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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.
Copeland's method, also called Llull's method or round-robin voting, is a ranked-choice voting system based on scoring pairwise wins and losses.
The Smith set, also known as the top cycle, is a concept from the theory of electoral systems that generalizes the Condorcet winner to cases where no such winner exists, by allowing cycles of candidates to be treated jointly as if they were a single Condorcet winner. Named after John H. Smith, the Smith set is the smallest non-empty set of candidates in a particular election, such that each member defeats every candidate outside the set in a pairwise election. The Smith set provides one standard of optimal choice for an election outcome. Voting systems that always elect a candidate from the Smith set pass the Smith criterion.
Ranked pairs, sometimes called the Tideman method, 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 rule developed by Markus Schulze that selects a using ranked ballots. It is also known as the beatpath method or Schwartz sequential dropping (SSD). The Schulze method is a Condorcet method, which means if there is a candidate who is preferred by a majority over every other candidate in pairwise comparisons, then this candidate will be the winner when the Schulze method is applied.
In an election, a candidate is called a Condorcet, beats-all, or majority-rule winner if more than half of voters would support them in any one-on-one matchup with another candidate. Such a candidate is also called an undefeated, or tournament champion, by analogy with round-robin tournaments. Voting systems where a majority-rule winner will always win the election are said to satisfy the Condorcetcriterion. Condorcet voting methods 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.
A voting system satisfies join-consistency if combining two sets of votes, both electing A over B, always results in a combined electorate that ranks A over B. It is a stronger form of the participation criterion, which only requires join-consistency when one of the sets of votes unanimously prefers A over B.
The mutual majority criterion, also known as majority for solid coalitions or the generalized majority criterion, is a voting system criterion that says that if a majority of voters ranks a certain group of candidates at the top of their ballot, then one of these candidates should win the election.
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.
Reversal symmetry is a voting system criterion which requires that if candidate A is the unique winner, and each voter's individual preferences are inverted, then A must not be elected. Methods that satisfy reversal symmetry include Borda count, ranked pairs, Kemeny–Young method, and Schulze method. Methods that fail include Bucklin voting, instant-runoff voting and Condorcet methods that fail the Condorcet loser criterion such as Minimax.
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.
The later-no-harm criterion is a voting system criterion first formulated by Douglas Woodall. Woodall defined the criterion by saying that "[a]dding a later preference to a ballot should not harm any candidate already listed." For example, a ranked voting method in which a voter adding a 3rd preference could reduce the likelihood of their 1st preference being selected, fails later-no-harm.
In voting systems theory, the independence of clones criterion measures an election method's robustness to strategic nomination. Nicolaus Tideman was the first to formulate this criterion, which states that the winner must not change due to the addition of a non-winning candidate who is similar to a candidate already present. It is a relative criterion: it states how changing an election should or shouldn't affect the outcome.
The term ranked voting, also known as preferential voting or ranked-choice voting, pertains to any voting system where voters indicate a rank to order candidates or options—in a sequence from first, second, third, and onwards—on their ballots. Ranked voting systems vary based on the ballot marking process, how preferences are tabulated and counted, the number of seats available for election, and whether voters are allowed to rank candidates equally.
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.
Round-robin voting refers to a set of ranked voting systems that elect winners by comparing all candidates in a round-robin tournament. Every candidate is matched up against every other candidate, where their point total is equal to the number of votes they receive; the method then selects a winner based on the results of these paired matchups.
References
- ↑ Woodall, Douglas (December 1994). "Properties of Preferential Election Rules, Voting matters - Issue 3, December 1994".
- ↑ Fishburn, Peter C.; Brams, Steven J. (1983-01-01). "Paradoxes of Preferential Voting". Mathematics Magazine. 56 (4): 207–214. doi:10.2307/2689808. JSTOR 2689808.
- 1 2 3 Moulin, Hervé (1988-06-01). "Condorcet's principle implies the no show paradox". Journal of Economic Theory. 45 (1): 53–64. doi:10.1016/0022-0531(88)90253-0.
- 1 2 3 Brandt, Felix; Geist, Christian; Peters, Dominik (2016-01-01). "Optimal Bounds for the No-Show Paradox via SAT Solving". Proceedings of the 2016 International Conference on Autonomous Agents & Multiagent Systems. AAMAS '16. Richland, SC: International Foundation for Autonomous Agents and Multiagent Systems: 314–322. arXiv: 1602.08063 . ISBN 9781450342391.
- ↑ Markus Schulze (1998-06-12). "Regretted Turnout. Insincere = ranking" . Retrieved 2011-05-14.
- ↑ Pérez, Joaquı´n (2001-07-01). "The Strong No Show Paradoxes are a common flaw in Condorcet voting correspondences". Social Choice and Welfare. 18 (3): 601–616. CiteSeerX 10.1.1.200.6444 . doi:10.1007/s003550000079. ISSN 0176-1714. S2CID 153489135.
- ↑ Jimeno, José L.; Pérez, Joaquín; García, Estefanía (2009-01-09). "An extension of the Moulin No Show Paradox for voting correspondences". Social Choice and Welfare. 33 (3): 343–359. doi:10.1007/s00355-008-0360-6. ISSN 0176-1714. S2CID 30549097.
- ↑ Duddy, Conal (2013-11-29). "Condorcet's principle and the strong no-show paradoxes". Theory and Decision. 77 (2): 275–285. doi: 10.1007/s11238-013-9401-4 . hdl: 10379/11267 . ISSN 0040-5833.
- ↑ Sanver, M. Remzi; Zwicker, William S. (2009-08-20). "One-way monotonicity as a form of strategy-proofness". International Journal of Game Theory. 38 (4): 553–574. doi:10.1007/s00182-009-0170-9. ISSN 0020-7276. S2CID 29563457.