Strategy-proof Location on a Network
We consider rules that choose a location on a graph (e.g. a network of roads) based on the report of agents' symmetric, single-peaked preferences over points on that graph. We show that while a strategy-poof, onto rule is not necessarily dictatorial, the existence of a cycle on the graph grants one agent a certain amount of decisive power. This result surprisingly characterizes the class of strategy-proof, onto rules both in terms of a certain subclass of such rules for trees and in terms of a parameterized set of generalized median voter schemes.
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