The Banzhaf Index for Multicandidate Presidential Elections

Abstract

John Banzhaf III [Villanova Law Rev., 13 (1968), pp. 304–332] introduced a measure of voting power for a two-candidate United States presidential election conducted under an electoral college system. This measure indicated that an individual voter in a large state has more voting power than an individual in a small state. In this paper we generalize the Banzhaf index of voting power to voting situations in which there are more than two candidates with one to be elected. We then measure the voting power of an individual voter in a three-candidate and in a four-candidate presidential election under an electoral college system. It is found that there is slightly more bias in favor of an individual in a large state. In the last section, we conjecture what the results will be for an r-candidate United States presidential election.