Quantum Voting and Violation of Gibbard-Satterthwaite's Impossibility Theorem

TL;DR

This paper explores how quantum voting systems can overcome classical impossibility theorems like Gibbard-Satterthwaite's, by extending concepts of truthfulness and social choice to the quantum domain.

Contribution

It introduces a quantum-specific notion of truthfulness and extends social choice frameworks to quantum voting, bypassing classical impossibility results.

Findings

Quantum voting can violate Gibbard-Satterthwaite's theorem.

New quantum social choice functions are proposed.

Quantum incentive compatibility is established.

Abstract

In the realm of algorithmic economics, voting systems are evaluated and compared by examining the properties or axioms they satisfy. While this pursuit has yielded valuable insights, it has also led to seminal impossibility results such as Arrow's and Gibbard-Satterthwaite's Impossibility Theorems, which pose challenges in designing ideal voting systems. Enter the domain of quantum computing: recent advancements have introduced the concept of quantum voting systems, which have many potential applications including in security and blockchain. Building on recent works that bypass Arrow's Impossibility Theorem using quantum voting systems, our research extends Quantum Condorcet Voting (QCV) to counter the Gibbard-Satterthwaite Impossibility Theorem in a quantum setting. To show this, we introduce a quantum-specific notion of truthfulness, extend ideas like incentive compatibility and the purpose of onto to the quantum domain, and introduce new tools to map social welfare functions to social choice functions in this domain.