yarn add votes

import { Borda } from 'votes'

const borda = new Borda({
  candidates: ['Lion', 'Bear', 'Sheep'],
  ballots: [
    { ranking: [['Lion'], ['Bear'], ['Sheep']], weight: 4 },
    { ranking: [['Sheep'], ['Bear'], ['Lion']], weight: 3 },
    { ranking: [['Bear', 'Sheep'], ['Lion']], weight: 2 },
  ],
})

const scores = borda.scores()
// -> { Bear: 10, Lion: 8, Sheep: 9}

const ranking = borda.ranking()
// -> [ [ 'Bear' ], [ 'Sheep' ], [ 'Lion' ] ]

• 🧪 Demo/Playground: rank-votes.vercel.app (work in progress!)

• 🧑‍🏫 Blog post on my website: 🗳 Ranked voting systems

• 💩 Library documentation: lzear.github.io/votes

• 🤓 Good Wikipedia article: Comparison of electoral systems

Absolute majority: Checks if a candidate is ranked first by more than 50% of voters.

Approval voting: Each voter can select (“approve”) any number of candidates. The winner is the most-approved candidate.

Baldwin method: Iterative Borda count in which, each round, candidates scoring the lowest score are eliminated.

Borda count: For each voter, every candidate is given a number of points which equals the number of candidates ranked lower in the voter's preference.

Bottom-two-runoff: take the two options with the fewest first preference votes. The pairwise loser out of those two options is eliminated. Repeat.

Contingent vote (immediate Two-round system): If no candidate receives 50% of the votes in the first round, then a second round of voting is held with only the top two candidates.

Coombs' method: Each round, the candidate with the most last rank is eliminated. The election repeats until there is a winner.

Copeland's method: Rank candidates by number of duels won against other candidates.

Instant-runoff: Considering only the top choice of each voter, the candidate with the fewest votes is eliminated. The election repeats until there is a winner. This voting system is very similar to single transferable vote method.

Kemeny–Young method: A relatively complex computation generating a preference order aiming to minimize dissatisfaction of the voters. Also known as Kemeny rule, VoteFair popularity ranking, the maximum likelihood method, and the median relation.

Maximal lotteries & Randomized Condorcet: Returns probabilities for each candidate that should be used for a lottery between the Candidates. If a candidate is the Condorcet winner, its probability will be 1. Despite being non-deterministic, those methods are the fairest. Currently, these methods give incorrect results in many cases because of mistakes in the codes!

Majority Judgement: (⚠️ cardinal voting system). Voters can rank candidates in an array corresponding to 6 categories ("Excellent", "Very good", "Good", "Passable", "Mediocre" and "Bad"). Candidates with the best median are ranked first.

Minimax Condorcet method: Ranking the candidates by smallest pairwise defeat.

Minimax-TD: Compute the Smith set . Then compute the Minimax ranking on that set. TD stands for Tideman-Darlington.

Nanson method: Iterative Borda count in which, each round, candidates scoring the average score or less are eliminated.

Plurality: Simple voting method where only the preferred candidate of each voter gets 1 point. AKA first-past-the-post.

Random candidate: Selects a random ranking, regardless of ballots.

Random dictator: Selects a random ballot that decides the ranking.

Ranked pairs: Using the duel results as edges, build an acyclic graph starting by the strongest score differences. The roots of the graph are the winners.

Schulze method: From the votes, compute the results of all possible duels. Then remove the most indecisive (closest to 50/50) duels until there is an undefeated candidate, the winner. This popular voting system is used by several organizations (Ubuntu, Debian, Wikimedia...).

Smith's method: All members of the top cycle (a.k.a. Smith set): "the smallest non-empty set of candidates in a particular election such that each member defeats every candidate outside the set in a pairwise election"

Contributions, issues and feature requests are welcome!
Feel free to check issues page.

The repository is split in 2 projects:

• /votes contains the source of the NPM package votes

• /demo contains the source of the demo website