# Arrow's Theorem Through a Fixpoint Argument

## TL;DR

This paper offers a novel proof of Arrow's theorem using a fixpoint approach, connecting social choice theory with fixed point theorems from mathematics, and conceptualizing dictatorships as fixpoints.

## Contribution

It introduces a new proof technique for Arrow's theorem based on Banach's fixpoint theorem, bridging social choice and mathematical analysis.

## Key findings

- Demonstrates that dictatorships are fixpoints of a specific process
- Provides a mathematically elegant proof of Arrow's theorem
- Links social choice concepts with fixed point theory

## Abstract

We present a proof of Arrow's theorem from social choice theory that uses a fixpoint argument. Specifically, we use Banach's result on the existence of a fixpoint of a contractive map defined on a complete metric space. Conceptually, our approach shows that dictatorships can be seen as fixpoints of a certain process.