Condorcet winner criterion

Condorcet methods Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results A Condorcet (French: [kɔ̃dɔʁsɛ], English: /kɒndɔːrˈseɪ/) winner is a candidate who would receive the support of more than half of the electorate in a one-on-one race against any one of their opponents.

The Condorcet winner criterion extends the principle of majority rule to elections with multiple candidates.

This is called Condorcet's voting paradox,[6] and is analogous to the counterintuitive intransitive dice phenomenon known in probability.

If voters are arranged on a sole 1-dimensional axis, such as the left-right political spectrum for a common example, and always prefer candidates who are more similar to themselves, a majority-rule winner always exists and is the candidate whose ideology is most representative of the electorate, a result known as the median voter theorem.

[8][9] Previous research has found cycles to be somewhat rare in real elections, with estimates of their prevalence ranging from 1-10% of races.

Most rated systems, like score voting and highest median, fail the majority winner criterion.

Condorcet methods were first studied in detail by the Spanish philosopher and theologian Ramon Llull in the 13th century, during his investigations into church governance.

Majority-rule winners can be determined from rankings by counting the number of voters who rated each candidate higher than another.

One disadvantage of majority-rule methods is they can all theoretically fail the participation criterion in constructed examples.

However, studies suggest this is empirically rare for modern Condorcet methods, like ranked pairs.

One study surveying 306 publicly-available election datasets found no examples of participation failures for methods in the ranked pairs-minimax family.

One real-life example of instant runoff failing the Condorcet criteria was the 2009 mayoral election of Burlington, Vermont.

Highest medians is a system in which the voter gives all candidates a rating out of a predetermined set (e.g. {"excellent", "good", "fair", "poor"}).