Decisive Margins in Differentially Private Voting

2026-08-19

AI Summary

研究通过差分隐私保护投票记录时，为保证结果准确性所需最小胜利差距，并提出相应算法及上下界分析。

Abstract

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.

Problem

• Differential Privacy
• Voting Rules
• Margin of Victory

Innovation

• Differential Privacy
• Voting Rules
• Margin of Victory
• Private Algorithms
• Computational Complexity