| Summary: | Abstract The shapes of electoral districts determine how votes translate into seats. When districts favor certain political parties, electoral results can be disproportionate and the public may lose faith in the political process. Disagreement about appropriate district shapes is subjective, rarely resolved, and often leads to lawsuits. Previously, many authors have called for objective districting criteria. We offer a novel synthesis of models that enables the proactive comparison of district maps, by relating a planar graph partition, the single-member plurality rule, the maximin decision rule, and any agreed measure of partisan bias with a territorial map and historical vote results. Historical vote totals avoid the complexity and uncertainty associated with counterfactual models of vote swing. Districting plans could be objectively compared on such criteria as party proportionality or compact shape to reject plans with worse bias. Objective tools to reduce partisan bias in district maps could boost collaborative participation, increase perceptions of fairness and justice, and reduce costs.
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