The vulnerability of four social choice functions to coalitional manipulation of preferences (Q1331066)

Consider a group of \(n\) voters voting over a set of three alternatives. Each voter can have any strong ordering over the three alternatives. Four voting rules are considered: plurality, anti-plurality, plurality with a runoff, and anti-plurality with a runoff. This remarkable paper computes exactly how often a configuration fails to be a strong equilibrium (and so can be manipulated by strategic voting on the part of some coalition). The limits as \(n\) goes to infinity are especially revealing. Plurality with a runoff (as in French presidential elections) does best -- only 11\% of the time is it manipulable. Anti-plurality does worst, being manipulable over 51\% of the time.