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

Abstract

Use of optimization models in science and policy applications is often problematic because the best available models are very inaccurate representations of the originating problems. Such is the case with electoral districting models, for which there exist no generally accepted measures of compactness, in spite of many proposals and much analytical study. This article reports on an experimental investigation of subjective judgments of compactness for electoral districts. The experiment draws on a unique database of 116 distinct, legally valid districting plans for the Philadelphia City Council, discovered with evolutionary computation. Subjects in the experiment displayed, in the aggregate, remarkable agreement with several standard measures of compactness, thus providing warrant for use of these measures that has heretofore been unavailable. The exercise also lends support to the underlying methodology on display here, which proposes to use models based on subjective judgments in combination with algorithms that find multiple solutions in order to support application of optimization models in contexts in which they are only very approximate representations.

The Philadelphia Districting Contest: Designing Territories for City Council Based Upon the 2010 Census

“…More generally, when do proxy objective functions give meaningful solutions? We investigated the relationship between compactness measures and peoples' perceptions of the goodness of districts in Chou et al (2013). The next question is more general in IP.…”

The Socialoid: A Computational Model of a City

“…For these reasons, we adopted the philosophy of solution pluralism and generalized optimization (Chou et al 2014, Hall et al 2013, Kimbrough and Lau 2016) in which we seek multiple good solutions to the question at hand, rather than a single "best" (optimal) solution. 13 The plurality of solutions-the discovered DoIs-are then to be used for collective deliberation, which we demonstrate next.…”

“…Under either perspective, we advocate the philosophy of solution pluralism: use the data and the models to generate multiple possible decisions, and then evaluate this plurality of options, taking into account information not present in the data and models (see Chou et al 2014, Hall et al 2013, Kimbrough and Lau 2016. MAD models are entirely apt tools for this purpose.…”

Seed-Fill-Shift-Repair: A redistricting heuristic for civic deliberation

“…Young [ 19 ] has shown how the different definitions of compactness can be gamed. Because of the lack of agreement, Kaufman et al [ 24 ] and Chou et al [ 25 , 26 ] have used surveys to observe how people value the different aspects of compactness.…”

“…These feasible solutions can be expected to be legally valid in most jurisdictions, although they cannot be expected to be especially good on any of the redistricting criteria. Our philosophy is one of solution pluralism [ 26 , 49 ].…”