Distance weighted voting and a single facility location problem

The paper generalizes the notion of a Condorcet point of a network by allowing an individual’s vote to be weighted by an integral power of his/her distance from a facilty to be sited. It shows that on a tree network this ‘generalized’ Condorcet point coincides with the solution of a certain nonlinear single facility location problem. This result may be viewed as a generalization of an earlier result due to Hansen and Thisse. The paper also gives a polynomial algorithm for solving this nonlinear location problem.