Condorcet efficiency: Difference between revisions
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[[File:Merrill 1984 Fig2d Condorcet Efficiency under Spatial-Model Assumptions (relative dispersion = 0.5).svg|thumb|350x350px|As candidates become more ideologically clustered relative to the voter distribution, some voting methods perform more poorly at finding the Condorcet winner.<ref name=":0" />]] |
[[File:Merrill 1984 Fig2d Condorcet Efficiency under Spatial-Model Assumptions (relative dispersion = 0.5).svg|thumb|350x350px|As candidates become more ideologically clustered relative to the voter distribution, some voting methods perform more poorly at finding the Condorcet winner.<ref name=":0" />]] |
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'''Condorcet efficiency''' is a measurement of the performance of [[Electoral system|voting methods]]. It is defined as the percentage of elections for which the [[Condorcet winner]] (the candidate who is preferred over all others in head-to-head races) is elected, provided there is one.<ref>{{Cite journal|last=Gehrlein|first=William V.|last2=Valognes|first2=Fabrice|date=2001-01-01|title=Condorcet efficiency: A preference for indifference|journal=Social Choice and Welfare|language=en|volume=18|issue=1|pages=193–205|doi=10.1007/s003550000071|issn=1432-217X}}</ref> |
'''Condorcet efficiency''' is a measurement of the performance of [[Electoral system|voting methods]]. It is defined as the percentage of elections for which the [[Condorcet winner]] (the candidate who is preferred over all others in head-to-head races) is elected, provided there is one.<ref>{{Cite journal|last=Gehrlein|first=William V.|last2=Valognes|first2=Fabrice|date=2001-01-01|title=Condorcet efficiency: A preference for indifference|journal=Social Choice and Welfare|language=en|volume=18|issue=1|pages=193–205|doi=10.1007/s003550000071|issn=1432-217X}}</ref><ref>{{Cite book|last=Gehrlein, William V.|url=https://www.worldcat.org/oclc/695387286|title=Voting paradoxes and group coherence : the condorcet efficiency of voting rules|date=2011|publisher=Springer|others=Lepelley, Dominique.|isbn=978-3-642-03107-6|location=Berlin|oclc=695387286}}</ref> |
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A voting method with 100% efficiency would always pick the Condorcet winner, when one exists, and a method that never chose the Condorcet winner would have 0% efficiency. The outcome of a referendum on policy can be efficient if the conditions of the [[Efficient Voter Rule|efficient voter rule]] are met.<ref>{{Cite journal|last=Anderson|first=David A.|date=2020|title=Environmental Exigencies and the Efficient Voter Rule|url=https://www.mdpi.com/2227-7099/8/4/100|journal=Economies|volume=8|issue=4|pages=7|doi=10.3390/economies8040100|doi-access=free}}</ref> |
A voting method with 100% efficiency would always pick the Condorcet winner, when one exists, and a method that never chose the Condorcet winner would have 0% efficiency. The outcome of a referendum on policy can be efficient if the conditions of the [[Efficient Voter Rule|efficient voter rule]] are met.<ref>{{Cite journal|last=Anderson|first=David A.|date=2020|title=Environmental Exigencies and the Efficient Voter Rule|url=https://www.mdpi.com/2227-7099/8/4/100|journal=Economies|volume=8|issue=4|pages=7|doi=10.3390/economies8040100|doi-access=free}}</ref> |
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Revision as of 05:34, 31 January 2021
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Condorcet efficiency is a measurement of the performance of voting methods. It is defined as the percentage of elections for which the Condorcet winner (the candidate who is preferred over all others in head-to-head races) is elected, provided there is one.[2][3]
A voting method with 100% efficiency would always pick the Condorcet winner, when one exists, and a method that never chose the Condorcet winner would have 0% efficiency. The outcome of a referendum on policy can be efficient if the conditions of the efficient voter rule are met.[4]
Efficiency is not only affected by the voting method, but is a function of the number of voters, number of candidates, and of any strategies used by the voters.[1]
It was initially developed in 1984 by Samuel Merrill III, along with Social utility efficiency.[1]
A related, generalized measure is Smith efficiency, which measures how often a voting method elects a candidate in the Smith set. Except in elections where the Smith set includes all candidates, Smith efficiency is a measure that can be used to differentiate between voting methods in all elections, because unlike the CW, the Smith set always exists. A 100% Smith-efficient method is guaranteed to be 100% Condorcet-efficient, and likewise with 0%.
References
- ^ a b c d Merrill, Samuel (1984). "A Comparison of Efficiency of Multicandidate Electoral Systems". American Journal of Political Science. 28 (1): 23–48. doi:10.2307/2110786. ISSN 0092-5853. JSTOR 2110786.
- ^ Gehrlein, William V.; Valognes, Fabrice (2001-01-01). "Condorcet efficiency: A preference for indifference". Social Choice and Welfare. 18 (1): 193–205. doi:10.1007/s003550000071. ISSN 1432-217X.
- ^ Gehrlein, William V. (2011). Voting paradoxes and group coherence : the condorcet efficiency of voting rules. Lepelley, Dominique. Berlin: Springer. ISBN 978-3-642-03107-6. OCLC 695387286.
- ^ Anderson, David A. (2020). "Environmental Exigencies and the Efficient Voter Rule". Economies. 8 (4): 7. doi:10.3390/economies8040100.
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