Defining “Compactness”: Meaningless Truism or Gerrymander Slayer?

By: Ben Williams 

This past week, an upstart election law reform organization in Virginia garnered national attention for a lawsuit that could redefine the legal strategies of anti-gerrymandering activists across the country. Per Article II, § 6 of the Virginia Constitution, “[e]very electoral district shall be composed of contiguous and compact territory…” (emphasis added). Virginia is not alone in requiring its districts to be compact—a majority of states have such a requirement. But while the word “contiguous” is easily defined (all parts of the district are connected in a single, unbroken shape), the political science community lacks a common understanding of what exactly contiguity is. As a threshold issue, there are two potential ways to measure a district’s compactness: spatially (the physical shape and area of the district) or demographically (calculating the spread of persons within a given district).  While many states do not define which of these measures should govern, or if one should be preferred over the other, the Virginia Supreme Court in Jamerson v. Womack said the language of Art. II (cited above) “clearly limits [the Article’s] meaning as definitions of spatial restrictions in the composition of electoral districts.” Thus, one of the key questions the Circuit Court judge and the attorneys in the case had to address was how to measure spatial compactness in Virginia?

Generally, there are two types of measures for spatial compactness: dispersion and indentation. Dispersion measures (sometimes called “Perimeter Tests”) quantify the extent to which the shape of a district is spread out from its center; indentation measures calculate how smooth or contorted the boundaries of a district are. Both measures begin with a presumption that the most compact shape is a perfect circle. While it is generally accepted each measure has its own pros and cons, judicial efforts to give content to compactness have been described by legal observers as “inconsistent, ad hoc, and unpredictable.”

Perhaps the most commonly used dispersion test is the “Reock Test.” It calculates the area of an individual district and then draws the smallest possible circle which entirely encompasses the district. The measure provides a score from 0 to 1, with 0 being the least compact shape possible, and 1 being a perfectly compact circle. Because circles are unrealistic, the possibility of using a square is sometimes suggested—perfect squares receive a score of .66 on Reock, a relatively high score.

Commonly cited beside Reock is the Polsby-Popper perimeter test. Polsby-Popper calculates the area of a district by computing the ration of a district’s area to the area of a circle with the same perimeter. As with Reock, the measure is always between 0 and 1, with 1 being a perfectly compact circle. The logic behind Reock and Polsby-Popper is simple: if a district has many protrusions and fingers extending from the district’s core, its shape is less compact and will receive a lower score under both measures. This is why the “poster child” district for non-compactness, Virginia House of Delegates District 72, scored a paltry .26 on Reock and .08 on Polsby-Popper. In fact, the district’s score was so poor that when OneVirginia2021 attorneys addressed the district during a motion before the Circuit Court Judge in the case, he noted that it resembled “a toilet bowl.”

Reock and Polsby-Popper were utilized by both parties during the trial. A decision is expected sometime in April. The case, titled Vesilind et al. v. Virginia Department of Elections et al., will ultimately be resolved by the Virginia Supreme Court, as the loser at trial will almost certainly appeal. Once this case reaches the Justices, all eyes will be on them: if they give Virginia’s compactness requirement teeth, it could fundamentally alter the way in which districts are drawn not only in this state, but in states across the country, during the 2020 redistricting cycle.

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