Legislative Redistricting - Compactness and Population Density Fairness

Abstract

ð This article discusses three measures proposed for evaluating the fairness and convenience of legislative redistricting plans: (1) Geographic compactness, (2) population compactness, and (3) a new population density fairness measure. There are over a dozen proposed competing measures of geographic compactness. Pictorial counterexamples demonstrate how most of these measures are unreliable. The isoperimetric quotient is recommended for measuring area compactness because it has a maximum value of one (1) when the district is as compact as a circle, a minimum value approaching zero, and enables direct comparison of any two districts' compactness regardless of size. On the other hand, population compactness helps to ensure districts are convenient for voters and politicians. Population compactness can be measured using the distance of a district's census blocks, weighted by its proportion of the district's population to the district's population centroid. However, due to population distribution patterns, neither area nor population compactness guarantee proportionally fair representation. To measure whether a legislative redistricting plan fairly represents both urban and rural dwellers' in proportion to their numbers, this article introduces a population density fairness (PDF) measure for evaluating proportional fairness of districts having diverse population densities. A responsive approach for drawing districts considers population equity, preservation of geographic, neighborhood, and political boundaries, proportional fairness, compactness, and administrative ease. NOTE FROM AUTHOR: The pictorial examples in this draft need to be redrawn for clarity.