In this brief note it is demonstrated that if all the conditions for the existence of a competitive equilibrium are satisfied, then simple majority voting to determine the distribution of goods may be less efficient than a price system.

The argument here may be somewhat cryptic for those not familiar with the work of Anthony Downs. A considerably more discursive presentation of the background material is given in “A Two Party System, General Equilibrium and the Voters' Paradox.” The tax and public goods aspect of the voting problem have been discussed elsewhere in “Notes on the Taxonomy of Problems Concerning Public Goods.” The result presented here, nevertheless, stands by itself, hence is presented in this brief form.

The political system is modeled at its simplest. We assume the existence of two players called “political parties.” The goal of each player is to win an election by as large a vote as possible. A strategy for each player is to name a policy that it will carry out if it is elected. A policy is any point in the set of feasible distributions of final product. It follows immediately that, although any policy may be considered as a strategy, any non-Pareto optimal policies are dominated by some policy that is optimal. A discussion of the reasons for modeling a party in this simple manner is given in detail elsewhere. It is assumed that all voters are passive or “mechanistic,” i.e., they do not form groups but merely vote individually, selecting optimally between the two policies offered.