Using interactive evolutionary computation (IEC) with validated surrogate fitness functions for redistricting

Abstract

We describe a novel use of evolutionary computation to discover good districting plans for the Philadelphia City Council. We discovered 116 distinct, high quality, legally valid plans. These constitute a rich resource for stakeholders to base deliberation. This raises the issue of how to deal with large numbers of plans, especially with the aim of avoiding gerrymandering and promoting fairness. Interactive Evolutionary Computation (IEC) is a natural approach here, if practicable. The paper proposes development of Validated Surrogate Fitness (VSF) functions as a workable and generalizable form of IEC.

On Empirical Validation of Compactness Measures for Electoral Redistricting and Its Significance for Application of Models in the Social Sciences

“…(Points (c) and (d) instantiate the more general concept of solution pluralism (Kimbrough, Kuo, Lau, Murphy, & Wood, 2011). ) While we agree that the VSF idea ((a)-(d), sketched above) has much to recommend it, the supporting evidence presented in Chou et al (2012) was rather modest, as we shall see. The purpose of this article is to report on an experiment that augments the unusual, even unique, data set produced by Chou et al (2012) and investigates the core idea more thoroughly.…”

“…Besides proposing the VSF concept, Chou et al (2012) succeeded in the technically challenging task of producing 116 good solutions for a difficult districting problem (Point (c), above). Every design was required to allocate each of the 66 wards to 1 of 10 councilmanic districts for the city of Philadelphia, using data from the 2010 census.…”

“…2. The measure of compactness used by Chou et al (2012) was the max-max distance. Their optimization sought to minimize the maximum of the largest intradistrict distance within a plan.…”

“…3. Further, Chou et al (2012) undertook three experiments that gave qualified support from human judgments for use of this compactness measure as a VSF in the context of electoral districting. Using paired comparisons of district plans that were chosen to be well separated in terms of the max-max distance measure, they were able to show, across 3 experiments, a discernible level of agreement between comparative compactness judgments of the subjects and the verdicts of the max-max distance metric.…”

“…Takagi and Iba (2005) call this ''the most pressing problem in IEC systems.'' As a partial remedy to this problem, Chou, Kimbrough, Sullivan, Woodard, and Murphy (2012) propose what they call validated surrogate fitness (VSF) functions. The nub of the idea is simple: (a) use human subjective judgment to validate a mathematical function that approximates the choices humans make when confronted with the pool of solutions to be considered; (b) use the mathematical function (as the VSF) during automated search (for optimal solutions); (c) produce by automated search a plurality of good solutions (according to the model); and (d) offer these good solutions as members of a consideration set for subsequent deliberation.…”