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][3][4]

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.^{[citation needed]} 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%.

See also

• Social utility efficiency
• Comparison of electoral systems