A Reexamination of Proof Approaches for the Impossibility Theorem

TL;DR

This paper introduces a formal logical proof approach for Arrow's impossibility theorem, emphasizing rigorous derivation and revealing the theorem's global structure, contrasting with previous more intuitive proofs.

Contribution

It develops a new formal proof method using proof calculus, providing a detailed and structured derivation of the theorem.

Findings

Formal proof calculus successfully derives the theorem.

Reveals the global structure of the social welfare function.

Contrasts with intuitive proof methods.

Abstract

Revised proofs of Kenneth Arrow's impossibility theorem have been presented in prose form, incorporating novel ideas such as decisive sets and pivotal voters. This study develops another approach to proving the theorem. Using a proof calculus in formal logic, we construct a proof with a full mathematical representation. While previous proofs emphasize intuitive accessibility, this one focuses on meticulous derivation and reveals the global structure of the social welfare function central to the theorem.