A Theorem About Voting

Abstract

The objective of this essay is to present a simple decision-theoretic model of individual rational voting in a single-member district, using the simple-majority single-ballot system of election, and to derive the following theorem from the model: The rational voter votes for the candidate (party) associated with the outcome he (the voter) most prefers.The model and theorem may interest students of voting for at least two reasons. First, the theorem contradicts the classical argument that “there is one eventuality in a multiparty system that does not arise in a two-party system: a rational voter may at times vote for a party other than the one he most prefers.” The theorem asserts, by contrast, that what is true for the two-party case is also true for the multi-party case. Thus, the model and theorem sharply differ from the classical theory of party systems. The ramifications of this conflict may affect some conventional views about the decline of third parties, the differences between two-party and multi-party systems, as well as (perhaps) other topics.