A Topological Proof of The Gibbard-Satterthwaite Theorem

TL;DR

This paper presents a novel topological proof of the Gibbard-Satterthwaite Theorem by constructing specific topological spaces and analyzing continuous mappings between them to establish the theorem's validity.

Contribution

It introduces a new topological approach to prove the Gibbard-Satterthwaite Theorem, offering a different perspective from traditional combinatorial proofs.

Findings

Topological spaces for preference profiles and outcomes are constructed.

Continuous mappings induced by social choice functions are analyzed.

The proof confirms the theorem using topological properties.

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.