Abstract
We generalize 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 facility to be sited. We show 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 (1985). We also give a polynomial algorithm for solving this nonlinear location problem.
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