Quantum voting and violation of Arrow's Impossibility Theorem

TL;DR

This paper introduces a quantum voting system that leverages quantum phenomena to violate a quantum analog of Arrow's Impossibility Theorem, demonstrating strategic advantages over classical voting rules.

Contribution

It constructs quantum analogs of voting constitutions and Arrow's Theorem, showing how quantum properties enable violations of classical impossibility results.

Findings

Quantum majority rule violates the quantum Arrow Conjecture

Quantum strategies utilize entanglement, interference, and superpositions

Quantum voting can circumvent classical dictatorship constraints

Abstract

We propose a quantum voting system, in the spirit of quantum games such as the quantum Prisoner's Dilemma. Our scheme enables a constitution to violate a quantum analog of Arrow's Impossibility Theorem. Arrow's Theorem is a claim proved deductively in economics: Every (classical) constitution endowed with three innocuous-seeming properties is a dictatorship. We construct quantum analogs of constitutions, of the properties, and of Arrow's Theorem. A quantum version of majority rule, we show, violates this Quantum Arrow Conjecture. Our voting system allows for tactical-voting strategies reliant on entanglement, interference, and superpositions. This contribution to quantum game theory helps elucidate how quantum phenomena can be harnessed for strategic advantage.