A topological proof of Terao's generalized Arrow's Impossibility Theorem

TL;DR

This paper offers a new proof of Terao's generalized Arrow's Impossibility Theorem by applying algebraic topology, providing a different perspective from the original combinatorial approach.

Contribution

It introduces an algebraic topology-based proof for Terao's generalized Arrow's Impossibility Theorem, expanding the methodological toolkit for social choice theory.

Findings

New topological proof of the theorem

Broader understanding of the theorem's mathematical structure

Potential for applying topology to other social choice problems

Abstract

In Terao [24], Hiroaki Terao defined and studied "admissible map", which is a generalization of "social welfare function" in the context of hyperplane arrangements. Using this, he proved a generalized Arrow's Impossibility Theorem using combinatorial arguments. This paper provides another proof of this generalized Arrow's Impossibility Theorem, using the idea of algebraic topology.