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Voting plays a central role in bringing crowd wisdom to collective decisionmaking, meanwhile data privacy has been a common ethical/legal issue ineliciting preferences from individuals. This work studies the problem ofaggregating individual's voting data under the local differential privacysetting, where usefulness and soundness of the aggregated scores are of majorconcern. One naive approach to the problem is adding Laplace random noises,however, it makes aggregated scores extremely fragile to new types of strategicbehaviors tailored to the local privacy setting: data amplification attack andview disguise attack. The data amplification attack means an attacker'smanipulation power is amplified by the privacy-preserving procedure whencontributing a fraud vote. The view disguise attack happens when an attackercould disguise malicious data as valid private views to manipulate the votingresult.  In this work, after theoretically quantifying the estimation error bound andthe manipulating risk bound of the Laplace mechanism, we propose two mechanismsimproving the usefulness and soundness simultaneously: the weighted samplingmechanism and the additive mechanism. The former one interprets the scorevector as probabilistic data. Compared to the Laplace mechanism for Bordavoting rule with $d$ candidates, it reduces the mean squared error bound byhalf and lowers the maximum magnitude risk bound from $+\infty$ to$O(\frac{d^3}{n\epsilon})$. The latter one randomly outputs a subset ofcandidates according to their total scores. Its mean squared error bound isoptimized from $O(\frac{d^5}{n\epsilon^2})$ to $O(\frac{d^4}{n\epsilon^2})$,and its maximum magnitude risk bound is reduced to $O(\frac{d^2}{n\epsilon})$.Experimental results validate that our proposed approaches averagely reduceestimation error by $50\%$ and are more robust to adversarial attacks.

Aggregating Votes with Local Differential Privacy: Usefulness, Soundness vs. Indistinguishability