The bargaining range in legislative district apportionment

One of the few “laws” of political science is the fairly regular relationship in any given plurality electoral system known as thecube law, transforming vote shares into seat shares. In this paper, we develop an altogether different and more robust paradigm relating seats to votes which generates similar results as the cube law. In our model, political parties bargain with each other for an expected number of seats using the ability to gerrymander in determining their bargaining strength. We find that an arbitrated solution to the seat-vote allocation problem generates solutions remarkably similar to the conventional cube-law-based solutions. Thus our model can in some way replace the cube law paradigm. With our model, we are able to evaluate the impact ofBaker v. Carr (1962) on gerrymandering. We also find that proportional representation results can be achieved within our model by allowing non-zero population deviations between districts.