Optimal districting with endogenous party platforms

• The socially optimal districting must be consonant with the population’s ideology.
• Parties condition platforms on the districting, internalizing voters’ preferences
• Contrary to previous research, the seat-vote curve is biased against the larger party
• Empirical simulation suggests that the impact on welfare is small.

Representation is one of the most important criteria by which to judge electoral systems. In this paper, I focus on one aspect of representative democracy: the formation of electoral district boundaries. It is well known that majoritarian systems give rise to highly biased seat–vote curves, causing representation to be less than ideal. What should, therefore, be the optimal constituency design when the objective is to maximize voters' welfare? I show that when parties take account of districting while setting platforms, then the district design problem reduces to a very simple rule: do nothing when voters are risk neutral, and — when voters are risk averse — choose a bias that is against the largest partisan group. Calibrating the model on data of the U.S. State legislative elections during the 1990s, I show that the welfare gain due to optimal districting is very small.