Voting Equilibria in Multidimensional Choice Spaces

This paper examines necessary and sufficient conditions for the existence of voting equilibria over a multidimensional issue space, following the lead of the seminal work of Davis and Hinich (Davis, O. A., M. J. Hinich. 1966. A mathematical model of policy formation in a democratic society. J. Bernard, ed. Mathematical Applications in Political Science II. Southern Methodist University Press, Dallas, 175–208.) and Plott (Plott, C. R. 1967. A notion of equilibrium and its possibility under majority rule. Amer. Econom. Rev.57 787–806.). We assume a finite number of voters who vote among alternatives located in an m-dimensional vector space and that the voters vote according to their preferences defined over the space. Here, we generalize and strengthen many of the existing theorems to deal with global rather than local equilibria and plurality as opposed to majority voting rules.