How Competitive Should a Fair Single Member Districting Plan Be?

Partisan unfairness is easily detected when the statewide vote is equally divided between two parties. But when the vote is not evenly divided, even the determination of which party is disfavored becomes controversial. This paper examines the ideal fair outcome in a two party single member district system when the statewide vote is not equally divided. It is shown that equal voter empowerment, implied by readings of the first amendment (Shapiro v. McManus and Whitford v. Nichol), requires that the fraction of seats be proportional to the fraction of the statewide vote. However, strict proportionality conflicts with the single member district system, so alternative approaches are explored. Generalized party inefficiency and voter effectiveness are defined and shown to encompass many possibilities for an ideal fair seats-votes function. The best choice is fundamentally determined by the degree of geographical heterogeneity of voters of like mind. Based upon historical election results, it appears that a good approximation to a normative seats-votes function of the American system of single member districts should have competitiveness (aka responsiveness) roughly twice as large as proportionality. This is consistent with the method employed by the plaintiffs in Whitford v. Nichol. This method is also basically consistent with the claim of the plaintiffs in Shapiro v. McManus, although in this case gerrymandering is better exposed by examining symmetry.