  Proportional representation (PR) is a fundamental principle of many
democracies world-wide which employ PR-based voting rules to elect their
representatives. The normative properties of these voting rules however, are
often only understood in the context of sincere voting.
  In this paper we consider PR in the presence of strategic voters. We
construct a voting rule such that for every preference profile there exists at
least one costly voting equilibrium satisfying PR with respect to voters'
private and unrevealed preferences - such a voting rule is said to be
strategically robust. In contrast, a commonly applied voting rule is shown not
be strategically robust. Furthermore, we prove a limit on `how strategically
robust' a PR-based voting rule can be; we show that there is no PR-based voting
rule which ensures that every equilibrium satisfies PR. Collectively, our
results highlight the possibility and limit of achieving PR in the presence of
strategic voters and a positive role for mechanisms, such as pre-election
polls, which coordinate voter behaviour towards equilibria which satisfy PR.
