Rotate puzzle pieces, study the clues, and try to place each piece! You’ll know it’s in the correct location when the piece becomes transparent. Explore the puzzle for other tools, tips, and full instructions.

The puzzle pieces show the district boundaries of the current U.S. House of Representatives in North Carolina. The clue box, visible when you choose a puzzle piece, has a ton of information on compactness measures. Geography compactness is one of many traditional redistricting principles, which are a set of redistricting guidelines that states and localities can choose to adopt (more here). The ‘ALL’ tab shows all four measures on one bar chart. The comparison is based on the compactness in all multi-district states. Values are plotted as the number of of standard deviations from the mean. It’s a great glimpse at the variation across measures. There’s also a list of cities in the district to help orient you. Other tabs detail single compactness measures, and includes the equation and a mini-map that shows the concept to scale. Tabs include R for the Reock test, PP for the Polsby-Popper test, MP for the Minimum Polygon test, and S for the Schwartzberg test. Each tab shows calculations for the district and the national average for reference. 


Basics of redistricting and compactness:

Since 1911, the US House of Representatives has had 435 seats. Every ten years the US Census Bureau conducts the Decennial Census which is a full count of every person in the country. Reapportionment is the process of using the Decennial Census count of people to adjust the number of congressional seats allocated to each state. Because districts require equal population, as a state population grows or shrinks, so does its allocation of seats in the US House of Representatives. Redistricting is the process of dividing the population into districts based on the number of seats allocated during reapportionment. More generally, redistricting is drawing boundaries for any political or electoral purpose. There is a cycle of redistricting that follows every Decennial reapportionment, but redistricting can be done at other times for other reasons.

Compactness is a traditional redistricting principle which are a set of redistricting guidelines that states can choose to adopt. Compactness and the other traditional redistricting principles are explored more hereCompactness was judicially recognized in Shaw v. Reno in 1993. Although the courts find compactness desirable, very few jurisdictions define it or say how to detect it. There are no official delineations or statistical thresholds of what counts as compact and what doesn’t. Some courts have given some weight to some of these but there’s been no consistent measure and the Supreme Court hasn’t weighed in on a definitive test. At least two states offer definitions: Colorado defines compactness as a function of the sum of the district parameters and Michigan State houses are to be as square or rectangular ‘as possible’. Districts that follow natural geography, like a meandering river, can have exaggerated scores.

There are over 30 measures for compactness. They all test for compactness in slightly different ways and so yield disparate results. This puzzle explores four of the most common compactness measures. This doesn’t necessarily mean they are the best measures - they’re just the most common.

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