  We consider a social choice problem where only a small number of people out
of a large population are sufficiently available or motivated to vote. A common
solution to increase participation is to allow voters use a proxy, that is,
transfer their voting rights to another voter. Considering social choice
problems on metric spaces, we compare voting with and without the use of
proxies to see which mechanism better approximates the optimal outcome, and
characterize the regimes in which proxy voting is beneficial. When voters'
opinions are located on an interval, both the median mechanism and the mean
mechanism are substantially improved by proxy voting. When voters vote on many
binary issues, proxy voting is better when the sample of active voters is too
small to provide a good outcome. Our theoretical results extend to situations
where available voters choose strategically whether to participate. We support
our theoretical findings with empirical results showing substantial benefits of
proxy voting on simulated and real preference data.
