  In this paper, we investigate tradeoffs between differential privacy (DP) and
several voting axioms for approval-based committee voting, including
proportionality, Pareto efficiency, Condorcet criterion, and strategyproofness.
For all the axioms except strategyproofness, we show their incompatibility with
DP, and provide both upper and lower bounds for their tradeoffs with DP.
Furthermore, we show that any $\epsilon$-DP mechanism satisfies
$e^{-\epsilon}$-cardinality strategyproofness, and the satisfaction can be
further improved if the mechanism satisfies monotonicity.
