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.

翻译：本文研究了差分隐私（Differential Privacy, DP）与若干重要投票公理——包括帕累托效率、SD效率、PC效率、孔多塞一致性以及孔多塞失败者准则——之间的权衡关系。我们给出了DP与每项公理之间双向权衡的上下界。此外，我们还分析了DP与所有公理两两组合之间的三方权衡，并给出了相应的上下界。结果表明，尽管在无DP约束下这些公理彼此兼容，但在DP约束下无法同时实现其理论最优上界。我们的研究揭示了DP对投票公理满足性与兼容性的影响。