In this paper, we investigate tradeoffs among differential privacy (DP) and
several important voting axioms: Pareto efficiency, SD-efficiency,
PC-efficiency, Condorcet consistency, and Condorcet loser criterion. We provide
upper and lower bounds on the two-way tradeoffs between DP and each axiom. We
also provide upper and lower bounds on three-way tradeoffs among DP and every
pairwise combination of all the axioms, showing that, while the axioms are
compatible without DP, their upper bounds cannot be achieved simultaneously
under DP. Our results illustrate the effect of DP on the satisfaction and
compatibility of voting axioms