Andrew C Eggers and Benjamin E Lauderdale, “Simulating Counterfactual Representation”, Political Analysis 24(2):281-290
We show how to use multilevel modeling and post-stratification to estimate legislative outcomes under counterfactual representation schemes that e.g. 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?