Condorcet efficiency

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]

Efficiency of several voting systems with a spatial model and candidates distributed similarly to the 201 voters[1]
As candidates become more ideologically clustered relative to the voter distribution, some voting methods perform more poorly at finding the Condorcet winner.[1]

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.[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
  1. 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.
  2. 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.
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