Approval voting is an electoral system in which voters can select any number of candidates instead of selecting only one.
A Condorcet method is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, whenever there is such a candidate. A candidate with this property, the pairwise champion or beats-all winner, is formally called the Condorcet winner. The head-to-head elections need not be done separately; a voter's choice within any given pair can be determined from the ranking.
Coombs' method or the Coombs rule is a ranked voting system, created by Clyde Coombs, which uses a ballot counting method for ranked voting. Coombs' method can be thought of as a cross between instant-runoff voting and anti-plurality voting.
The Copeland or Llull method is a ranked-choice voting system based on counting each candidate's pairwise wins and losses.
Ranked Pairs (RP) is a tournament-style system of ranked-choice voting first proposed by Nicolaus Tideman in 1987.
The Schulze method is a single winner ranked-choice voting rule developed by Markus Schulze. It is also known as the beatpath method. The Schulze method is a Condorcet method, which means it will elect a majority-choice candidate if one exists; in other words, if most people rank A above B, A will defeat B.
In an election, a candidate is called a Condorcet, beats-all, or majority winner if a majority of voters would support them in a race against any other candidate. Such a candidate is also called an undefeated or tournament champion. Voting systems in which a majority-rule winner will always win the election are said to satisfy the majority-rule principle, also called the Condorcet criterion. Methods that satisfy this criterion extend majority rule to elections with more than one candidate.
The Smith criterion is a voting system criterion that formalizes the concept of a majority rule. A voting system satisfies the Smith criterion if it always elects a candidate from the Smith set, which generalizes the idea of a "Condorcet winner" to cases where there may be cycles or ties, by allowing for several who together can be thought of as being "Condorcet winners." A Smith method will always elect a candidate from the Smith set.
The participation criterion, also called vote or population monotonicity, is a voting system criterion that says that a candidate should never lose an election as a result of receiving too many votes in support. It says that adding a voter who prefers Alice to Bob should not cause Alice to lose the election to Bob.
The majority favorite or absolute majority criterion is a voting system criterion. The criterion states that "if only one candidate is ranked first by a majority of voters, then that candidate must win." It is sometimes referred to simply as the majority criterion, but this term is more often used to refer to Condorcet's majority-rule principle.
The mutual majority criterion is a criterion for evaluating electoral system. It requires that whenever a majority of voters prefer a group of candidates above all others, someone from that group must win. It is the single-winner case of Droop-Proportionality for Solid Coalitions.
The Borda count electoral system can be combined with an instant-runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method. Both methods are designed to satisfy the Condorcet criterion, and allow for incomplete ballots and equal rankings.
In single-winner voting system theory, the Condorcet loser criterion (CLC) is a measure for differentiating voting systems. It implies the majority loser criterion but does not imply the Condorcet winner criterion.
In voting systems, the Minimax Condorcet method is a single-winner ranked-choice voting method that always elects the majority (Condorcet) winner. Minimax compares all candidates against each other in a round-robin tournament, then ranks candidates by their worst election result. The candidate with the largest (maximum) number of votes in their worst (minimum) matchup is declared the winner.
The summability criterion is a voting system criterion, used to objectively compare electoral systems. The criterion states:
The majority loser criterion is a criterion to evaluate single-winner voting systems. The criterion states that if a majority of voters prefers every other candidate over a given candidate, then that candidate must not win.
There are a number of different criteria which can be used for voting systems in an election:
The later-no-help criterion is a voting system criterion formulated by Douglas Woodall. The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less-preferred candidate can not cause a more-preferred candidate to win. Voting systems that fail the later-no-help criterion are vulnerable to the tactical voting strategy called mischief voting, which can deny victory to a sincere Condorcet winner.
Black's method is an election method proposed by Duncan Black in 1958 as a compromise between the Condorcet method and the Borda count. This method selects a Condorcet winner. If a Condorcet winner does not exist, then the candidate with the highest Borda score is selected.
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