A Topological Proof of The Gibbard-Satterthwaite Theorem
Theoretical Economics
2023-09-07 v1 Algebraic Topology
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.
Keywords
Cite
@article{arxiv.2309.03123,
title = {A Topological Proof of The Gibbard-Satterthwaite Theorem},
author = {Yuliy Baryshnikov and Joseph Root},
journal= {arXiv preprint arXiv:2309.03123},
year = {2023}
}