Approval voting is a single-winner electoral system where each voter may select ("approve") any number of candidates. The winner is the most-approved candidate.
A Condorcet method is one of several election methods that elects the candidate that wins a majority of the vote in every head-to-head election against each of the other candidates, that is, a candidate preferred by more voters than any others, whenever there is such a candidate. A candidate with this property, the pairwise champion or beats-all winner, is formally called the Condorcet winner. Note that the head-to-head elections aren't necessarily done separately; a voter's preference between every pair of candidates can be found by asking them to rank the candidates, and then assuming they would vote for the candidate they ranked higher for each pairing.
Independence of Smith-dominated alternatives is a voting system criterion defined such that its satisfaction by a voting system occurs when the selection of the winner is independent of candidates who are not within the Smith set.
Ranked pairs (RP) or the Tideman method is an electoral system developed in 1987 by Nicolaus Tideman that selects a single winner using votes that express preferences. RP can also be used to create a sorted list of winners.
An electoral system satisfies the Condorcet criterion if it always chooses the Condorcet winner when one exists. Any voting method conforming to the Condorcet criterion is known as a Condorcet method. The Condorcet winner is the person who would win a two-candidate election against each of the other candidates in a plurality vote. For a set of candidates, the Condorcet winner is always the same regardless of the voting system in question, and can be discovered by using pairwise counting on voters' ranked preferences.
The Smith criterion is a voting systems criterion defined such that it's satisfied when a voting system always elects a candidate that is in the Smith set, which is the smallest non-empty subset of the candidates such that every candidate in the subset is majority-preferred over every candidate not in the subset. The Smith set is named for mathematician John H Smith, whose version of the Condorcet criterion is actually stronger than that defined above for social welfare functions. Benjamin Ward was probably the first to write about this set, which he called the "majority set".
The participation criterion is a voting system criterion. Voting systems that fail the participation criterion are said to exhibit the no show paradox and allow a particularly unusual strategy of tactical voting: abstaining from an election can help a voter's preferred choice win. The criterion has been defined as follows:
The majority criterion is a single-winner voting system criterion, used to compare such systems. The criterion states that "if one candidate is ranked first by a majority of voters, then that candidate must win".
The mutual majority criterion is a criterion used to compare voting systems. It is also known as the majority criterion for solid coalitions and the generalized majority criterion. The criterion states that if there is a subset S of the candidates, such that more than half of the voters strictly prefer every member of S to every candidate outside of S, this majority voting sincerely, the winner must come from S. This is similar to but stricter than the majority criterion, where the requirement applies only to the case that S contains a single candidate. This is also stricter than the majority loser criterion, where the requirement applies only to the case that S contains all but one candidate. The mutual majority criterion is the single-winner case of the Droop proportionality criterion.
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.
In voting systems, the minimax method is one of several Condorcet methods used for tabulating votes and determining a winner when using ranked voting in a single-winner election. It is also known as the Simpson–Kramer method, and the successive reversal method.
Resolvability criterion can refer to any voting system criterion that ensures a low possibility of tie votes.
The later-no-harm 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 lose. Voting systems that fail the later-no-harm criterion are vulnerable to the tactical voting strategy called bullet voting, which can deny victory to a sincere Condorcet winner.
Condorcet is a commune in the Drôme department in the Auvergne-Rhône-Alpes region in southeastern France.
The Borda count is a family of single-winner election methods in which voters rank options or candidates in order of preference. The Borda count determines the outcome of a debate or the winner of an election by giving each candidate, for each ballot, a number of points corresponding to the number of candidates ranked lower. Once all votes have been counted the option or candidate with the most points is the winner. The Borda count is intended to elect broadly acceptable options or candidates, rather than those preferred by a majority, and so is often described as a consensus-based voting system rather than a majoritarian one.
Instant-runoff voting (IRV) is a type of ranked preferential voting method used in single-seat elections with more than two candidates. Instead of indicating support for only one candidate, voters in IRV elections can rank the candidates in order of preference. Ballots are initially counted for each voter's top choice. If a candidate has more than half of the vote based on first-choices, that candidate wins. If not, then the candidate with the fewest votes is eliminated. The voters who selected the defeated candidate as a first choice then have their votes added to the totals of their next choice. This process continues until a candidate has more than half of the votes. When the field is reduced to two, it has become an "instant runoff" that allows a comparison of the top two candidates head-to-head. Compared to plurality voting, IRV can reduce the effect of vote-splitting when multiple candidates earn support from like-minded voters.
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 2007 by Michel Balinski and Rida Laraki. Unlike other voting methods, MJ guarantees that the winner between three or more candidates will be the candidate who had received an absolute majority of the highest grades given by all the voters.
Electoral systems are the rules for conducting elections. Comparisons between different systems can focus on different aspects: on suffrage or rules for voter eligibility; on candidate eligibility and the rules governing political parties; on the way elections are scheduled, sequenced, and combined; or on the rules for determining the winner within a given election.
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