A note on plurality distortion in large committees

Abstract

Simple plurality voting allows the somewhat surprising possibility that a majority of a committee or an electorate may prefer one of the defeated alternatives to the plurality winner. This paradox is distinct from Condorcet's paradox and has received less attention in the literature. Recently, however, the frequency of the Borda effect anticipated under different cultures has been computed and some empirical results have also been reported. Here results are obtained for both impartial and partial cultures using a class of Polya urn models. Emphasis is on asymptotic investigations and results valid for large committees.