AI 中文总结
该研究针对差分隐私投票，分析了多种投票规则下私有机制返回正确获胜者所需的优势幅度，证明了相关上下界，还发现STV的对应保证无法在多项式时间内实现，是兼具差分隐私与效用时任务变难解的罕见案例。
AI 中文摘要
差分隐私通过向发布的选举结果中注入随机性来保护个人投票记录，但当选举结果接近时，这种噪声可能会导致错误结果。我们研究了中心差分隐私和本地差分隐私在常见投票规则（包括相对多数制、孔多塞制、最大平局制、相对多数决胜制及可转移单票制（STV））下的精度表现。我们的精度衡量标准是：私有机制返回的获胜者与非私有规则以高概率返回的获胜者一致时所需的获胜优势幅度。我们给出了发布获胜者的私有算法，并证明了这些算法所需优势幅度的上界；同时还证明了下界，表明需要非平凡的优势幅度，且其中许多下界与对应上界的对数因子内匹配。对于STV，信息论上的上界与下界匹配，但我们证明，除非NP包含于BPP，否则该保证无法在多项式时间内实现，这提供了一个罕见的例子：一项计算上可处理的任务，在同时要求差分隐私和效用时会变得难以处理。
英文摘要
Differential privacy protects individual voting records by injecting randomness into the published outcome, but this noise can lead to erroneous results when an election is close. We study how precise central differential privacy and local differential privacy can be for common voting rules, including Plurality, Condorcet, Maximin, Plurality with Runoff, and Single Transferable Vote (STV). Our measure of precision is the margin of victory needed for a private mechanism to return the same winner as the non-private rule with high probability. We give private algorithms for publishing the winner and prove upper bounds on the required margin for these algorithms. We also prove lower bounds showing that nontrivial margins are necessary; many of these bounds match the corresponding upper bounds up to logarithmic factors. For STV, an information-theoretic upper bound matches the lower bound, but we prove that this guarantee cannot be achieved in polynomial time unless NP $\subseteq$ BPP. This gives a rare example of a computationally tractable task that becomes intractable when one simultaneously requires differential privacy and utility.
