Recent Approaches to the Definition and Measurement of Compactness

The aim of this essay is to consider recent developments in the measurement of compactness for purposes of redistricting. Compactness of districts is one of the four redistricting criteria most often found in state constitutions (Kim and Chen, 2021). But the plethora of compactness measures continues to lead to dispute about how best to interpret such provisions since, in the vast majority of cases, no specific measurement rule is specified in the constitution. Here, we review the traditional measures of district compactness, usually based on the shape of the district, graph-theory based measures that have been introduced over the previous decade, a new measure that uses deep learning to quantify human conceptions of compactness, and finally a measure under development that is based on transportation networks. We also reiterate what we believe is the intent of compactness criteria, namely, representational benefits.