Differentially Private Condorcet Voting

TL;DR

This paper introduces differentially private Condorcet voting rules, ensuring privacy while maintaining key voting properties, and explores their theoretical relationships and guarantees.

Contribution

It proposes a new family of differentially private Condorcet-based voting rules with proven properties and analyzes differential privacy as a voting axiom.

Findings

All proposed rules satisfy key voting axioms.

Different rules satisfy different probabilistic Condorcet criteria.

The paper discusses differential privacy as a voting axiom.

Abstract

Designing private voting rules is an important and pressing problem for trustworthy democracy. In this paper, under the framework of differential privacy, we propose a novel famliy of randomized voting rules based on the well-known Condorcet method, and focus on three classes of voting rules in this family: Laplacian Condorcet method ($\CMLAP_\lambda$), exponential Condorcet method ($\CMEXP_\lambda$), and randomized response Condorcet method ($\CMRR_\lambda$), where $\lambda$ represents the level of noise. We prove that all of our rules satisfy absolute monotonicity, lexi-participation, probabilistic Pareto efficiency, approximate probabilistic Condorcet criterion, and approximate SD-strategyproofness. In addition, $\CMRR_\lambda$ satisfies (non-approximate) probabilistic Condorcet criterion, while $\CMLAP_\lambda$ and $\CMEXP_\lambda$ satisfy strong lexi-participation. Finally, we regard differential privacy as a voting axiom, and discuss its relations to other axioms.