 | 10 | 7.321mb | 0.000038s | ±11.93% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,10 | 1 | 10 | 7.343mb | 0.003360s | ±8.59% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,10 | 1 | 10 | 7.350mb | 0.023538s | ±0.45% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,10 | 1 | 10 | 7.368mb | 0.000007s | ±15.07% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,10 | 1 | 10 | 7.343mb | 0.002383s | ±3.89% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,10 | 1 | 10 | 7.343mb | 0.006007s | ±1.82% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,10 | 1 | 10 | 7.321mb | 0.000041s | ±38.78% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,10 | 1 | 10 | 7.321mb | 0.000041s | ±3.66% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,10 | 1 | 10 | 7.321mb | 0.000039s | ±3.33% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,10 | 1 | 10 | 7.403mb | 0.000503s | ±12.11% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,10 | 1 | 10 | 7.403mb | 0.000520s | ±14.33% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,10 | 1 | 10 | 7.328mb | 0.000089s | ±1.48% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,10 | 1 | 10 | 7.328mb | 0.000094s | ±1.89% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,10 | 1 | 10 | 7.375mb | 0.001436s | ±114.24% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,20 | 1 | 10 | 12.566mb | 0.006712s | ±12.42% | | MethodsNonProportionalBench | benchByCandidates | Copeland,20 | 1 | 10 | 12.563mb | 0.000081s | ±139.57% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,20 | 1 | 10 | 12.507mb | 0.000054s | ±188.52% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,20 | 1 | 10 | 12.536mb | 0.000067s | ±205.54% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,20 | 1 | 10 | 12.510mb | 0.006443s | ±1.21% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,20 | 1 | 10 | 12.554mb | 0.080874s | ±2.86% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,20 | 1 | 10 | 12.473mb | 0.000007s | ±13.61% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,20 | 1 | 10 | 12.509mb | 0.004153s | ±2.27% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,20 | 1 | 10 | 12.509mb | 0.010935s | ±2.79% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,20 | 1 | 10 | 12.502mb | 0.000066s | ±9.52% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,20 | 1 | 10 | 12.502mb | 0.000066s | ±2.94% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,20 | 1 | 10 | 12.502mb | 0.000066s | ±2.51% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,20 | 1 | 10 | 12.798mb | 0.012576s | ±10.90% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,20 | 1 | 10 | 12.804mb | 0.012314s | ±11.26% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,20 | 1 | 10 | 12.563mb | 0.000429s | ±76.02% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,20 | 1 | 10 | 12.541mb | 0.000446s | ±2.50% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,20 | 1 | 10 | 12.558mb | 0.005883s | ±89.26% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,30 | 1 | 10 | 17.042mb | 0.010397s | ±3.89% | | MethodsNonProportionalBench | benchByCandidates | Copeland,30 | 1 | 10 | 17.046mb | 0.000104s | ±13.62% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,30 | 1 | 10 | 17.053mb | 0.000073s | ±5.49% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,30 | 1 | 10 | 17.047mb | 0.000107s | ±4.60% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,30 | 1 | 10 | 17.042mb | 0.010148s | ±3.27% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,30 | 1 | 10 | 17.084mb | 0.181320s | ±9.11% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,30 | 1 | 10 | 17.006mb | 0.000009s | ±4.55% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,30 | 1 | 10 | 17.042mb | 0.006459s | ±4.71% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,30 | 1 | 10 | 17.077mb | 0.017216s | ±5.29% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,30 | 1 | 10 | 17.046mb | 0.000107s | ±2.39% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,30 | 1 | 10 | 17.044mb | 0.000105s | ±3.36% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,30 | 1 | 10 | 17.046mb | 0.000106s | ±4.30% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,30 | 1 | 10 | 17.674mb | 0.095572s | ±6.65% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,30 | 1 | 10 | 17.691mb | 0.102611s | ±13.10% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,30 | 1 | 10 | 17.105mb | 0.001341s | ±36.46% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,30 | 1 | 10 | 17.104mb | 0.001306s | ±3.18% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,30 | 1 | 10 | 17.104mb | 0.006312s | ±51.42% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,40 | 1 | 10 | 23.131mb | 0.014433s | ±9.34% | | MethodsNonProportionalBench | benchByCandidates | Copeland,40 | 1 | 10 | 23.132mb | 0.000156s | ±218.86% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,40 | 1 | 10 | 23.173mb | 0.000108s | ±172.81% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,40 | 1 | 10 | 23.099mb | 0.000152s | ±4.32% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,40 | 1 | 10 | 23.086mb | 0.013914s | ±5.24% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,40 | 1 | 10 | 23.181mb | 0.319985s | ±5.15% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,40 | 1 | 10 | 23.044mb | 0.000007s | ±14.02% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,40 | 1 | 10 | 23.093mb | 0.008670s | ±5.04% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,40 | 1 | 10 | 23.095mb | 0.023546s | ±2.91% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,40 | 1 | 10 | 23.090mb | 0.000151s | ±2.76% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,40 | 1 | 10 | 23.089mb | 0.000148s | ±11.23% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,40 | 1 | 10 | 23.157mb | 0.000149s | ±142.96% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,40 | 1 | 10 | 24.233mb | 0.428470s | ±12.23% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,40 | 1 | 10 | 24.192mb | 0.386814s | ±7.69% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,40 | 1 | 10 | 23.277mb | 0.002867s | ±2.14% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,40 | 1 | 10 | 23.269mb | 0.002939s | ±1.61% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,40 | 1 | 10 | 23.276mb | 0.006179s | ±47.41% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,50 | 1 | 10 | 27.650mb | 0.018801s | ±4.38% | | MethodsNonProportionalBench | benchByCandidates | Copeland,50 | 1 | 10 | 27.663mb | 0.000208s | ±11.64% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,50 | 1 | 10 | 27.723mb | 0.000131s | ±12.28% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,50 | 1 | 10 | 27.667mb | 0.000210s | ±2.78% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,50 | 1 | 10 | 27.650mb | 0.018225s | ±2.90% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,50 | 1 | 10 | 27.787mb | 0.485798s | ±5.60% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,50 | 1 | 10 | 27.600mb | 0.000009s | ±11.13% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,50 | 1 | 10 | 27.630mb | 0.011091s | ±0.92% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,50 | 1 | 10 | 27.630mb | 0.030712s | ±0.76% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,50 | 1 | 10 | 27.652mb | 0.000206s | ±4.21% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,50 | 1 | 10 | 27.659mb | 0.000204s | ±13.61% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,50 | 1 | 10 | 27.652mb | 0.000207s | ±5.47% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,50 | 1 | 10 | 29.310mb | 1.206939s | ±10.50% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,50 | 1 | 10 | 29.390mb | 1.320606s | ±14.78% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,50 | 1 | 10 | 27.886mb | 0.005423s | ±3.75% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,50 | 1 | 10 | 27.885mb | 0.005669s | ±2.27% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,50 | 1 | 10 | 27.887mb | 0.011125s | ±3.40% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,60 | 1 | 10 | 32.214mb | 0.023670s | ±0.80% | | MethodsNonProportionalBench | benchByCandidates | Copeland,60 | 1 | 10 | 32.231mb | 0.000278s | ±2.58% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,60 | 1 | 10 | 32.300mb | 0.000165s | ±3.40% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,60 | 1 | 10 | 32.234mb | 0.000280s | ±1.53% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,60 | 1 | 10 | 32.214mb | 0.022865s | ±0.68% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,60 | 1 | 10 | 32.376mb | 0.686883s | ±6.15% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,60 | 1 | 10 | 32.156mb | 0.000008s | ±13.22% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,60 | 1 | 10 | 32.185mb | 0.013784s | ±1.14% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,60 | 1 | 10 | 32.201mb | 0.038390s | ±3.17% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,60 | 1 | 10 | 32.222mb | 0.000281s | ±10.97% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,60 | 1 | 10 | 32.223mb | 0.000271s | ±2.46% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,60 | 1 | 10 | 32.220mb | 0.000277s | ±12.89% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,60 | 1 | 10 | 34.723mb | 3.552521s | ±13.97% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,60 | 1 | 10 | 34.738mb | 3.476462s | ±14.63% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,60 | 1 | 10 | 32.496mb | 0.009344s | ±1.57% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,60 | 1 | 10 | 32.498mb | 0.009387s | ±3.33% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,60 | 1 | 10 | 32.495mb | 0.019263s | ±6.10% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,70 | 1 | 10 | 44.438mb | 0.029599s | ±3.34% | | MethodsNonProportionalBench | benchByCandidates | Copeland,70 | 1 | 10 | 44.433mb | 0.000359s | ±12.38% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,70 | 1 | 10 | 44.726mb | 0.000208s | ±3.93% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,70 | 1 | 10 | 44.461mb | 0.000365s | ±11.99% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,70 | 1 | 10 | 44.438mb | 0.028667s | ±0.84% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,70 | 1 | 10 | 44.794mb | 0.997542s | ±6.81% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,70 | 1 | 10 | 44.360mb | 0.000008s | ±14.31% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,70 | 1 | 10 | 44.391mb | 0.017181s | ±0.65% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,70 | 1 | 10 | 44.391mb | 0.048083s | ±0.67% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,70 | 1 | 10 | 44.420mb | 0.000351s | ±12.13% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,70 | 1 | 10 | 44.421mb | 0.000351s | ±5.41% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,70 | 1 | 10 | 44.420mb | 0.000351s | ±3.01% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,70 | 1 | 10 | 47.741mb | 8.258612s | ±11.24% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,70 | 1 | 10 | 47.702mb | 7.574171s | ±14.00% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,70 | 1 | 10 | 45.529mb | 0.015059s | ±1.48% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,70 | 1 | 10 | 45.533mb | 0.015142s | ±2.79% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,70 | 1 | 10 | 45.531mb | 0.030803s | ±7.93% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,80 | 1 | 10 | 49.284mb | 0.035633s | ±7.12% | | MethodsNonProportionalBench | benchByCandidates | Copeland,80 | 1 | 10 | 49.304mb | 0.000453s | ±0.95% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,80 | 1 | 10 | 49.635mb | 0.000254s | ±12.19% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,80 | 1 | 10 | 49.310mb | 0.000472s | ±3.59% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,80 | 1 | 10 | 49.284mb | 0.035766s | ±1.52% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,80 | 1 | 10 | 49.724mb | 1.294201s | ±7.97% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,80 | 1 | 10 | 49.197mb | 0.000007s | ±13.42% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,80 | 1 | 10 | 49.232mb | 0.020609s | ±1.12% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,80 | 1 | 10 | 49.232mb | 0.058361s | ±3.16% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,80 | 1 | 10 | 49.266mb | 0.000440s | ±1.60% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,80 | 1 | 10 | 49.266mb | 0.000444s | ±4.79% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,80 | 1 | 10 | 49.266mb | 0.000443s | ±10.14% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,80 | 1 | 10 | 53.461mb | 16.095014s | ±15.87% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,80 | 1 | 10 | 53.590mb | 17.480178s | ±15.05% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,80 | 1 | 10 | 50.531mb | 0.022074s | ±1.95% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,80 | 1 | 10 | 50.534mb | 0.022177s | ±2.54% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,80 | 1 | 10 | 50.533mb | 0.045875s | ±1.76% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,90 | 1 | 10 | 54.129mb | 0.042823s | ±0.75% | | MethodsNonProportionalBench | benchByCandidates | Copeland,90 | 1 | 10 | 54.151mb | 0.000553s | ±6.90% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,90 | 1 | 10 | 54.500mb | 0.000302s | ±2.45% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,90 | 1 | 10 | 54.159mb | 0.000565s | ±2.31% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,90 | 1 | 10 | 54.129mb | 0.041830s | ±1.53% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,90 | 1 | 10 | 54.518mb | 1.524077s | ±9.39% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,90 | 1 | 10 | 54.035mb | 0.000009s | ±15.11% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,90 | 1 | 10 | 54.073mb | 0.024268s | ±3.10% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,90 | 1 | 10 | 54.073mb | 0.068611s | ±0.86% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,90 | 1 | 10 | 54.110mb | 0.000534s | ±1.59% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,90 | 1 | 10 | 54.108mb | 0.000534s | ±2.85% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,90 | 1 | 10 | 54.109mb | 0.000536s | ±1.37% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,90 | 1 | 10 | 59.332mb | 28.202594s | ±14.13% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,90 | 1 | 10 | 59.359mb | 30.213354s | ±13.33% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,90 | 1 | 10 | 55.538mb | 0.030684s | ±5.05% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,90 | 1 | 10 | 55.536mb | 0.031059s | ±2.32% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,90 | 1 | 10 | 55.535mb | 0.065110s | ±2.80% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,100 | 1 | 10 | 58.975mb | 0.049534s | ±1.17% | | MethodsNonProportionalBench | benchByCandidates | Copeland,100 | 1 | 10 | 59.000mb | 0.000659s | ±0.98% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,100 | 1 | 10 | 59.411mb | 0.000359s | ±1.42% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,100 | 1 | 10 | 59.008mb | 0.000672s | ±2.88% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,100 | 1 | 10 | 58.975mb | 0.048570s | ±0.47% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,100 | 1 | 10 | 59.498mb | 1.692495s | ±8.43% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,100 | 1 | 10 | 58.872mb | 0.000007s | ±14.79% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,100 | 1 | 10 | 58.914mb | 0.027877s | ±1.41% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,100 | 1 | 10 | 58.914mb | 0.078369s | ±4.47% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,100 | 1 | 10 | 58.950mb | 0.000642s | ±25.20% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,100 | 1 | 10 | 58.954mb | 0.000644s | ±4.31% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,100 | 1 | 10 | 58.951mb | 0.000633s | ±3.12% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,100 | 1 | 10 | 65.485mb | 51.116404s | ±11.11% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,100 | 1 | 10 | 65.473mb | 46.500300s | ±12.30% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,100 | 1 | 10 | 60.536mb | 0.041783s | ±4.37% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,100 | 1 | 10 | 60.541mb | 0.043380s | ±1.90% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,100 | 1 | 10 | 60.537mb | 0.089583s | ±5.19% | +-----------------------------+-------------------+-----------------------------------+------+-----+-----------+------------+----------+

Proportional

Subjects: 1, Assertions: 0, Failures: 0, Errors: 0 +--------------------------+-------------------+-------------+------+-----+-----------+-------------+---------+ | benchmark | subject | set | revs | its | mem_peak | mode | rstdev | +--------------------------+-------------------+-------------+------+-----+-----------+-------------+---------+ | MethodsProportionalBench | benchByCandidates | STV,3 | 1 | 10 | 5.827mb | 0.002783s | ±7.72% | | MethodsProportionalBench | benchByCandidates | CPO STV,3 | 1 | 10 | 5.950mb | 0.006918s | ±90.37% | | MethodsProportionalBench | benchByCandidates | STV,4 | 1 | 10 | 6.610mb | 0.003713s | ±8.19% | | MethodsProportionalBench | benchByCandidates | CPO STV,4 | 1 | 10 | 6.754mb | 0.011379s | ±20.24% | | MethodsProportionalBench | benchByCandidates | STV,5 | 1 | 10 | 7.402mb | 0.004458s | ±2.57% | | MethodsProportionalBench | benchByCandidates | CPO STV,5 | 1 | 10 | 7.678mb | 0.019062s | ±19.13% | | MethodsProportionalBench | benchByCandidates | STV,6 | 1 | 10 | 8.224mb | 0.004669s | ±8.40% | | MethodsProportionalBench | benchByCandidates | CPO STV,6 | 1 | 10 | 10.395mb | 0.160481s | ±1.31% | | MethodsProportionalBench | benchByCandidates | STV,7 | 1 | 10 | 9.045mb | 0.005661s | ±18.25% | | MethodsProportionalBench | benchByCandidates | CPO STV,7 | 1 | 10 | 13.321mb | 0.332263s | ±1.08% | | MethodsProportionalBench | benchByCandidates | STV,8 | 1 | 10 | 10.505mb | 0.007117s | ±9.94% | | MethodsProportionalBench | benchByCandidates | CPO STV,8 | 1 | 10 | 18.022mb | 0.614972s | ±0.90% | | MethodsProportionalBench | benchByCandidates | STV,9 | 1 | 10 | 11.342mb | 0.007548s | ±4.08% | | MethodsProportionalBench | benchByCandidates | CPO STV,9 | 1 | 10 | 84.893mb | 5.877915s | ±0.57% | | MethodsProportionalBench | benchByCandidates | STV,10 | 1 | 10 | 12.165mb | 0.008954s | ±13.21% | | MethodsProportionalBench | benchByCandidates | CPO STV,10 | 1 | 10 | 155.658mb | 12.608246s | ±0.61% | | MethodsProportionalBench | benchByCandidates | STV,11 | 1 | 10 | 12.988mb | 0.009892s | ±12.51% | | MethodsProportionalBench | benchByCandidates | CPO STV,11 | 1 | 10 | 290.940mb | 25.131801s | ±0.51% | | MethodsProportionalBench | benchByCandidates | STV,12 | 1 | 10 | 13.811mb | 0.009862s | ±4.28% | | MethodsProportionalBench | benchByCandidates | CPO STV,12 | 1 | 10 | 2.417gb | 288.783020s | ±1.93% | | MethodsProportionalBench | benchByCandidates | STV,13 | 1 | 10 | 14.632mb | 0.010369s | ±1.90% | | MethodsProportionalBench | benchByCandidates | CPO STV,13 | 1 | 10 | 8.642mb | 0.000008s | ±9.13% | | MethodsProportionalBench | benchByCandidates | STV,14 | 1 | 10 | 15.455mb | 0.011096s | ±15.92% | | MethodsProportionalBench | benchByCandidates | CPO STV,14 | 1 | 10 | 9.088mb | 0.000008s | ±6.82% | | MethodsProportionalBench | benchByCandidates | STV,15 | 1 | 10 | 16.278mb | 0.011425s | ±1.81% | | MethodsProportionalBench | benchByCandidates | CPO STV,15 | 1 | 10 | 9.534mb | 0.000008s | ±11.18% | | MethodsProportionalBench | benchByCandidates | STV,16 | 1 | 10 | 18.380mb | 0.012343s | ±2.40% | | MethodsProportionalBench | benchByCandidates | CPO STV,16 | 1 | 10 | 10.621mb | 0.000009s | ±10.91% | | MethodsProportionalBench | benchByCandidates | STV,17 | 1 | 10 | 19.260mb | 0.013621s | ±7.09% | | MethodsProportionalBench | benchByCandidates | CPO STV,17 | 1 | 10 | 11.123mb | 0.000008s | ±7.91% | | MethodsProportionalBench | benchByCandidates | STV,18 | 1 | 10 | 20.088mb | 0.013799s | ±2.16% | | MethodsProportionalBench | benchByCandidates | CPO STV,18 | 1 | 10 | 11.575mb | 0.000007s | ±11.94% | | MethodsProportionalBench | benchByCandidates | STV,19 | 1 | 10 | 20.916mb | 0.014612s | ±0.75% | | MethodsProportionalBench | benchByCandidates | CPO STV,19 | 1 | 10 | 12.024mb | 0.000009s | ±5.27% | | MethodsProportionalBench | benchByCandidates | STV,20 | 1 | 10 | 21.743mb | 0.015802s | ±3.77% | | MethodsProportionalBench | benchByCandidates | CPO STV,20 | 1 | 10 | 12.473mb | 0.000008s | ±10.84% | | MethodsProportionalBench | benchByCandidates | STV,30 | 1 | 10 | 30.044mb | 0.023349s | ±3.99% | | MethodsProportionalBench | benchByCandidates | CPO STV,30 | 1 | 10 | 17.006mb | 0.000009s | ±10.26% | | MethodsProportionalBench | benchByCandidates | STV,40 | 1 | 10 | 41.181mb | 0.032300s | ±4.33% | | MethodsProportionalBench | benchByCandidates | CPO STV,40 | 1 | 10 | 23.044mb | 0.000009s | ±10.37% | | MethodsProportionalBench | benchByCandidates | STV,50 | 1 | 10 | 49.535mb | 0.040636s | ±4.98% | | MethodsProportionalBench | benchByCandidates | CPO STV,50 | 1 | 10 | 27.600mb | 0.000008s | ±7.71% | | MethodsProportionalBench | benchByCandidates | STV,60 | 1 | 10 | 57.888mb | 0.051150s | ±2.49% | | MethodsProportionalBench | benchByCandidates | CPO STV,60 | 1 | 10 | 32.156mb | 0.000009s | ±10.91% | | MethodsProportionalBench | benchByCandidates | STV,70 | 1 | 10 | 79.741mb | 0.062366s | ±2.51% | | MethodsProportionalBench | benchByCandidates | CPO STV,70 | 1 | 10 | 44.360mb | 0.000009s | ±13.15% | | MethodsProportionalBench | benchByCandidates | STV,80 | 1 | 10 | 88.468mb | 0.074088s | ±3.38% | | MethodsProportionalBench | benchByCandidates | CPO STV,80 | 1 | 10 | 49.197mb | 0.000008s | ±8.98% | | MethodsProportionalBench | benchByCandidates | STV,90 | 1 | 10 | 97.212mb | 0.083958s | ±4.51% | | MethodsProportionalBench | benchByCandidates | CPO STV,90 | 1 | 10 | 54.035mb | 0.000010s | ±12.74% | | MethodsProportionalBench | benchByCandidates | STV,100 | 1 | 10 | 105.939mb | 0.097074s | ±3.65% | | MethodsProportionalBench | benchByCandidates | CPO STV,100 | 1 | 10 | 58.872mb | 0.000009s | ±16.69% | +--------------------------+-------------------+-------------+------+-----+-----------+-------------+---------+

v3.3.3

1000 random votes different for each test, variable number of candidates (look at column "set")

• AMD Ryzen 9 5900X

PHPBench (1.2.5) with PHP version 8.1.6, xdebug ❌, opcache ✔ (with JIT Tracing)

    #[Bench\Warmup(1)]
    #[Bench\Iterations(3)]
    #[Bench\Revs(1)]

Non-Proportional

Subjects: 1, Assertions: 0, Failures: 0, Errors: 0 +-----------------------------+-------------------+-----------------------------------+------+-----+-----------+------------+----------+ | benchmark | subject | set | revs | its | mem_peak | mode | rstdev | +-----------------------------+-------------------+-----------------------------------+------+-----+-----------+------------+----------+ | MethodsNonProportionalBench | benchByCandidates | BordaCount,3 | 1 | 3 | 4.155mb | 0.001963s | ±26.64% | | MethodsNonProportionalBench | benchByCandidates | Copeland,3 | 1 | 3 | 3.821mb | 0.000021s | ±5.85% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,3 | 1 | 3 | 3.749mb | 0.000019s | ±2.44% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,3 | 1 | 3 | 3.750mb | 0.000022s | ±5.58% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,3 | 1 | 3 | 3.811mb | 0.001702s | ±9.12% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,3 | 1 | 3 | 3.819mb | 0.005508s | ±50.37% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,3 | 1 | 3 | 3.815mb | 0.001621s | ±75.46% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,3 | 1 | 3 | 3.820mb | 0.001854s | ±10.30% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,3 | 1 | 3 | 3.818mb | 0.003639s | ±31.01% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,3 | 1 | 3 | 3.750mb | 0.000024s | ±5.27% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,3 | 1 | 3 | 3.750mb | 0.000024s | ±4.04% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,3 | 1 | 3 | 3.750mb | 0.000022s | ±4.16% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,3 | 1 | 3 | 3.819mb | 0.001493s | ±78.21% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,3 | 1 | 3 | 3.814mb | 0.000117s | ±131.05% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,3 | 1 | 3 | 3.813mb | 0.002645s | ±1.45% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,3 | 1 | 3 | 3.817mb | 0.001402s | ±3.32% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,3 | 1 | 3 | 3.815mb | 0.001413s | ±1.82% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,5 | 1 | 3 | 4.708mb | 0.003679s | ±20.48% | | MethodsNonProportionalBench | benchByCandidates | Copeland,5 | 1 | 3 | 4.641mb | 0.000029s | ±1.64% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,5 | 1 | 3 | 4.639mb | 0.000025s | ±3.87% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,5 | 1 | 3 | 4.641mb | 0.000029s | ±4.35% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,5 | 1 | 3 | 4.671mb | 0.002098s | ±0.18% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,5 | 1 | 3 | 4.702mb | 0.009091s | ±27.69% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,5 | 1 | 3 | 4.840mb | 0.000275s | ±2.76% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,5 | 1 | 3 | 4.702mb | 0.001902s | ±49.63% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,5 | 1 | 3 | 4.672mb | 0.004162s | ±0.18% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,5 | 1 | 3 | 4.641mb | 0.000061s | ±30.28% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,5 | 1 | 3 | 4.641mb | 0.000030s | ±4.11% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,5 | 1 | 3 | 4.641mb | 0.000030s | ±3.21% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,5 | 1 | 3 | 4.722mb | 0.003208s | ±101.35% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,5 | 1 | 3 | 4.662mb | 0.000069s | ±7.68% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,5 | 1 | 3 | 4.704mb | 0.005819s | ±49.15% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,5 | 1 | 3 | 4.701mb | 0.000128s | ±129.71% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,5 | 1 | 3 | 4.702mb | 0.016854s | ±43.28% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,6 | 1 | 3 | 5.115mb | 0.002719s | ±4.32% | | MethodsNonProportionalBench | benchByCandidates | Copeland,6 | 1 | 3 | 5.157mb | 0.001274s | ±88.64% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,6 | 1 | 3 | 5.146mb | 0.001564s | ±78.43% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,6 | 1 | 3 | 5.145mb | 0.000116s | ±133.45% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,6 | 1 | 3 | 5.115mb | 0.002493s | ±3.71% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,6 | 1 | 3 | 5.155mb | 0.012630s | ±14.09% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,6 | 1 | 3 | 5.892mb | 0.001688s | ±1.13% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,6 | 1 | 3 | 5.115mb | 0.001975s | ±5.80% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,6 | 1 | 3 | 5.116mb | 0.004745s | ±1.49% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,6 | 1 | 3 | 5.087mb | 0.000030s | ±3.21% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,6 | 1 | 3 | 5.087mb | 0.000030s | ±1.59% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,6 | 1 | 3 | 5.146mb | 0.000117s | ±132.89% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,6 | 1 | 3 | 5.183mb | 0.002663s | ±39.44% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,6 | 1 | 3 | 5.160mb | 0.002587s | ±67.19% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,6 | 1 | 3 | 5.155mb | 0.007516s | ±26.07% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,6 | 1 | 3 | 5.142mb | 0.000046s | ±8.09% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,6 | 1 | 3 | 5.145mb | 0.009898s | ±28.00% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,7 | 1 | 3 | 5.560mb | 0.002982s | ±6.98% | | MethodsNonProportionalBench | benchByCandidates | Copeland,7 | 1 | 3 | 5.532mb | 0.000030s | ±1.55% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,7 | 1 | 3 | 5.598mb | 0.000195s | ±137.37% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,7 | 1 | 3 | 5.594mb | 0.002681s | ±26.87% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,7 | 1 | 3 | 5.560mb | 0.002726s | ±4.55% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,7 | 1 | 3 | 5.597mb | 0.015668s | ±3.78% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,7 | 1 | 3 | 11.403mb | 0.014314s | ±0.84% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,7 | 1 | 3 | 5.560mb | 0.002040s | ±0.84% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,7 | 1 | 3 | 5.560mb | 0.005043s | ±0.56% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,7 | 1 | 3 | 5.594mb | 0.000115s | ±132.92% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,7 | 1 | 3 | 5.591mb | 0.000115s | ±132.92% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,7 | 1 | 3 | 5.590mb | 0.001316s | ±68.39% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,7 | 1 | 3 | 5.613mb | 0.001571s | ±30.65% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,7 | 1 | 3 | 5.570mb | 0.000148s | ±7.12% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,7 | 1 | 3 | 5.533mb | 0.000051s | ±0.00% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,7 | 1 | 3 | 5.588mb | 0.000137s | ±126.51% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,7 | 1 | 3 | 5.590mb | 0.011652s | ±9.33% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,8 | 1 | 3 | 6.324mb | 0.003245s | ±2.60% | | MethodsNonProportionalBench | benchByCandidates | Copeland,8 | 1 | 3 | 6.351mb | 0.000121s | ±131.83% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,8 | 1 | 3 | 6.355mb | 0.002881s | ±36.70% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,8 | 1 | 3 | 6.299mb | 0.000030s | ±0.00% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,8 | 1 | 3 | 6.324mb | 0.002904s | ±6.87% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,8 | 1 | 3 | 6.360mb | 0.019624s | ±1.95% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,8 | 1 | 3 | 86.609mb | 0.161120s | ±0.56% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,8 | 1 | 3 | 6.324mb | 0.002280s | ±0.32% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,8 | 1 | 3 | 6.324mb | 0.005577s | ±0.18% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,8 | 1 | 3 | 6.299mb | 0.000030s | ±3.07% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,8 | 1 | 3 | 6.299mb | 0.000030s | ±3.21% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,8 | 1 | 3 | 6.299mb | 0.000030s | ±3.07% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,8 | 1 | 3 | 6.348mb | 0.000191s | ±10.55% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,8 | 1 | 3 | 6.352mb | 0.000243s | ±7.51% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,8 | 1 | 3 | 6.300mb | 0.000063s | ±2.93% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,8 | 1 | 3 | 6.353mb | 0.000152s | ±122.80% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,8 | 1 | 3 | 6.353mb | 0.001166s | ±87.98% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,9 | 1 | 3 | 6.783mb | 0.003559s | ±2.27% | | MethodsNonProportionalBench | benchByCandidates | Copeland,9 | 1 | 3 | 6.759mb | 0.000034s | ±4.80% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,9 | 1 | 3 | 6.757mb | 0.000029s | ±9.12% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,9 | 1 | 3 | 6.759mb | 0.000033s | ±3.82% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,9 | 1 | 3 | 6.783mb | 0.003158s | ±0.32% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,9 | 1 | 3 | 6.813mb | 0.023297s | ±3.77% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,9 | 1 | 3 | 684.621mb | 1.772223s | ±0.04% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,9 | 1 | 3 | 6.783mb | 0.002401s | ±0.14% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,9 | 1 | 3 | 6.783mb | 0.006061s | ±1.52% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,9 | 1 | 3 | 6.759mb | 0.000036s | ±4.04% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,9 | 1 | 3 | 6.759mb | 0.000036s | ±7.03% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,9 | 1 | 3 | 6.759mb | 0.000034s | ±3.63% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,9 | 1 | 3 | 6.836mb | 0.000386s | ±88.55% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,9 | 1 | 3 | 6.828mb | 0.000291s | ±17.69% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,9 | 1 | 3 | 6.762mb | 0.000080s | ±10.50% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,9 | 1 | 3 | 6.762mb | 0.000087s | ±2.76% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,9 | 1 | 3 | 6.815mb | 0.003755s | ±69.19% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,10 | 1 | 3 | 7.230mb | 0.003945s | ±2.48% | | MethodsNonProportionalBench | benchByCandidates | Copeland,10 | 1 | 3 | 7.208mb | 0.000036s | ±2.67% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,10 | 1 | 3 | 7.206mb | 0.000030s | ±0.00% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,10 | 1 | 3 | 7.208mb | 0.000036s | ±2.27% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,10 | 1 | 3 | 7.230mb | 0.003460s | ±1.93% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,10 | 1 | 3 | 7.238mb | 0.025816s | ±0.86% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,10 | 1 | 3 | 7.256mb | 0.000006s | ±35.79% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,10 | 1 | 3 | 7.230mb | 0.002606s | ±2.04% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,10 | 1 | 3 | 7.230mb | 0.006761s | ±1.65% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,10 | 1 | 3 | 7.208mb | 0.000038s | ±3.31% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,10 | 1 | 3 | 7.208mb | 0.000036s | ±2.67% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,10 | 1 | 3 | 7.208mb | 0.000038s | ±3.31% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,10 | 1 | 3 | 7.290mb | 0.000477s | ±8.17% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,10 | 1 | 3 | 7.293mb | 0.000578s | ±6.35% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,10 | 1 | 3 | 7.215mb | 0.000095s | ±0.99% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,10 | 1 | 3 | 7.215mb | 0.000101s | ±1.24% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,10 | 1 | 3 | 7.263mb | 0.000234s | ±111.07% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,11 | 1 | 3 | 7.676mb | 0.004294s | ±0.68% | | MethodsNonProportionalBench | benchByCandidates | Copeland,11 | 1 | 3 | 7.654mb | 0.000039s | ±5.22% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,11 | 1 | 3 | 7.653mb | 0.000032s | ±4.56% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,11 | 1 | 3 | 7.655mb | 0.000036s | ±6.26% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,11 | 1 | 3 | 7.676mb | 0.004028s | ±3.51% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,11 | 1 | 3 | 7.683mb | 0.029958s | ±4.71% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,11 | 1 | 3 | 7.639mb | 0.000005s | ±8.84% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,11 | 1 | 3 | 7.676mb | 0.002762s | ±6.54% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,11 | 1 | 3 | 7.676mb | 0.007102s | ±0.87% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,11 | 1 | 3 | 7.655mb | 0.000040s | ±2.40% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,11 | 1 | 3 | 7.655mb | 0.000038s | ±1.23% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,11 | 1 | 3 | 7.655mb | 0.000039s | ±2.38% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,11 | 1 | 3 | 7.751mb | 0.000748s | ±3.51% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,11 | 1 | 3 | 7.745mb | 0.000702s | ±20.15% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,11 | 1 | 3 | 7.708mb | 0.000205s | ±112.79% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,11 | 1 | 3 | 7.663mb | 0.000130s | ±4.27% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,11 | 1 | 3 | 7.709mb | 0.000356s | ±116.94% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,20 | 1 | 3 | 12.464mb | 0.008312s | ±7.15% | | MethodsNonProportionalBench | benchByCandidates | Copeland,20 | 1 | 3 | 12.464mb | 0.000229s | ±131.77% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,20 | 1 | 3 | 12.411mb | 0.000210s | ±133.66% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,20 | 1 | 3 | 12.406mb | 0.000061s | ±2.03% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,20 | 1 | 3 | 12.413mb | 0.006806s | ±0.73% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,20 | 1 | 3 | 12.456mb | 0.091459s | ±1.23% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,20 | 1 | 3 | 12.388mb | 0.000005s | ±23.57% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,20 | 1 | 3 | 12.453mb | 0.004731s | ±16.00% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,20 | 1 | 3 | 12.413mb | 0.012274s | ±2.14% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,20 | 1 | 3 | 12.406mb | 0.000068s | ±4.29% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,20 | 1 | 3 | 12.406mb | 0.000066s | ±2.11% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,20 | 1 | 3 | 12.406mb | 0.000065s | ±1.91% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,20 | 1 | 3 | 12.702mb | 0.013209s | ±12.23% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,20 | 1 | 3 | 12.692mb | 0.011353s | ±25.71% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,20 | 1 | 3 | 12.464mb | 0.000573s | ±68.31% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,20 | 1 | 3 | 12.445mb | 0.000496s | ±0.59% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,20 | 1 | 3 | 12.444mb | 0.000774s | ±0.82% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,30 | 1 | 3 | 16.946mb | 0.011932s | ±1.26% | | MethodsNonProportionalBench | benchByCandidates | Copeland,30 | 1 | 3 | 16.966mb | 0.000191s | ±116.41% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,30 | 1 | 3 | 16.956mb | 0.000074s | ±9.30% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,30 | 1 | 3 | 16.950mb | 0.000107s | ±2.78% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,30 | 1 | 3 | 16.946mb | 0.010802s | ±1.99% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,30 | 1 | 3 | 17.002mb | 0.190024s | ±1.38% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,30 | 1 | 3 | 16.928mb | 0.000008s | ±14.97% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,30 | 1 | 3 | 16.990mb | 0.008383s | ±20.97% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,30 | 1 | 3 | 16.981mb | 0.018721s | ±15.29% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,30 | 1 | 3 | 17.014mb | 0.000273s | ±125.55% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,30 | 1 | 3 | 16.948mb | 0.000103s | ±13.59% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,30 | 1 | 3 | 16.948mb | 0.000105s | ±3.52% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,30 | 1 | 3 | 17.577mb | 0.090871s | ±11.64% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,30 | 1 | 3 | 17.571mb | 0.100091s | ±6.46% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,30 | 1 | 3 | 17.007mb | 0.001403s | ±1.58% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,30 | 1 | 3 | 17.008mb | 0.001483s | ±1.41% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,30 | 1 | 3 | 17.006mb | 0.002474s | ±22.77% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,40 | 1 | 3 | 23.032mb | 0.017442s | ±16.43% | | MethodsNonProportionalBench | benchByCandidates | Copeland,40 | 1 | 3 | 23.043mb | 0.000399s | ±127.17% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,40 | 1 | 3 | 23.070mb | 0.000351s | ±132.04% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,40 | 1 | 3 | 23.003mb | 0.000159s | ±3.21% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,40 | 1 | 3 | 22.990mb | 0.014845s | ±0.38% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,40 | 1 | 3 | 23.066mb | 0.328225s | ±0.95% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,40 | 1 | 3 | 22.981mb | 0.000006s | ±7.44% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,40 | 1 | 3 | 22.981mb | 0.009713s | ±0.70% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,40 | 1 | 3 | 22.999mb | 0.026552s | ±3.05% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,40 | 1 | 3 | 22.991mb | 0.000150s | ±1.66% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,40 | 1 | 3 | 22.991mb | 0.000150s | ±1.92% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,40 | 1 | 3 | 22.993mb | 0.000153s | ±3.03% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,40 | 1 | 3 | 24.058mb | 0.416988s | ±8.69% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,40 | 1 | 3 | 24.113mb | 0.412503s | ±13.98% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,40 | 1 | 3 | 23.174mb | 0.003404s | ±2.64% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,40 | 1 | 3 | 23.173mb | 0.003211s | ±0.75% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,40 | 1 | 3 | 23.180mb | 0.005581s | ±2.42% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,50 | 1 | 3 | 27.569mb | 0.022380s | ±0.49% | | MethodsNonProportionalBench | benchByCandidates | Copeland,50 | 1 | 3 | 27.569mb | 0.000227s | ±4.03% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,50 | 1 | 3 | 27.646mb | 0.000231s | ±112.45% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,50 | 1 | 3 | 27.571mb | 0.000223s | ±3.56% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,50 | 1 | 3 | 27.569mb | 0.019937s | ±0.16% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,50 | 1 | 3 | 27.692mb | 0.517816s | ±9.10% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,50 | 1 | 3 | 27.569mb | 0.000007s | ±11.66% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,50 | 1 | 3 | 27.569mb | 0.012613s | ±1.68% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,50 | 1 | 3 | 27.569mb | 0.036053s | ±1.19% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,50 | 1 | 3 | 27.569mb | 0.000230s | ±2.40% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,50 | 1 | 3 | 27.569mb | 0.000212s | ±1.23% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,50 | 1 | 3 | 27.569mb | 0.000220s | ±9.60% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,50 | 1 | 3 | 29.229mb | 1.345662s | ±1.92% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,50 | 1 | 3 | 29.236mb | 1.587747s | ±5.93% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,50 | 1 | 3 | 27.786mb | 0.005877s | ±1.04% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,50 | 1 | 3 | 27.788mb | 0.006018s | ±3.38% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,50 | 1 | 3 | 27.788mb | 0.010559s | ±4.81% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,60 | 1 | 3 | 32.125mb | 0.028504s | ±0.93% | | MethodsNonProportionalBench | benchByCandidates | Copeland,60 | 1 | 3 | 32.133mb | 0.000283s | ±2.35% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,60 | 1 | 3 | 32.200mb | 0.000177s | ±6.66% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,60 | 1 | 3 | 32.138mb | 0.000298s | ±1.10% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,60 | 1 | 3 | 32.125mb | 0.027369s | ±1.79% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,60 | 1 | 3 | 32.258mb | 0.754619s | ±6.02% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,60 | 1 | 3 | 32.125mb | 0.000007s | ±11.66% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,60 | 1 | 3 | 32.125mb | 0.016028s | ±10.55% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,60 | 1 | 3 | 32.125mb | 0.044753s | ±5.16% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,60 | 1 | 3 | 32.125mb | 0.000287s | ±1.63% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,60 | 1 | 3 | 32.126mb | 0.000272s | ±2.14% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,60 | 1 | 3 | 32.125mb | 0.000278s | ±2.67% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,60 | 1 | 3 | 34.508mb | 3.316166s | ±11.62% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,60 | 1 | 3 | 34.505mb | 3.178537s | ±8.28% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,60 | 1 | 3 | 32.398mb | 0.010044s | ±1.64% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,60 | 1 | 3 | 32.399mb | 0.010514s | ±2.29% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,60 | 1 | 3 | 32.401mb | 0.018374s | ±1.32% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,70 | 1 | 3 | 44.389mb | 0.035290s | ±2.09% | | MethodsNonProportionalBench | benchByCandidates | Copeland,70 | 1 | 3 | 44.389mb | 0.000369s | ±1.94% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,70 | 1 | 3 | 44.618mb | 0.000225s | ±5.49% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,70 | 1 | 3 | 44.389mb | 0.000465s | ±81.93% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,70 | 1 | 3 | 44.389mb | 0.032422s | ±1.44% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,70 | 1 | 3 | 44.679mb | 1.037296s | ±10.52% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,70 | 1 | 3 | 44.389mb | 0.000007s | ±11.66% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,70 | 1 | 3 | 44.389mb | 0.019715s | ±1.45% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,70 | 1 | 3 | 44.389mb | 0.054181s | ±0.77% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,70 | 1 | 3 | 44.389mb | 0.000367s | ±0.78% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,70 | 1 | 3 | 44.389mb | 0.000355s | ±3.92% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,70 | 1 | 3 | 44.389mb | 0.000376s | ±2.39% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,70 | 1 | 3 | 47.592mb | 9.151059s | ±17.67% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,70 | 1 | 3 | 47.574mb | 7.939814s | ±10.66% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,70 | 1 | 3 | 45.430mb | 0.016193s | ±1.04% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,70 | 1 | 3 | 45.429mb | 0.016592s | ±1.85% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,70 | 1 | 3 | 45.433mb | 0.029352s | ±1.38% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,80 | 1 | 3 | 49.226mb | 0.044011s | ±0.15% | | MethodsNonProportionalBench | benchByCandidates | Copeland,80 | 1 | 3 | 49.226mb | 0.000477s | ±0.94% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,80 | 1 | 3 | 49.522mb | 0.000287s | ±3.17% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,80 | 1 | 3 | 49.226mb | 0.000470s | ±3.63% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,80 | 1 | 3 | 49.226mb | 0.040215s | ±0.08% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,80 | 1 | 3 | 49.544mb | 1.422216s | ±7.65% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,80 | 1 | 3 | 49.226mb | 0.000007s | ±0.00% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,80 | 1 | 3 | 49.226mb | 0.024139s | ±0.52% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,80 | 1 | 3 | 49.226mb | 0.069787s | ±7.07% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,80 | 1 | 3 | 49.226mb | 0.000468s | ±0.46% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,80 | 1 | 3 | 49.226mb | 0.000468s | ±0.20% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,80 | 1 | 3 | 49.226mb | 0.000473s | ±2.93% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,80 | 1 | 3 | 53.379mb | 17.652835s | ±19.68% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,80 | 1 | 3 | 53.414mb | 16.093006s | ±12.74% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,80 | 1 | 3 | 50.432mb | 0.024409s | ±3.25% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,80 | 1 | 3 | 50.433mb | 0.024826s | ±1.25% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,80 | 1 | 3 | 50.437mb | 0.044515s | ±1.02% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,90 | 1 | 3 | 54.063mb | 0.051046s | ±5.67% | | MethodsNonProportionalBench | benchByCandidates | Copeland,90 | 1 | 3 | 54.063mb | 0.000782s | ±55.30% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,90 | 1 | 3 | 54.355mb | 0.000324s | ±0.77% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,90 | 1 | 3 | 54.063mb | 0.000590s | ±1.98% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,90 | 1 | 3 | 54.063mb | 0.048183s | ±2.90% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,90 | 1 | 3 | 54.455mb | 1.773768s | ±7.30% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,90 | 1 | 3 | 54.063mb | 0.000007s | ±7.07% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,90 | 1 | 3 | 54.063mb | 0.027222s | ±0.65% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,90 | 1 | 3 | 54.063mb | 0.076666s | ±1.09% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,90 | 1 | 3 | 54.063mb | 0.000551s | ±3.36% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,90 | 1 | 3 | 54.063mb | 0.000543s | ±1.06% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,90 | 1 | 3 | 54.063mb | 0.000540s | ±4.98% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,90 | 1 | 3 | 59.248mb | 30.973354s | ±8.26% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,90 | 1 | 3 | 59.257mb | 30.272496s | ±12.70% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,90 | 1 | 3 | 55.438mb | 0.034383s | ±1.00% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,90 | 1 | 3 | 55.440mb | 0.033415s | ±1.86% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,90 | 1 | 3 | 55.440mb | 0.060644s | ±2.29% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,100 | 1 | 3 | 59.031mb | 0.060027s | ±1.77% | | MethodsNonProportionalBench | benchByCandidates | Copeland,100 | 1 | 3 | 59.031mb | 0.000669s | ±2.31% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,100 | 1 | 3 | 59.329mb | 0.000383s | ±1.13% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,100 | 1 | 3 | 59.031mb | 0.000664s | ±1.62% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,100 | 1 | 3 | 59.031mb | 0.052348s | ±0.86% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,100 | 1 | 3 | 59.224mb | 1.946463s | ±4.10% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,100 | 1 | 3 | 59.031mb | 0.000007s | ±7.07% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,100 | 1 | 3 | 59.031mb | 0.032341s | ±1.92% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,100 | 1 | 3 | 59.031mb | 0.089906s | ±0.23% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,100 | 1 | 3 | 59.031mb | 0.000647s | ±2.31% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,100 | 1 | 3 | 59.031mb | 0.000649s | ±0.50% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,100 | 1 | 3 | 59.031mb | 0.000638s | ±0.37% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,100 | 1 | 3 | 65.349mb | 58.002654s | ±7.60% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,100 | 1 | 3 | 65.212mb | 50.089861s | ±4.77% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,100 | 1 | 3 | 60.436mb | 0.044041s | ±1.80% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,100 | 1 | 3 | 60.443mb | 0.044564s | ±1.62% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,100 | 1 | 3 | 60.442mb | 0.081513s | ±0.27% | +-----------------------------+-------------------+-----------------------------------+------+-----+-----------+------------+----------+

Proportional

Subjects: 1, Assertions: 0, Failures: 0, Errors: 0 +--------------------------+-------------------+---------+------+-----+----------+-----------+---------+ | benchmark | subject | set | revs | its | mem_peak | mode | rstdev | +--------------------------+-------------------+---------+------+-----+----------+-----------+---------+ | MethodsProportionalBench | benchByCandidates | STV,3 | 1 | 3 | 3.849mb | 0.004075s | ±19.71% | | MethodsProportionalBench | benchByCandidates | STV,4 | 1 | 3 | 4.228mb | 0.006325s | ±14.87% | | MethodsProportionalBench | benchByCandidates | STV,5 | 1 | 3 | 4.672mb | 0.008955s | ±1.32% | | MethodsProportionalBench | benchByCandidates | STV,6 | 1 | 3 | 5.119mb | 0.009425s | ±18.91% | | MethodsProportionalBench | benchByCandidates | STV,7 | 1 | 3 | 5.563mb | 0.014790s | ±14.17% | | MethodsProportionalBench | benchByCandidates | STV,8 | 1 | 3 | 6.327mb | 0.016129s | ±7.76% | | MethodsProportionalBench | benchByCandidates | STV,9 | 1 | 3 | 6.788mb | 0.019538s | ±0.74% | | MethodsProportionalBench | benchByCandidates | STV,10 | 1 | 3 | 7.235mb | 0.023839s | ±2.54% | | MethodsProportionalBench | benchByCandidates | STV,11 | 1 | 3 | 7.682mb | 0.028752s | ±2.09% | | MethodsProportionalBench | benchByCandidates | STV,12 | 1 | 3 | 8.129mb | 0.029920s | ±1.95% | | MethodsProportionalBench | benchByCandidates | STV,13 | 1 | 3 | 8.575mb | 0.035721s | ±1.74% | | MethodsProportionalBench | benchByCandidates | STV,14 | 1 | 3 | 9.022mb | 0.041041s | ±0.85% | | MethodsProportionalBench | benchByCandidates | STV,15 | 1 | 3 | 9.467mb | 0.042278s | ±0.71% | | MethodsProportionalBench | benchByCandidates | STV,16 | 1 | 3 | 10.570mb | 0.048256s | ±1.55% | | MethodsProportionalBench | benchByCandidates | STV,17 | 1 | 3 | 11.073mb | 0.054690s | ±0.28% | | MethodsProportionalBench | benchByCandidates | STV,18 | 1 | 3 | 11.529mb | 0.057881s | ±12.45% | | MethodsProportionalBench | benchByCandidates | STV,19 | 1 | 3 | 11.977mb | 0.065760s | ±1.32% | | MethodsProportionalBench | benchByCandidates | STV,20 | 1 | 3 | 12.428mb | 0.071830s | ±0.89% | | MethodsProportionalBench | benchByCandidates | STV,30 | 1 | 3 | 16.967mb | 0.146342s | ±3.07% | | MethodsProportionalBench | benchByCandidates | STV,40 | 1 | 3 | 23.056mb | 0.262451s | ±0.98% | | MethodsProportionalBench | benchByCandidates | STV,50 | 1 | 3 | 27.666mb | 0.438554s | ±1.09% | | MethodsProportionalBench | benchByCandidates | STV,60 | 1 | 3 | 32.266mb | 0.617602s | ±2.68% | | MethodsProportionalBench | benchByCandidates | STV,70 | 1 | 3 | 44.724mb | 0.877067s | ±2.16% | | MethodsProportionalBench | benchByCandidates | STV,80 | 1 | 3 | 49.657mb | 1.217623s | ±2.48% | | MethodsProportionalBench | benchByCandidates | STV,90 | 1 | 3 | 54.599mb | 1.660393s | ±2.53% | | MethodsProportionalBench | benchByCandidates | STV,100 | 1 | 3 | 59.679mb | 2.057089s | ±1.32% | +--------------------------+-------------------+---------+------+-----+----------+-----------+---------+

v3.2 Branch

1000 random votes different for each test, variable number of candidates (look at column "set")

• AMD Ryzen 9 5900X

PHPBench (1.2.5) with PHP version 8.1.6, xdebug ❌, opcache ✔ (with JIT Tracing)

    #[Bench\Warmup(1)]
    #[Bench\Iterations(3)]
    #[Bench\Revs(1)]

Non-Proportional

Subjects: 1, Assertions: 0, Failures: 0, Errors: 0 +-----------------------------+-------------------+-----------------------------------+------+-----+-----------+------------+----------+ | benchmark | subject | set | revs | its | mem_peak | mode | rstdev | +-----------------------------+-------------------+-----------------------------------+------+-----+-----------+------------+----------+ | MethodsNonProportionalBench | benchByCandidates | BordaCount,3 | 1 | 3 | 3.802mb | 0.001524s | ±11.42% | | MethodsNonProportionalBench | benchByCandidates | Copeland,3 | 1 | 3 | 3.732mb | 0.000022s | ±2.11% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,3 | 1 | 3 | 3.659mb | 0.000020s | ±2.32% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,3 | 1 | 3 | 3.660mb | 0.000022s | ±2.18% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,3 | 1 | 3 | 3.721mb | 0.001586s | ±3.03% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,3 | 1 | 3 | 3.729mb | 0.004477s | ±48.72% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,3 | 1 | 3 | 3.729mb | 0.000321s | ±133.35% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,3 | 1 | 3 | 3.725mb | 0.001545s | ±35.59% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,3 | 1 | 3 | 3.728mb | 0.003228s | ±20.81% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,3 | 1 | 3 | 3.660mb | 0.000023s | ±3.98% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,3 | 1 | 3 | 3.660mb | 0.000023s | ±2.08% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,3 | 1 | 3 | 3.660mb | 0.000023s | ±0.00% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,3 | 1 | 3 | 3.728mb | 0.002659s | ±26.81% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,3 | 1 | 3 | 3.731mb | 0.003048s | ±74.21% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,3 | 1 | 3 | 3.661mb | 0.000029s | ±1.64% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,3 | 1 | 3 | 3.661mb | 0.000030s | ±1.59% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,3 | 1 | 3 | 3.661mb | 0.000030s | ±1.55% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,5 | 1 | 3 | 4.611mb | 0.002110s | ±27.68% | | MethodsNonProportionalBench | benchByCandidates | Copeland,5 | 1 | 3 | 4.551mb | 0.000031s | ±7.90% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,5 | 1 | 3 | 4.550mb | 0.000027s | ±8.31% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,5 | 1 | 3 | 4.551mb | 0.000030s | ±4.88% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,5 | 1 | 3 | 4.581mb | 0.002234s | ±33.60% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,5 | 1 | 3 | 4.612mb | 0.008804s | ±29.45% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,5 | 1 | 3 | 4.750mb | 0.000333s | ±8.48% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,5 | 1 | 3 | 4.612mb | 0.001945s | ±48.24% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,5 | 1 | 3 | 4.582mb | 0.004119s | ±26.82% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,5 | 1 | 3 | 4.551mb | 0.000030s | ±9.76% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,5 | 1 | 3 | 4.551mb | 0.000030s | ±3.07% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,5 | 1 | 3 | 4.551mb | 0.000030s | ±8.84% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,5 | 1 | 3 | 4.634mb | 0.001457s | ±119.79% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,5 | 1 | 3 | 4.570mb | 0.000072s | ±10.25% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,5 | 1 | 3 | 4.616mb | 0.007621s | ±75.79% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,5 | 1 | 3 | 4.611mb | 0.000134s | ±127.63% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,5 | 1 | 3 | 4.614mb | 0.019109s | ±18.08% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,6 | 1 | 3 | 5.025mb | 0.002424s | ±3.93% | | MethodsNonProportionalBench | benchByCandidates | Copeland,6 | 1 | 3 | 5.065mb | 0.001195s | ±95.20% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,6 | 1 | 3 | 5.057mb | 0.001578s | ±78.29% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,6 | 1 | 3 | 5.058mb | 0.000119s | ±133.48% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,6 | 1 | 3 | 5.026mb | 0.002764s | ±9.60% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,6 | 1 | 3 | 5.060mb | 0.011146s | ±0.61% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,6 | 1 | 3 | 5.803mb | 0.001708s | ±1.08% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,6 | 1 | 3 | 5.026mb | 0.001975s | ±2.18% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,6 | 1 | 3 | 5.057mb | 0.004808s | ±13.70% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,6 | 1 | 3 | 5.055mb | 0.000117s | ±133.46% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,6 | 1 | 3 | 4.997mb | 0.000031s | ±3.98% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,6 | 1 | 3 | 4.997mb | 0.000030s | ±14.21% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,6 | 1 | 3 | 5.090mb | 0.003927s | ±68.56% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,6 | 1 | 3 | 5.061mb | 0.001344s | ±63.57% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,6 | 1 | 3 | 5.065mb | 0.008249s | ±42.21% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,6 | 1 | 3 | 5.057mb | 0.000140s | ±127.64% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,6 | 1 | 3 | 5.056mb | 0.005456s | ±58.70% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,7 | 1 | 3 | 5.470mb | 0.002529s | ±0.86% | | MethodsNonProportionalBench | benchByCandidates | Copeland,7 | 1 | 3 | 5.505mb | 0.001398s | ±80.88% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,7 | 1 | 3 | 5.509mb | 0.000118s | ±133.57% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,7 | 1 | 3 | 5.511mb | 0.001358s | ±81.14% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,7 | 1 | 3 | 5.470mb | 0.002498s | ±1.33% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,7 | 1 | 3 | 5.510mb | 0.016885s | ±13.43% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,7 | 1 | 3 | 11.313mb | 0.014489s | ±0.44% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,7 | 1 | 3 | 5.470mb | 0.001977s | ±3.64% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,7 | 1 | 3 | 5.470mb | 0.004855s | ±0.99% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,7 | 1 | 3 | 5.501mb | 0.001342s | ±68.36% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,7 | 1 | 3 | 5.442mb | 0.000031s | ±2.98% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,7 | 1 | 3 | 5.442mb | 0.000033s | ±14.72% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,7 | 1 | 3 | 5.521mb | 0.001549s | ±34.02% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,7 | 1 | 3 | 5.519mb | 0.000237s | ±106.41% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,7 | 1 | 3 | 5.500mb | 0.000138s | ±126.56% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,7 | 1 | 3 | 5.500mb | 0.000139s | ±126.76% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,7 | 1 | 3 | 5.503mb | 0.023529s | ±47.80% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,8 | 1 | 3 | 6.234mb | 0.002813s | ±1.25% | | MethodsNonProportionalBench | benchByCandidates | Copeland,8 | 1 | 3 | 6.208mb | 0.000035s | ±2.75% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,8 | 1 | 3 | 6.271mb | 0.001368s | ±68.40% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,8 | 1 | 3 | 6.263mb | 0.000118s | ±132.31% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,8 | 1 | 3 | 6.234mb | 0.002856s | ±2.60% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,8 | 1 | 3 | 6.270mb | 0.018567s | ±3.23% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,8 | 1 | 3 | 86.520mb | 0.161483s | ±0.97% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,8 | 1 | 3 | 6.235mb | 0.002310s | ±0.80% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,8 | 1 | 3 | 6.235mb | 0.005669s | ±3.64% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,8 | 1 | 3 | 6.209mb | 0.000035s | ±4.95% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,8 | 1 | 3 | 6.263mb | 0.000134s | ±132.55% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,8 | 1 | 3 | 6.209mb | 0.000038s | ±15.96% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,8 | 1 | 3 | 6.260mb | 0.000224s | ±5.62% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,8 | 1 | 3 | 6.292mb | 0.000300s | ±97.60% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,8 | 1 | 3 | 6.210mb | 0.000065s | ±1.91% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,8 | 1 | 3 | 6.210mb | 0.000070s | ±0.68% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,8 | 1 | 3 | 6.265mb | 0.010512s | ±58.91% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,9 | 1 | 3 | 6.693mb | 0.003095s | ±0.95% | | MethodsNonProportionalBench | benchByCandidates | Copeland,9 | 1 | 3 | 6.669mb | 0.000037s | ±1.29% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,9 | 1 | 3 | 6.669mb | 0.000113s | ±132.80% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,9 | 1 | 3 | 6.669mb | 0.000036s | ±0.00% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,9 | 1 | 3 | 6.737mb | 0.003168s | ±16.73% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,9 | 1 | 3 | 6.723mb | 0.020616s | ±9.56% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,9 | 1 | 3 | 684.597mb | 1.759478s | ±0.43% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,9 | 1 | 3 | 6.693mb | 0.002496s | ±3.81% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,9 | 1 | 3 | 6.693mb | 0.005934s | ±3.85% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,9 | 1 | 3 | 6.669mb | 0.000036s | ±0.00% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,9 | 1 | 3 | 6.669mb | 0.000036s | ±4.54% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,9 | 1 | 3 | 6.669mb | 0.000036s | ±2.57% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,9 | 1 | 3 | 6.746mb | 0.000464s | ±80.49% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,9 | 1 | 3 | 6.754mb | 0.000386s | ±87.16% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,9 | 1 | 3 | 6.724mb | 0.000242s | ±130.20% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,9 | 1 | 3 | 6.672mb | 0.000081s | ±1.17% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,9 | 1 | 3 | 6.726mb | 0.015371s | ±29.12% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,10 | 1 | 3 | 7.149mb | 0.003372s | ±1.17% | | MethodsNonProportionalBench | benchByCandidates | Copeland,10 | 1 | 3 | 7.172mb | 0.000120s | ±131.10% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,10 | 1 | 3 | 7.116mb | 0.000031s | ±3.11% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,10 | 1 | 3 | 7.118mb | 0.000037s | ±6.00% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,10 | 1 | 3 | 7.149mb | 0.003277s | ±0.85% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,10 | 1 | 3 | 7.155mb | 0.024746s | ±1.43% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,10 | 1 | 3 | 7.166mb | 0.000005s | ±16.64% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,10 | 1 | 3 | 7.148mb | 0.002491s | ±0.34% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,10 | 1 | 3 | 7.148mb | 0.006318s | ±0.67% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,10 | 1 | 3 | 7.118mb | 0.000038s | ±3.31% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,10 | 1 | 3 | 7.118mb | 0.000037s | ±4.51% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,10 | 1 | 3 | 7.118mb | 0.000039s | ±13.05% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,10 | 1 | 3 | 7.199mb | 0.000637s | ±15.45% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,10 | 1 | 3 | 7.195mb | 0.000542s | ±25.69% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,10 | 1 | 3 | 7.125mb | 0.000096s | ±0.00% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,10 | 1 | 3 | 7.125mb | 0.000102s | ±5.28% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,10 | 1 | 3 | 7.172mb | 0.000817s | ±135.94% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,11 | 1 | 3 | 7.594mb | 0.003904s | ±2.70% | | MethodsNonProportionalBench | benchByCandidates | Copeland,11 | 1 | 3 | 7.565mb | 0.000042s | ±1.13% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,11 | 1 | 3 | 7.564mb | 0.000036s | ±5.76% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,11 | 1 | 3 | 7.565mb | 0.000038s | ±3.63% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,11 | 1 | 3 | 7.594mb | 0.003622s | ±0.45% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,11 | 1 | 3 | 7.626mb | 0.028215s | ±8.72% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,11 | 1 | 3 | 7.549mb | 0.000006s | ±14.14% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,11 | 1 | 3 | 7.594mb | 0.002663s | ±0.38% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,11 | 1 | 3 | 7.594mb | 0.006780s | ±1.90% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,11 | 1 | 3 | 7.565mb | 0.000041s | ±0.00% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,11 | 1 | 3 | 7.565mb | 0.000041s | ±0.00% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,11 | 1 | 3 | 7.565mb | 0.000041s | ±0.00% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,11 | 1 | 3 | 7.654mb | 0.000733s | ±7.38% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,11 | 1 | 3 | 7.660mb | 0.000896s | ±6.96% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,11 | 1 | 3 | 7.573mb | 0.000117s | ±2.54% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,11 | 1 | 3 | 7.573mb | 0.000122s | ±0.67% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,11 | 1 | 3 | 7.618mb | 0.000264s | ±106.00% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,20 | 1 | 3 | 12.366mb | 0.007824s | ±8.70% | | MethodsNonProportionalBench | benchByCandidates | Copeland,20 | 1 | 3 | 12.362mb | 0.001393s | ±65.94% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,20 | 1 | 3 | 12.312mb | 0.001167s | ±98.99% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,20 | 1 | 3 | 12.308mb | 0.000064s | ±14.33% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,20 | 1 | 3 | 12.315mb | 0.006407s | ±4.24% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,20 | 1 | 3 | 12.335mb | 0.081311s | ±2.61% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,20 | 1 | 3 | 12.289mb | 0.000006s | ±8.32% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,20 | 1 | 3 | 12.314mb | 0.004337s | ±2.07% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,20 | 1 | 3 | 12.314mb | 0.011260s | ±0.41% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,20 | 1 | 3 | 12.307mb | 0.000067s | ±14.51% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,20 | 1 | 3 | 12.306mb | 0.000064s | ±1.49% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,20 | 1 | 3 | 12.306mb | 0.000063s | ±2.21% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,20 | 1 | 3 | 12.596mb | 0.012358s | ±11.33% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,20 | 1 | 3 | 12.591mb | 0.013436s | ±10.97% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,20 | 1 | 3 | 12.370mb | 0.000541s | ±72.09% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,20 | 1 | 3 | 12.345mb | 0.000470s | ±1.76% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,20 | 1 | 3 | 12.362mb | 0.001062s | ±98.11% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,30 | 1 | 3 | 16.868mb | 0.010368s | ±12.04% | | MethodsNonProportionalBench | benchByCandidates | Copeland,30 | 1 | 3 | 16.874mb | 0.001211s | ±87.03% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,30 | 1 | 3 | 16.863mb | 0.000159s | ±122.81% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,30 | 1 | 3 | 16.811mb | 0.000105s | ±2.99% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,30 | 1 | 3 | 16.806mb | 0.009620s | ±1.73% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,30 | 1 | 3 | 16.872mb | 0.187050s | ±2.29% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,30 | 1 | 3 | 16.788mb | 0.000007s | ±17.01% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,30 | 1 | 3 | 16.805mb | 0.007006s | ±1.68% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,30 | 1 | 3 | 16.841mb | 0.021321s | ±7.10% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,30 | 1 | 3 | 16.807mb | 0.000101s | ±4.00% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,30 | 1 | 3 | 16.808mb | 0.000099s | ±4.57% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,30 | 1 | 3 | 16.807mb | 0.000107s | ±2.29% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,30 | 1 | 3 | 17.421mb | 0.093493s | ±5.52% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,30 | 1 | 3 | 17.443mb | 0.104010s | ±2.17% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,30 | 1 | 3 | 16.867mb | 0.001384s | ±5.49% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,30 | 1 | 3 | 16.868mb | 0.001406s | ±2.41% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,30 | 1 | 3 | 16.867mb | 0.002296s | ±2.15% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,40 | 1 | 3 | 22.913mb | 0.015279s | ±13.36% | | MethodsNonProportionalBench | benchByCandidates | Copeland,40 | 1 | 3 | 22.895mb | 0.000435s | ±128.97% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,40 | 1 | 3 | 22.936mb | 0.000189s | ±116.58% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,40 | 1 | 3 | 22.863mb | 0.000158s | ±2.90% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,40 | 1 | 3 | 22.848mb | 0.013507s | ±0.93% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,40 | 1 | 3 | 22.945mb | 0.291114s | ±10.19% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,40 | 1 | 3 | 22.841mb | 0.000006s | ±8.32% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,40 | 1 | 3 | 22.853mb | 0.009024s | ±13.62% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,40 | 1 | 3 | 22.857mb | 0.025075s | ±2.78% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,40 | 1 | 3 | 22.853mb | 0.000151s | ±1.96% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,40 | 1 | 3 | 22.853mb | 0.000151s | ±0.83% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,40 | 1 | 3 | 22.852mb | 0.000150s | ±0.83% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,40 | 1 | 3 | 23.967mb | 0.461000s | ±2.30% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,40 | 1 | 3 | 23.983mb | 0.467482s | ±6.05% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,40 | 1 | 3 | 23.039mb | 0.003041s | ±2.43% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,40 | 1 | 3 | 23.039mb | 0.003024s | ±2.47% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,40 | 1 | 3 | 23.040mb | 0.005450s | ±10.49% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,50 | 1 | 3 | 27.429mb | 0.019048s | ±0.77% | | MethodsNonProportionalBench | benchByCandidates | Copeland,50 | 1 | 3 | 27.429mb | 0.000205s | ±1.80% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,50 | 1 | 3 | 27.481mb | 0.000131s | ±1.57% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,50 | 1 | 3 | 27.429mb | 0.000211s | ±1.48% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,50 | 1 | 3 | 27.429mb | 0.018321s | ±1.88% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,50 | 1 | 3 | 27.533mb | 0.466429s | ±6.92% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,50 | 1 | 3 | 27.429mb | 0.000007s | ±0.00% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,50 | 1 | 3 | 27.429mb | 0.011725s | ±1.17% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,50 | 1 | 3 | 27.429mb | 0.031058s | ±0.39% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,50 | 1 | 3 | 27.429mb | 0.000201s | ±2.11% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,50 | 1 | 3 | 27.429mb | 0.000202s | ±1.62% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,50 | 1 | 3 | 27.429mb | 0.000209s | ±0.82% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,50 | 1 | 3 | 29.101mb | 1.375436s | ±8.57% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,50 | 1 | 3 | 29.062mb | 1.306662s | ±10.02% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,50 | 1 | 3 | 27.650mb | 0.005984s | ±1.00% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,50 | 1 | 3 | 27.646mb | 0.005817s | ±1.80% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,50 | 1 | 3 | 27.646mb | 0.010318s | ±16.23% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,60 | 1 | 3 | 31.984mb | 0.024316s | ±1.00% | | MethodsNonProportionalBench | benchByCandidates | Copeland,60 | 1 | 3 | 31.991mb | 0.000272s | ±1.20% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,60 | 1 | 3 | 32.058mb | 0.000170s | ±7.50% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,60 | 1 | 3 | 31.996mb | 0.000272s | ±1.30% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,60 | 1 | 3 | 31.984mb | 0.023471s | ±1.97% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,60 | 1 | 3 | 32.114mb | 0.725998s | ±3.91% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,60 | 1 | 3 | 31.984mb | 0.000005s | ±16.64% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,60 | 1 | 3 | 31.984mb | 0.014803s | ±0.94% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,60 | 1 | 3 | 31.984mb | 0.040944s | ±2.69% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,60 | 1 | 3 | 31.984mb | 0.000272s | ±0.91% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,60 | 1 | 3 | 31.984mb | 0.000272s | ±1.81% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,60 | 1 | 3 | 31.984mb | 0.000275s | ±1.73% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,60 | 1 | 3 | 34.517mb | 3.339907s | ±9.85% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,60 | 1 | 3 | 34.478mb | 3.625151s | ±7.60% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,60 | 1 | 3 | 32.255mb | 0.009959s | ±1.61% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,60 | 1 | 3 | 32.257mb | 0.009910s | ±1.81% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,60 | 1 | 3 | 32.256mb | 0.021020s | ±5.02% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,70 | 1 | 3 | 44.247mb | 0.030676s | ±0.91% | | MethodsNonProportionalBench | benchByCandidates | Copeland,70 | 1 | 3 | 44.247mb | 0.000349s | ±1.19% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,70 | 1 | 3 | 44.486mb | 0.000210s | ±3.75% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,70 | 1 | 3 | 44.247mb | 0.000356s | ±0.99% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,70 | 1 | 3 | 44.247mb | 0.029905s | ±0.71% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,70 | 1 | 3 | 44.481mb | 1.003590s | ±7.87% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,70 | 1 | 3 | 44.247mb | 0.000007s | ±7.07% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,70 | 1 | 3 | 44.247mb | 0.018283s | ±0.08% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,70 | 1 | 3 | 44.247mb | 0.050120s | ±0.75% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,70 | 1 | 3 | 44.247mb | 0.000348s | ±0.49% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,70 | 1 | 3 | 44.247mb | 0.000348s | ±1.20% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,70 | 1 | 3 | 44.247mb | 0.000355s | ±12.89% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,70 | 1 | 3 | 47.505mb | 7.590197s | ±16.35% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,70 | 1 | 3 | 47.410mb | 7.557485s | ±5.37% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,70 | 1 | 3 | 45.295mb | 0.015402s | ±2.51% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,70 | 1 | 3 | 45.291mb | 0.015401s | ±0.70% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,70 | 1 | 3 | 45.294mb | 0.028018s | ±0.32% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,80 | 1 | 3 | 49.084mb | 0.037037s | ±0.25% | | MethodsNonProportionalBench | benchByCandidates | Copeland,80 | 1 | 3 | 49.084mb | 0.000443s | ±0.11% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,80 | 1 | 3 | 49.370mb | 0.000257s | ±1.43% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,80 | 1 | 3 | 49.084mb | 0.000441s | ±2.97% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,80 | 1 | 3 | 49.084mb | 0.036051s | ±0.70% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,80 | 1 | 3 | 49.347mb | 1.215646s | ±3.64% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,80 | 1 | 3 | 49.084mb | 0.000007s | ±7.07% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,80 | 1 | 3 | 49.084mb | 0.021718s | ±0.57% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,80 | 1 | 3 | 49.084mb | 0.060641s | ±0.71% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,80 | 1 | 3 | 49.084mb | 0.000432s | ±0.85% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,80 | 1 | 3 | 49.084mb | 0.000435s | ±0.78% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,80 | 1 | 3 | 49.084mb | 0.000427s | ±0.83% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,80 | 1 | 3 | 53.274mb | 14.873456s | ±21.68% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,80 | 1 | 3 | 53.346mb | 15.733408s | ±16.64% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,80 | 1 | 3 | 50.295mb | 0.022662s | ±2.31% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,80 | 1 | 3 | 50.294mb | 0.023019s | ±3.50% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,80 | 1 | 3 | 50.292mb | 0.041399s | ±1.72% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,90 | 1 | 3 | 53.920mb | 0.044067s | ±1.03% | | MethodsNonProportionalBench | benchByCandidates | Copeland,90 | 1 | 3 | 53.920mb | 0.000540s | ±0.54% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,90 | 1 | 3 | 54.270mb | 0.000414s | ±82.76% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,90 | 1 | 3 | 53.920mb | 0.000546s | ±0.60% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,90 | 1 | 3 | 53.920mb | 0.042732s | ±0.28% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,90 | 1 | 3 | 54.186mb | 1.534839s | ±4.49% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,90 | 1 | 3 | 53.920mb | 0.000008s | ±5.66% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,90 | 1 | 3 | 53.920mb | 0.025321s | ±0.90% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,90 | 1 | 3 | 53.920mb | 0.072044s | ±0.53% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,90 | 1 | 3 | 53.920mb | 0.000530s | ±1.08% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,90 | 1 | 3 | 53.920mb | 0.000527s | ±0.09% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,90 | 1 | 3 | 53.920mb | 0.000540s | ±4.15% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,90 | 1 | 3 | 59.325mb | 28.542581s | ±14.47% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,90 | 1 | 3 | 59.069mb | 28.519612s | ±8.88% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,90 | 1 | 3 | 55.295mb | 0.032344s | ±1.29% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,90 | 1 | 3 | 55.296mb | 0.031541s | ±1.60% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,90 | 1 | 3 | 55.291mb | 0.057553s | ±0.56% | | MethodsNonProportionalBench | benchByCandidates | BordaCount,100 | 1 | 3 | 58.888mb | 0.051550s | ±1.33% | | MethodsNonProportionalBench | benchByCandidates | Copeland,100 | 1 | 3 | 58.888mb | 0.000641s | ±0.96% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Quick,100 | 1 | 3 | 59.152mb | 0.000353s | ±0.71% | | MethodsNonProportionalBench | benchByCandidates | Dodgson Tideman Approximation,100 | 1 | 3 | 58.888mb | 0.000646s | ±1.07% | | MethodsNonProportionalBench | benchByCandidates | DowdallSystem,100 | 1 | 3 | 58.888mb | 0.050364s | ±0.64% | | MethodsNonProportionalBench | benchByCandidates | Instant-runoff,100 | 1 | 3 | 59.071mb | 1.853938s | ±3.54% | | MethodsNonProportionalBench | benchByCandidates | Kemeny–Young,100 | 1 | 3 | 58.888mb | 0.000008s | ±16.27% | | MethodsNonProportionalBench | benchByCandidates | First-past-the-post voting,100 | 1 | 3 | 58.888mb | 0.029426s | ±0.22% | | MethodsNonProportionalBench | benchByCandidates | Multiple Rounds System,100 | 1 | 3 | 58.888mb | 0.084283s | ±0.29% | | MethodsNonProportionalBench | benchByCandidates | Minimax Winning,100 | 1 | 3 | 58.888mb | 0.000627s | ±0.98% | | MethodsNonProportionalBench | benchByCandidates | Minimax Margin,100 | 1 | 3 | 58.888mb | 0.000628s | ±0.75% | | MethodsNonProportionalBench | benchByCandidates | Minimax Opposition,100 | 1 | 3 | 58.888mb | 0.000622s | ±0.66% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Margin,100 | 1 | 3 | 65.109mb | 43.207162s | ±10.17% | | MethodsNonProportionalBench | benchByCandidates | Ranked Pairs Winning,100 | 1 | 3 | 65.087mb | 47.362454s | ±5.24% | | MethodsNonProportionalBench | benchByCandidates | Schulze Winning,100 | 1 | 3 | 60.295mb | 0.044037s | ±0.95% | | MethodsNonProportionalBench | benchByCandidates | Schulze Margin,100 | 1 | 3 | 60.298mb | 0.044785s | ±0.54% | | MethodsNonProportionalBench | benchByCandidates | Schulze Ratio,100 | 1 | 3 | 60.297mb | 0.076305s | ±2.64% | +-----------------------------+-------------------+-----------------------------------+------+-----+-----------+------------+----------+