Searching for Optimal Positions through Directional Data in a Political Competition Model

Abstract

This paper considers an application of directional data to political science. A model is presented in which the political preferences of the type of voters of a population are represented as points of the circumference unit with the political parties searching for optimal positions on this in order to gain the most support of that finite set of voter types. Strategies have been developed to search for optimal positions in the case of one party and Nash equilibrium positions are found in the game with two parties. The results reveal how the different parties redirect their stances to adapt to changing situations generated by economic or social circumstances affecting citizen preferences.