  Recent research in differential privacy demonstrated that (sub)sampling can
amplify the level of protection. For example, for $\epsilon$-differential
privacy and simple random sampling with sampling rate $r$, the actual privacy
guarantee is approximately $r\epsilon$, if a value of $\epsilon$ is used to
protect the output from the sample. In this paper, we study whether this
amplification effect can be exploited systematically to improve the accuracy of
the privatized estimate. Specifically, assuming the agency has information for
the full population, we ask under which circumstances accuracy gains could be
expected, if the privatized estimate would be computed on a random sample
instead of the full population. We find that accuracy gains can be achieved for
certain regimes. However, gains can typically only be expected, if the
sensitivity of the output with respect to small changes in the database does
not depend too strongly on the size of the database. We only focus on
algorithms that achieve differential privacy by adding noise to the final
output and illustrate the accuracy implications for two commonly used
statistics: the mean and the median. We see our research as a first step
towards understanding the conditions required for accuracy gains in practice
and we hope that these findings will stimulate further research broadening the
scope of differential privacy algorithms and outputs considered.
