Representing the Insincere: Strategically Robust Proportional Representation
This addresses the challenge of maintaining fair representation in democratic elections when voters act strategically, though it is incremental in extending PR theory to strategic contexts.
The paper tackles the problem of achieving proportional representation (PR) in voting systems with strategic voters, constructing a voting rule that ensures at least one costly equilibrium satisfies PR based on private preferences, while showing that common rules fail and proving a limit on full strategic robustness.
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.