## Why Same Party Candidates Seem So Similar

Continuing in the vein of solving maximization problems with graph or game theory models in class, an introduction to Hotelling’s Game is a good way to familiarize yourself with strategy in location competition and political stance alignment in politics.

Hotelling’s Game is a model which can be used to explain positioning strategy in spatial positioning games, where competition is based solely on location and not branding, etc. The natural applications of Hotelling’s Game model are in positioning of gas stations and fast food restaurants. The model explains why gas stations and fast food joints are usually positioned together in clumps. A simple explanation of the game is as follows: Imagine a boardwalk with endpoints (-1,1). Two food carts compete for position on the boardwalk where a cart gets all the customers, who are distributed uniformly from -1 to 1, closer to him than to the other cart and the point equidistant to the two carts is neglected. The first cart positioning itself at -1<k1<1 where k=/=0. If the second cart positions itself closer to 0 than k1, then it will get more customers since there will be more area on the boardwalk closer to it, so it picks -|k1|<k2<|k1|. If the first cart gets a chance to change its position, then it will similarly pick a point closer to 0 than k2 selecting -|k2|<k1<|k2|. The process repeats itself until k1 = k2 = 0, or if both carts are smart enough to realize 0 is the best spot from the beginning, then they select 0 as their first move.

A more interesting application of Hotelling’s Game is in politics, for which it can explain why constituents of the same party seem so similar. In a two party system, we can assume on a spectrum of leftist to rightists a bimodal distribution of citizens’ political inclinations. We’ll also assume that on the left the distribution is uniform and that on the right the distribution is uniform, with citizens voting for constituents closest to them on the spectrum. In a setup like this, it makes sense why there would be a sharp divide between parties but on either side there is a clumping of politicians who aim to perfectly capture the average citizen in their party.