Condorcet efficiency
File:Merrill 1984 Fig2c Condorcet Efficiency under Spatial-Model Assumptions (relative dispersion = 1.0).svg and candidates distributed similarly to the 201 voters]]
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.{{Cite journal|last1=Gehrlein|first1=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|s2cid=10493112|issn=1432-217X}}{{Cite journal|last=Merrill|first=Samuel|date=1985|title=A statistical model for Condorcet efficiency based on simulation under spatial model assumptions|url=http://link.springer.com/10.1007/BF00127534|journal=Public Choice|language=en|volume=47|issue=2|pages=389–403|doi=10.1007/BF00127534|s2cid=153922166|issn=0048-5829|via=|url-access=subscription}}{{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}}
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.
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.{{Cite journal|last=Merrill|first=Samuel|author-link=Samuel Merrill III|date=1984|title=A Comparison of Efficiency of Multicandidate Electoral Systems|journal=American Journal of Political Science|volume=28|issue=1|pages=23–48|doi=10.2307/2110786|issn=0092-5853|jstor=2110786}}
It was initially developed in 1984 by Samuel Merrill III, along with social utility efficiency.
A related, generalized measure is Smith efficiency, which measures how often a voting method elects a candidate in the Smith set.{{Citation needed|date=February 2024}} Smith efficiency can be used to differentiate between voting methods across all elections, because unlike the Condorcet winner, the Smith set always exists. A 100% Smith-efficient method is guaranteed to be 100% Condorcet-efficient, and likewise with 0%.