Recent Approaches to the Definition and Measurement of Compactness

11 Pages Posted: 16 Oct 2021

See all articles by Bernard Grofman

Bernard Grofman

University of California, Irvine

Jonathan Cervas

Carnegie Mellon University

Date Written: September 7, 2021


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.

Suggested Citation

Grofman, Bernard and Cervas, Jonathan, Recent Approaches to the Definition and Measurement of Compactness (September 7, 2021). Available at SSRN: or

Bernard Grofman (Contact Author)

University of California, Irvine ( email )

School of Social Sciences
SSPB 2291
Irvine, CA 92697
United States
19497331094 (Phone)


Jonathan Cervas

Carnegie Mellon University ( email )

Pittsburgh, PA 15213-3890
United States

HOME PAGE: http://jonathan

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