The compactness standard is one of several traditional redistricting principles used to evaluate whether an electoral district has been drawn fairly. A compact district is one whose territory is closely packed together, without long tendrils, narrow corridors, or oddly disconnected appendages. The intuition is geometric: a district shaped like a circle or square is presumptively neutral, while one shaped like a salamander invites suspicion of gerrymandering.
Compactness is typically measured by mathematical scores rather than visual inspection. Common metrics include:
- Polsby–Popper score, which compares a district's area to the area of a circle with the same perimeter.
- Reock score, which compares the district's area to the smallest circle that can enclose it.
- Convex hull ratio, comparing district area to the area of its convex hull.
No single metric is dominant, and courts and commissions often consider several together.
In the United States, compactness is required or encouraged by the constitutions or statutes of most states for state legislative and congressional maps. It is also one of the "traditional districting principles" the U.S. Supreme Court has repeatedly recognized, including in Shaw v. Reno (1993) and Miller v. Johnson (1995), where extreme non-compactness was treated as circumstantial evidence that race had been the predominant factor in drawing district lines. The Court has not, however, set a numerical threshold.
Compactness sits in tension with other goals. Preserving communities of interest, complying with the Voting Rights Act's requirement to create majority-minority districts where appropriate, and respecting existing political subdivisions can all justify less compact shapes. Independent redistricting commissions in states like California, Arizona, and Michigan explicitly rank these criteria, with compactness usually subordinate to equal population and VRA compliance.
Outside the U.S., compactness considerations also appear in the work of boundary commissions in the United Kingdom, Canada, and Australia, though those systems lean more heavily on respecting local government boundaries than on geometric scoring.
Example
In *Miller v. Johnson* (1995), the U.S. Supreme Court struck down Georgia's 11th Congressional District in part because its sprawling, non-compact shape suggested race had predominated in its design.
Frequently asked questions
Through geometric scores such as Polsby–Popper (area-to-perimeter), Reock (area vs. smallest bounding circle), and convex hull ratios. Most analysts report several scores because each captures different shape irregularities.
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