Simulating counterfactual representation

We show how to use multilevel modeling and post-stratification to estimate legislative outcomes under counterfactual representation schemes that, for example, boost the representation of women or translate votes into seats differently. We apply this technique to two research questions: (1) Would the U.S. Congress be less polarized if state delegations were formed according to the principle of party proportional representation? (2) Would there have been stronger support for legalizing same-sex marriage in the U.K. House of Commons if Parliament more closely reflected the population in gender and age?