  Voting plays a central role in bringing crowd wisdom to collective decision
making, meanwhile data privacy has been a common ethical/legal issue in
eliciting preferences from individuals. This work studies the problem of
aggregating individual's voting data under the local differential privacy
setting, where usefulness and soundness of the aggregated scores are of major
concern. One naive approach to the problem is adding Laplace random noises,
however, it makes aggregated scores extremely fragile to new types of strategic
behaviors tailored to the local privacy setting: data amplification attack and
view disguise attack. The data amplification attack means an attacker's
manipulation power is amplified by the privacy-preserving procedure when
contributing a fraud vote. The view disguise attack happens when an attacker
could disguise malicious data as valid private views to manipulate the voting
result.
  In this work, after theoretically quantifying the estimation error bound and
the manipulating risk bound of the Laplace mechanism, we propose two mechanisms
improving the usefulness and soundness simultaneously: the weighted sampling
mechanism and the additive mechanism. The former one interprets the score
vector as probabilistic data. Compared to the Laplace mechanism for Borda
voting rule with $d$ candidates, it reduces the mean squared error bound by
half and lowers the maximum magnitude risk bound from $+\infty$ to
$O(\frac{d^3}{n\epsilon})$. The latter one randomly outputs a subset of
candidates according to their total scores. Its mean squared error bound is
optimized 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 reduce
estimation error by $50\%$ and are more robust to adversarial attacks.
