| Part of the Politics and Economics series |
| Electoral systems |
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 Politicsportal  Economicsportal |
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. [1]
Among methods satisfying the majority criterion, Black's method gives the minimum power to the majority and hence the method is best at protecting minorities. [2]
Black's method satisfies the following criteria:
Black's method does not satisfy the following criteria:
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.
Independence of Smith-dominated alternatives is a voting system criterion which says that the winner of an election should not be affected by candidates who are not in the Smith set.
Strategic nomination refers to the entry of a candidate into an election with the intention of changing the ranking of other candidates. The name is an echo of ‘tactical voting’ and is intended to imply that it is the candidates rather than the voters who are seeking to manipulate the result in a manner unfaithful to voters’ true preferences.
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.
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.
Positional voting is a ranked voting electoral system in which the options or candidates receive points based on their rank position on each ballot and the one with the most points overall wins. The lower-ranked preference in any adjacent pair is generally of less value than the higher-ranked one. Although it may sometimes be weighted the same, it is never worth more. A valid progression of points or weightings may be chosen at will or it may form a mathematical sequence such as an arithmetic progression, a geometric one or a harmonic one. The set of weightings employed in an election heavily influences the rank ordering of the candidates. The steeper the initial decline in preference values with descending rank, the more polarised and less consensual the positional voting system becomes.
The Kemeny–Young method is an electoral system that uses ranked ballots and pairwise comparison counts to identify the most popular choices in an election. It is a Condorcet method because if there is a Condorcet winner, it will always be ranked as the most popular choice.
In social choice theory, the independence of (irrelevant) clones criterion says that adding a clone, i.e. a new candidate very similar to an already-existing candidate, should not spoil the results. It can be considered a very weak form of the independence of irrelevant alternatives (IIA) criterion.
The Borda method or order of merit is a positional voting rule which gives each candidate a number of points equal to the number of candidates ranked below them: the lowest-ranked candidate gets 0 points, the second-lowest gets 1 point, and so on. Once all votes have been counted, the option or candidate with the most points is 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.
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.
The sequential elimination methods are a class of voting systems that repeatedly eliminate the last-place finisher of another voting method until a single candidate remains. The method used to determine the loser is called the base method. Common are the two-round system, instant-runoff voting, and systems where parties nominate candidates in partisan primaries.