On party-proportional representation under district distortions

The paper presents the problem of choosing the representatives in an assembly when the whole electoral region is subdivided into electoral districts. Because of the two dimensions, geographical (districts) and political (parties), the problem is called bi-apportionment. Often the allocation of seats to districts is pre-determined and furthermore distorted—meaning that the ratios of the number of assigned seats to population size vary significantly across districts. The paper surveys proposed bi-apportionment methods with a focus on the conflict that may arise between party-proportional representation and district distortions.