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A Topological Proof of The Gibbard-Satterthwaite Theorem (2309.03123v1)
Published 6 Sep 2023 in econ.TH and math.AT
Abstract: We give a new proof of the Gibbard-Satterthwaite Theorem. We construct two topological spaces: one for the space of preference profiles and another for the space of outcomes. We show that social choice functions induce continuous mappings between the two spaces. By studying the properties of this mapping, we prove the theorem.