  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 ($\CMLAP_\lambda$), exponential Condorcet
method ($\CMEXP_\lambda$), and randomized response Condorcet method
($\CMRR_\lambda$), where $\lambda$ 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, $\CMRR_\lambda$ satisfies
(non-approximate) probabilistic Condorcet criterion, while $\CMLAP_\lambda$ and
$\CMEXP_\lambda$ satisfy strong lexi-participation. Finally, we regard
differential privacy as a voting axiom, and discuss its relations to other
axioms.
