Some multivariate problems of a spatial model of voting under majority rule

Abstract

This dissertation is concerned with a number of outstanding problems in the analysis of collective decision-making. More specifically, we specify the mathematical foundation for a spatial model of voting under majority rule, and, building upon that foundation, we make three contributions to the formal theory of public choice.

First, we formulate a spatial model in which voters are heterogeneous both with respect to their most preferred social states and the manner in which they measure loss relative to their preferences, and within the structure of this model we identify various optimal strategies for the candidates for office.

Second, we show that all existing spatial models which purport to encompass voting abstentions by citizens who are alienated from the candidates are either mathematically inaccurate or else they include interpersonal comparisons of utility by the electorate.

Finally, we show that the set of optimal strategies for a candidate is invariant with respect to any one of seven objective functions which he may be attempting to maximize. This result is dependent upon the utilization of the family of Dirichlet distributions to model the joint distribution of the estimated proportions of the vote which the candidates will receive.