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.
The Copeland or Llull method is a ranked-choice voting system based on counting each candidate's pairwise wins and losses.
The Smith or Schwartz set, sometimes called the top-cycle, generalizes the idea of a Condorcet winner to cases where no such winner exists. It does so by allowing cycles of candidates to be treated jointly, as if they were a single Condorcet winner.
Bucklin voting is a class of voting methods that can be used for single-member and multi-member districts. As in highest median rules like the majority judgment, the Bucklin winner will be one of the candidates with the highest median ranking or rating. It is named after its original promoter, the Georgist politician James W. Bucklin of Grand Junction, Colorado, and is also known as the Grand Junction system.
Ranked Pairs (RP) is a tournament-style system of ranked 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 majority winner or majority-preferred candidate if more than half of all voters would support them in a one-on-one race against any one of their opponents. Voting systems where a majority winner will always win are said to satisfy the majority-rule principle, because they extend the principle of majority rule to elections with multiple candidates.
In political science and social choice theory, Black'smedian voter theorem states that if voters and candidates are distributed along a one-dimensional spectrum and voters have single peaked preferences, any voting method that is compatible with majority-rule will elect the candidate preferred by the median voter. The median voter theorem thus shows that under a realistic model of voter behavior, Arrow's theorem does not apply, and rational social choice is in fact possible if using a Condorcet method.
The majority favorite criterion is a voting system criterion that says that, if a candidate would win more than half the vote in a first-preference plurality election, that candidate should win. Equivalently, if only one candidate is ranked first by a over 50% of voters, that candidate must win. It is occasionally referred to simply as the "majority criterion", but this term is more often used to refer to Condorcet's majority-rule principle.
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.
Instant-runoff voting (IRV), also known as ranked-choice voting (RCV), preferential voting (PV), or the alternative vote (AV), is a multi-round elimination method where the loser of each round is determined by the first-past-the-post method. In academic contexts, the term instant-runoff voting is generally preferred as it does not run the risk of conflating the method with methods of ranked voting in general.
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.
Majority judgment (MJ) is a single-winner voting system proposed in 2010 by Michel Balinski and Rida Laraki. It is a kind of highest median rule, a cardinal voting system that elects the candidate with the highest median rating.
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.
A major branch of social choice theory is devoted to the comparison of electoral systems, otherwise known as social choice functions. Viewed from the perspective of political science, electoral systems are rules for conducting elections and determining winners from the ballots cast. From the perspective of economics, mathematics, and philosophy, a social choice function is a mathematical function that determines how a society should make choices, given a collection of individual preferences.
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.
