Condorcet method: Difference between revisions

Each voter fills out a [[preferential voting|ranked ballot]]. or [[Cardinal voting|rated ballot]]. The voter can include less than all candidates under consideration. Usually when a candidate ''is not listed'' on the voter's ballot they are considered less preferred than listed candidates, and ranked accordingly. However, some variations allow a "no opinion" default option where no for- or against- preference is counted for that candidate. Write-ins are possible, but are somewhat more difficult to implement for automatic counting than in other election methods. This is a counting issue, but results in the frequent omission of the write-in option in ballot software.

Ballots are counted by considering all possible sets of two-candidate elections from all available candidates. That is, each candidate is considered against each and every other candidate. A candidate is considered to "win" against another on a single ballot and receive that ballot's vote in the matchup against their opponent if they are ranked or rated higher than their opponent. All the votes for candidate Alice over candidate Bob are counted, as are all of the votes for Bob over Alice. Whoever has the most votes in each one-on-one election wins.

If a candidate is preferred over all other candidates, that candidate is the [[Condorcet Criterionwinner|Condorcet candidate]] (Condorcet winner). However, a Condorcet candidate may not exist, due to a fundamental [[Voting paradox|paradox]]: It is possible for the electorate to prefer A over B, B over C, and C over A simultaneously. This is called a majority rule cycle or Condorcet cycle, and it must be resolved by some other mechanism.