Zhechen Li, Ao Liu, Lirong Xia et al.
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 ($\CMLAP_λ$), exponential Condorcet method ($\CMEXP_λ$), and randomized response Condorcet method ($\CMRR_λ$), 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, $\CMRR_λ$ satisfies (non-approximate) probabilistic Condorcet criterion, while $\CMLAP_λ$ and $\CMEXP_λ$ satisfy strong lexi-participation. Finally, we regard differential privacy as a voting axiom, and discuss its relations to other axioms.