On empirical validation of compactness measures for electoral redistricting and its significance for application of models in the social sciences (Extended)∗

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 paper 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.