In this paper, we investigate tradeoffs between differential privacy (DP) and several voting axioms for approval-based committee voting, including proportionality, Pareto efficiency, Condorcet criterion, and strategyproofness. For all the axioms except strategyproofness, we show their incompatibility with DP, and provide both upper and lower bounds for their tradeoffs with DP. Furthermore, we show that any $\epsilon$-DP mechanism satisfies $e^{-\epsilon}$-cardinality strategyproofness, and the satisfaction can be further improved if the mechanism satisfies monotonicity.

翻译：本文研究了差分隐私（DP）与赞同式委员会投票中若干投票公理（包括比例性、帕累托效率、孔多塞准则和策略防护性）之间的权衡关系。对于除策略防护性外的所有公理，我们证明了其与DP的不兼容性，并给出了这些公理与DP之间权衡的上下界。此外，我们证明任何$\epsilon$-DP机制都满足$e^{-\epsilon}$-基数策略防护性，且若该机制满足单调性，则其满足程度可进一步提升。