  The potential risk of privacy leakage prevents users from sharing their
honest opinions on social platforms. This paper addresses the problem of
privacy preservation if the query returns the histogram of rankings. The
framework of differential privacy is applied to rank aggregation. The error
probability of the aggregated ranking is analyzed as a result of noise added in
order to achieve differential privacy. Upper bounds on the error rates for any
positional ranking rule are derived under the assumption that profiles are
uniformly distributed. Simulation results are provided to validate the
probabilistic analysis.
