Asymptotic properties of the paths in a specific voting model (Q1087453)

This paper considers the majority rule game played by two candidates on an m-dimensional Euclidean issue space, with \(2n+1\) voters. Voters measure disutility as distance from their ideal points. Candidates, who also have ideal points, respond to rivals' platforms by adopting the winning platform closest to their own ideal point. Let \((a_ n,b_ n)\) be a sequence of such alternating best responses. The main result is the existence and characterization of the limits of such sequences \((a^*,b^*)\). In particular, every winning path approaches a two- cycle, with n voters arrayed on each side of a median of \(a^*\) and \(b^*\). In general, this cycle can be outside the Pareto set.