Representing the Insincere: Strategically Robust Proportional Representation

TL;DR

This paper explores the challenge of maintaining proportional representation in elections when voters act strategically, proposing a voting rule that guarantees PR in some equilibria and analyzing the inherent limitations of such rules.

Contribution

It introduces a strategically robust voting rule that ensures PR in at least one equilibrium for any preference profile and establishes fundamental limits on such robustness.

Findings

A voting rule exists that guarantees PR in some equilibrium for any preference profile.

Common voting rules are not strategically robust and may fail to ensure PR.

There are theoretical limits on how robust PR can be in strategic voting contexts.

Abstract

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.