Simple Majority Voting, Game Theory, and Resource Use

Abstract

I propose in this paper to examine majority voting with the tools of elementary game theory. This, in itself, represents nothing new. The “majority game” has been analysed by numerous game theorists. I propose, however, to derive certain implications from the analysis for the utilization of resources in the public or collective sector of the economy.The models of collective decision-making that must be employed are necessarily abstract; so much so that the analyses may seem to appear to some observers as caricatures of actual political processes. Analysis must start somewhere, however, and even the most abstract of models, by isolating specific features of real-world institutions, may prove helpful to our over-all understanding. I shall introduce a model of pure democracy. That is to say, I shall assume that all collective decisions are to be made by a simple majority voting process in which all citizens participate. All problems of representation, leadership, parties, and coalitions shall be left out of account. Furthermore, I shall assume that the individual citizens in the model are motivated by utility-maximizing considerations; that is, each individual is assumed to vote in such a manner as to maximize his own utility. This assumption allows numerical values to be placed in the expected pay-offs that individuals receive through political processes. If the expected pay-offs can be numerically correlated with observable economic quantities or magnitudes, some provisional and tentative implications may be drawn concerning the tendency of majority voting rules to “over-extend” or to “starve” the public sector of the economy relative to the private sector.