Condorcet winner criterion: Difference between revisions
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[[Approval voting]], [[Range voting]], [[Borda count]], [[plurality voting]], and [[instant-runoff voting]] do not comply with the Condorcet Criterion. However, any voting method that collects enough information to detect pairwise preferences (i.e. scoring or ranking methods) can be "forced" to comply with the Condorcet criterion by automatically electing the Condorcet winner if one exists (or alternatively, eliminating all candidates not in the Smith Set) before doing anything else.
== Occurrences in real elections ==
Most real elections have a Condorcet winner. Andrew Myers, who operates the [[online poll|Condorcet Internet Voting Service]], found that 83% of the nonpolitical CIVS elections with at least 10 votes had a Condorcet winner, with the figure rising to 98.8% for elections with at least 300 votes.<ref name="CIVS">{{cite conference |url=https://www.cs.cornell.edu/andru/papers/civs24/ |title=The Frequency of Condorcet Winners in Real Non-Political Elections |last=Myers |first=A. C. |author-link=https://www.cs.cornell.edu/andru/ |date=March 2024 |conference=61st Public Choice Society Conference}}</ref>
A database of 189 ranked United States election from 2004 to 2022 contained only one Condorcet cycle: the [[2021 Minneapolis Ward 2 city council election]].<ref name="GSM2023">{{cite arXiv | last=Graham-Squire | first=Adam | last2=McCune | first2=David | title=An Examination of Ranked Choice Voting in the United States, 2004-2022 |eprint=2301.12075v2 | date=2023-01-28 | class=econ.GN}}</ref> While this indicates a very high rate of Condorcet winners, it's possible that some of the effect is due to general [[two-party domination]].
==Commentary==
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===Equilibrium point for various voting methods===
The
An example for [[Approval voting]]:
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31: C>B|>A
B is the CW. If voters approve everyone they ranked before the "|", then B is approved by all voters, and wins. If any of the three groups of voters here raises their approval threshold (only approves their 1st choice), then another group has an incentive to maintain their approval threshold where it is i.e. if C-top voters stop approving B, then the 69 voters who prefer B>C have an incentive to move their approval thresholds between B and C to ensure B is approved by a majority and C is not. Note that this requires both accurate polling and coordinated [[Strategic voting|strategic voting]].
===Non-complying methods===
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In this case, B is preferred to A by 501 votes to 499, and B is
preferred to C by 502 to 498, hence B is preferred to both A and C. So according to the Condorcet criteria, B should win. By contrast, according to the rules of IRV, B is ranked first by the fewest voters and is eliminated, and C wins with the transferred voted from B; in plurality voting A wins with the most first choices. Note that B and C are a [[Mutual majority criterion|mutual majority]], so most majority rule-based methods would rule A out of winning. If A drops out, then B becomes the majority's 1st choice; so this is an example of IRV failing [[Independence of irrelevant alternatives|independence of irrelevant alternatives]].▼
▲according to the Condorcet criteria, B should win. By contrast, according to the rules of IRV, B is ranked first by the fewest voters and is eliminated, and C wins with the transferred voted from B; in plurality voting A wins with the most first choices. Note that B and C are a [[Mutual majority criterion|mutual majority]], so most majority rule-based methods would rule A out of winning. If A drops out, then B becomes the majority's 1st choice; so this is an example of IRV failing [[Independence of irrelevant alternatives|independence of irrelevant alternatives]].
See [[Score voting#Majority-related criteria]] to see how Score can fail the Condorcet criterion. In general however, it is expected that the Condorcet winner (and Smith Set candidates in general) will
===Independence of Irrelevant Alternatives===
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===Alternative definitions===
The [[tied at the top]] rule redefines the Condorcet beat relation so that methods using it can pass Condorcet whenever there are no equal-rank, and in addition passes the [[favorite betrayal criterion]]. Doing so in effect trades some Condorcet winner compliance for FBC compliance.
[[Category:Voting system criteria]]
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