IJPAM: Volume 47, No. 4 (2008)


S. Gikiri Thuo
Department of Mathematics
Florida A&M University
Tallahassee, FL 32307, USA
e-mail: gikiri.thuo@famu.edu

Abstract.This paper analyzes the proximity spatial models for cumulative voting. We will identify conditions necessary for a symmetric equilibrium to exist when voters' ideal points have a standard normal distribution. We will show, through a proposition and proving it, that under a cumulative voting heuristic, candidates tend to adopt centrifugal positions, away from the median voter. With this in mind, we will place two candidates away from the median, on the opposite sides and investigate conditions necessary for a symmetric equilibrium to exist. We will accomplish this by placing a third candidate within an $\epsilon$ neighborhood of either one of the other two candidates. From this analysis, we will develop an equation whose solutions provide the only possibility for a symmetric equilibrium to exist. Using optimization techniques, see Kushner et al [#!kushner!#] and Thuo [#!thuo!#], we will approximate those solutions by a nice elementary function whose properties we know.

Received: August 13, 2008

AMS Subject Classification: 91B12

Key Words and Phrases: spatial models, optimization, cumulative voting, equilibrium

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 47
Issue: 4