Our goal is to translate academic research on voting into a beneficial service for the public, as well as to improve our understanding of voting by the study of real elections. We offer Stable Voting as a free service, we maintain your privacy, and we hope to improve the site with your feedback.

Stable Voting respects majority preferences and mitigates the threats of vote splitting and spoiler effects that can undermine elections run with traditional voting systems.

The key idea of stability is that if a candidate A would win without another candidate B in the election, and a majority of voters prefer A to B, then A should still win when B is included in the election.

The only exception to stability should be for tie-breaking: if there is another candidate C who has the same kind of claim to winning as A does—that is, C would win without a candidate D in the election, and a majority of voters prefer C to D—then it is legitimate to choose between A and C (and any other candidates with the same kind of claim to winning).

Voters rank the candidates. Then Stable Voting determines the winner of an election by looking at head-to-head matches between candidates:

If more voters rank candidate A above candidate B than rank B above A, then A wins their head-to-head match and B loses their head-to-head match.

If one candidate wins its matches against all other candidates, this candidate—known as the Condorcet winner—is the winner of the election.

It is possible that every candidate loses a head-to-head match to some other candidate. For example, in an election with three candidates, A, B, and C, it may be that A wins head-to-head against B, B wins head-to-head against C, and C wins head-to-head against A, so each candidate has one loss. This is an example of a majority cycle.

To deal with majority cycles, we look at the margins of victory or loss in head-to-head matches. The margin of A vs. B is the number of voters who rank A above B minus the number of voters who rank B above A. If the margin is positive, it is a margin of victory for A; if the margin is negative, it is a margin of loss for A.

We resolve majority cycles as follows:

• For each majority cycle, the match with the smallest margin of victory in that cycle is discarded.
  For example, if A wins against B by 1,000 votes, B wins against C by 2,000 votes, and C wins against A by 3,000 votes, then A’s win against B is discarded.
• The wins in the remaining matches are considered defeats of the losing candidates.

There is always an undefeated candidate. If there is only one, that candidate wins the election.

If there is more than one undefeated candidate, we break the tie as follows:

• List all head-to-head matches of the form A vs. B, where A is undefeated, in order from the largest to smallest margin of A vs. B. Find the first match A vs. B in the list such that A is a Stable Voting winner after B is removed from all ballots; this A is the Stable Voting winner for the original set of ballots.

This rule guarantees that the only exceptions to stability occur when multiple candidates have a claim to winning based on stability, in which case the winner is the candidate with the strongest claim, as measured by the margin of A vs. B where A would win without B in the election.

In the unlikely event that there are multiple Stable Voting winners, we report all the Stable Voting winners and a randomly selected ultimate winner.

See the research or FAQ pages for more information or the demo page to see Stable Voting in action.