The Pennsylvania Supreme Court has drawn a new congressional district map for the state after finding that the previous map, drawn by Republicans following the 2010 Census, was an illegal gerrymander that deprived the state's voters of their right to participate in free and equal elections.

One of the criteria used by the court in drawing the new districts is “compactness.” This means, in short, that wherever possible districts should avoid the sprawling, winding, inkblot-like shapes that characterized the old Pennsylvania map, and gerrymandered maps in a number of other states, as well.

A Washington Post analysis shows that the court-drawn map is indeed considerably more compact than the Republican-drawn version, eliminating more than 1,100 miles of borders drawn by Republicans to give themselves a partisan advantage.

Redistricting experts have a lot of ways to objectively measure compactness, using geometric qualities like district area, perimeter and so on. But the best way to understand compactness is visually. The three districts below, for instance, are geometrically compact.

The following three districts, on the other hand, are not.

Many states require districts to be as compact as possible because it's one way of ensuring that all the voters in that district have at least one thing in common: geographic proximity. “A district in which people generally live near each other is usually more compact than one in which they do not,” explained redistricting expert Justin Levitt of Loyola Law School.

District borders necessarily divide populations, so districts that are more compact put fewer divisions between and within communities. We can look at Pennsylvania as an example. Here, for instance, are the state's interior district borders under the 2011 Republican-drawn map. (I've eliminated the external state borders, because those are a constant in every district map.)

Now let's look at the interior borders under the court-drawn map.

It's obvious that these districts are more compact, less sprawling and less squiggly than the ones drawn by Republicans in 2011. And a visual inspection suggests that, compared with the Republican-drawn map, there are fewer internal borders overall. If, for instance, you were to unravel each district's boundaries and place them all end to end, it looks as though the total length of the boundaries would be shorter for the court-drawn map.

Fortunately, we don't have to just eyeball this. For each of the above maps, I've calculated the total length of the interior district borders as follows: First, I added up the perimeters of all 18 districts in each map. Then I subtracted the total perimeter of the state of Pennsylvania, to eliminate that constant quantity that never changes among maps.

Finally, for each map I divided the remaining sum by two: Each interior border is a boundary between two adjacent districts, so simply adding up the perimeters would double-count the length of the interior borders.

That calculation shows that in 2011, Republicans drew roughly 3,047 miles of interior district boundaries to divvy up the state into 18 districts. The 2018 court-drawn map, on the other hand, accomplished the same feat with 1,908 miles of boundary — a reduction of 37 percent, or 1,139 miles.

That works out to roughly the driving distance between Philadelphia and Miami. Or, to use a Pennsylvania-centric measure, it's like driving from Philadelphia to Pittsburgh 3½ times. Or like driving from Scranton to Wilkes-Barre and back, 26 times.

From a redistricting standpoint, the Pennsylvania Supreme Court removed 1,139 miles of unnecessary divisions between and within communities of Pennsylvania voters, divisions that Republican lawmakers put in place primarily to give themselves a political advantage over their Democratic opponents.

Compactness isn't the only measure of a district's fairness. After all, in response to the state Supreme Court's challenge, Pennsylvania Republican leaders submitted a revised map that was much more compact than their 2011 effort but which showed just as much partisan skew toward the GOP.

The new, court-drawn map is not only more compact than either Republican offering — but it also splits up fewer counties and municipal areas, it and more closely reflects the total partisan divide of the state.

The state's Republican leaders, for their part, have vowed to challenge the new state court-drawn map in federal court.