Condorcet loser criterion

In single-winner voting system theory, the Condorcet loser criterion (CLC) is a measure for differentiating voting systems. It implies the majority loser criterion.

A voting system complying with the Condorcet loser criterion will never allow a Condorcet loser to win. A Condorcet loser is a candidate who can be defeated in a head-to-head competition against each other candidate.[1] (Not all elections will have a Condorcet loser since it is possible for three or more candidates to be mutually defeatable in different head-to-head competitions.)

A slightly weaker (easier to pass) version is the majority Condorcet loser criterion (MCLC), which requires that a candidate who can be defeated by a majority in a head-to-head competition against each other candidate, lose. It is possible for a system, such as Majority Judgment, which allows voters not to state a preference between two candidates, to pass the MCLC but not the CLC.[citation needed]

The Smith criterion implies the Condorcet loser criterion, because no candidate in the Smith set can lose a head-to-head matchup against a candidate not in the Smith set.

Compliant methods include: two-round system, instant-runoff voting (AV), contingent vote, borda count, Schulze method, ranked pairs, and Kemeny-Young method. Any voting method that ends in a runoff passes the criterion, so long as all voters are able to express their preferences in that runoff i.e. STAR voting passes only when voters can always indicate their ranked preference in their scores; if there are more than 6 candidates, then this is impossible.

Noncompliant methods include: plurality voting, supplementary voting, Sri Lankan contingent voting, approval voting, range voting, Bucklin voting and minimax Condorcet.