Weakly unimodal domains, anti-exchange properties, and coalitional strategy-proofness of aggregation rules

It is shown that simple and coalitional strategy-proofness of an aggregation rule on any rich weakly unimodal domain of an idempotent interval space are equivalent properties if that space satisfies interval anti-exchange, a basic property also shared by a large class of convex geometries including–but not reducing to–trees and Euclidean convex spaces. Therefore, strategy-proof location problems in a vast class of networks fall under the scope of that proposition. It is also established that a much weaker minimalanti-exchangeproperty is necessary to ensure equivalence of simple and coalitional strategy-proofness in that setting. An immediate corollary to that result is that such equivalence fails to hold both in certain median interval spaces including those induced by bounded distributive lattices that are not chains, and in certain non-median interval spaces including those induced by partial cubes that are not trees. Thus, it turns out that anti-exchange properties of the relevant interval space provide a powerful general common principle that explains the varying relationship between simple and coalitional strategy-proofness of aggregation rules for rich weakly unimodal domains across different interval spaces, both median and non-median