Trading Off Voting Axioms for Privacy

TL;DR

This paper explores the fundamental tradeoffs between differential privacy and key voting axioms, establishing bounds that show how privacy constraints impact voting rule properties and their compatibility.

Contribution

It provides the first comprehensive bounds on the tradeoffs between differential privacy and multiple voting axioms, revealing inherent incompatibilities under privacy constraints.

Findings

Upper and lower bounds on two-way tradeoffs between DP and voting axioms

Bounds on three-way tradeoffs among DP and pairs of voting axioms

Demonstration that DP limits simultaneous satisfaction of multiple voting axioms

Abstract

In this paper, we investigate tradeoffs among differential privacy (DP) and several important voting axioms: Pareto efficiency, SD-efficiency, PC-efficiency, Condorcet consistency, and Condorcet loser criterion. We provide upper and lower bounds on the two-way tradeoffs between DP and each axiom. We also provide upper and lower bounds on three-way tradeoffs among DP and every pairwise combination of all the axioms, showing that, while the axioms are compatible without DP, their upper bounds cannot be achieved simultaneously under DP. Our results illustrate the effect of DP on the satisfaction and compatibility of voting axioms.