Differentially Private Condorcet Voting
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Designing private voting rules is an important and pressing problem for trustworthy democracy. In this paper, under the framework of differential privacy, we propose a novel famliy of randomized voting rules based on the well-known Condorcet method, and focus on three classes of voting rules in this family: Laplacian Condorcet method (_λ), exponential Condorcet method (_λ), and randomized response Condorcet method (_λ), where λ represents the level of noise. We prove that all of our rules satisfy absolute monotonicity, lexi-participation, probabilistic Pareto efficiency, approximate probabilistic Condorcet criterion, and approximate SD-strategyproofness. In addition, _λ satisfies (non-approximate) probabilistic Condorcet criterion, while _λ and _λ satisfy strong lexi-participation. Finally, we regard differential privacy as a voting axiom, and discuss its relations to other axioms.
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