  We study a model of proxy voting where the candidates, voters, and proxies
are all located on the real line, and instead of voting directly, each voter
delegates its vote to the closest proxy. The goal is to find a set of proxies
that is $\theta$-representative, which entails that for any voter located
anywhere on the line, its favorite candidate is within a distance $\theta$ of
the favorite candidate of its closest proxy. This property guarantees a strong
form of representation as the set of voters is not required to be fixed in
advance, or even be finite. We show that for candidates located on a line, an
optimal proxy arrangement can be computed in polynomial time. Moreover, we
provide upper and lower bounds on the number of proxies required to form a
$\theta$-representative set, thus showing that a relatively small number of
proxies is enough to capture the preferences of any set of voters. An
additional beneficial property of a $\theta$-representative proxy arrangement
is that for strict-Condorcet voting rules, the outcome of proxy voting is
similarly close to the outcome of direct voting.
