  Local Differential Privacy (LDP) protocols allow an aggregator to obtain
population statistics about sensitive data of a userbase, while protecting the
privacy of the individual users. To understand the tradeoff between aggregator
utility and user privacy, we introduce new information-theoretic metrics for
utility and privacy. Contrary to other LDP metrics, these metrics highlight the
fact that the users and the aggregator are interested in fundamentally
different domains of information. We show how our metrics relate to
$\varepsilon$-LDP, the \emph{de facto} standard privacy metric, giving an
information-theoretic interpretation to the latter. Furthermore, we use our
metrics to quantitatively study the privacy-utility tradeoff for a number of
popular protocols.
