Condorcet efficiency

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]

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][4]

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.[5]

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%.

## See also

* Social utility efficiency
* Comparison of electoral systems

## References

1. ↑ 1.0 1.1 1.2 1.3 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.
2. ↑ Gehrlein, William V.; Valognes, Fabrice (2001-01-01). "Condorcet efficiency: A preference for indifference" (in en). Social Choice and Welfare 18 (1): 193–205. doi:10.1007/s003550000071. ISSN 1432-217X.
3. ↑ Merrill, Samuel (1985). "A statistical model for Condorcet efficiency based on simulation under spatial model assumptions" (in en). Public Choice 47 (2): 389–403. doi:10.1007/BF00127534. ISSN 0048-5829. http://link.springer.com/10.1007/BF00127534.
4. ↑ 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. https://www.worldcat.org/oclc/695387286.
5. ↑ Anderson, David A. (2020). "Environmental Exigencies and the Efficient Voter Rule". Economies 8 (4): 7. doi:10.3390/economies8040100.

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