The Condorcet efficiency of approval voting and the probability of electing the Condorcet loser

Abstract

The Condorcet winner in an election is an alternative that would defeat each of the other alternatives in a series of pairwise elections. The Condorcet efficiency of a voting rule is the conditional probability that the voting rule will elect the Condorcet winner, given that a Condorcet winner exists. The paper assumes the impartial culture condition for large electorates and shows that approval voting has greater Condorcet efficiency than plurality rule, and that it has smaller Condorcet efficiency than the voting rule in which voters must vote for half of the available alternatives. The likelihood that election rules select the Condorcet loser is also considered.