Steven Shechter (University of British Columbia (UBC) - Sauder School of Business) has posted Congressional Apportionment: A Multi-Objective Optimization Approach on SSRN. Here is the abstract:
Two events, with major implications for U.S. voters, occur after each decennial census. First, congressional ``apportionment'' takes place, followed by congressional ``districting.'' Apportionment determines how to allocate the 435 seats in the House of Representatives across the 50 states, whereas districting determines the geographic boundaries assigned to representatives within each state. While districting and the practice of gerrymandering often receive great attention in the media and courts, the best way to apportion representatives across states has been debated for nearly 250 years. Historical methods (including the present method) each satisfy some desirable optimality criteria that the others are not guaranteed to satisfy. Moreover, none are guaranteed to optimize certain reasonable fairness measures (e.g., minimum range). To our knowledge, we are the first to formulate and analyze a multi-objective optimization approach to apportionment, allowing policy makers to identify Pareto-optimal allocations and quantify their tradeoffs between several competing criteria. Pareto curves from historical censuses and simulations suggest opportunities for improvement in some objectives at little sacrifice to others.
