Canadian Prime Minister Justin Trudeau attends a meeting at the United Nations in New York on Sept. 24. (PETER FOLEY/EPA-EFE/REX/Shutterstock/Peter Foley/Epa-Efe/Rex/Shutterstock)

Speaking Tuesday at the Council on Foreign Relations, Canadian Prime Minister Justin Trudeau took an offhand swipe at the United States' notoriously gerrymandered congressional districts.

“Our electoral district boundaries are determined every year — every 10 years by fully independent commissions,” Trudeau said, referring to Canada’s 338 House of Commons districts. “So you get actual, you know, reasonable-looking electoral districts, and not some of the zigzags that you guys have.”

Ouch.

Here’s the thing, though: Trudeau has a point. In the United States, politicians are typically in charge of drawing state and federal electoral districts. That creates a strong incentive to draw the districts in a way that gives their own political party an advantage, and disadvantages the other guys — a process known as gerrymandering.

Canada used to have a problem with this, as well. But in 1964, legislators passed a federal law mandating that each of the country’s provinces draw their districts via a three-person independent commission. Each commission is chaired by a judge selected by the chief justice of each province, and the additional two members of each commission are selected from the general population by the speaker of the House of Commons.

How has that worked out in practice? Let’s start with a look at the map.


Federal electoral districts of the United States and Canada (Christopher Ingraham)

The map above shows all House of Commons districts in Canada, as well as House of Representatives districts in the United States. You’ll notice that parts of some Canadian coastlines, such as along British Columbia and in the Great Lakes, are simplified. I’ll get to why in a moment.

The districts are colored according to their compactness, which is a term that comes up a lot in gerrymandering discussions. It’s what Trudeau alluded to in his remarks — oddly shaped districts are often, but not always, a sign that gerrymandering shenanigans are afoot. A sprawling map isn’t necessarily a smoking gun, and a nicely compact one doesn’t necessarily mean that no gerrymandering has occurred. But compactness is usually a good place to start the gerrymandering discussion, in part because it’s easy to see and understand.

In the map above, lighter-colored districts are less compact, while darker ones are more compact. Connoisseurs of gerrymandering will want to know that we used the Polsby-Popper method, which compares the area to the perimeter of each district, to compute compactness. The score basically runs from 0 to 100, with zero being not at all compact and 100 being a perfect circle.

The country-level view doesn’t really show us much, however. A lot of the action in redistricting happens in densely populated areas, in geographically tiny districts that don’t necessarily show up well on a continent-level map. So I’ve created, below, a box-and-whisker plot for the compactness of Canadian and U.S. districts.

These plots are handy because they give us a whole lot of information: They show the minimum and maximum values for district compactness in the United States and Canada, as well as the median compactness in each country. They also show the range between the lower (bottom 25 percent) and upper (top 25 percent) quartiles of the distribution — in other words, the range between which half of the districts fall.


Compactness distributions. (Christopher Ingraham)

On a scale of 0 (not at all compact) to 100 (a perfect circle), the median or typical Canadian district scores a 42. The least-compact district comes in at 13, while the most-compact district earns a 77. Half of Canadian districts fall in the range from 33 to 52.

Compare those numbers with U.S. districts. The median here is 26, significantly below the Canadian median. The least-compact district scores an abysmal 4 (hello, Maryland’s infamous 3rd District), while the most is a 69. Half of U.S. districts fall between a 19 and a 36.

It’s important to note that for these calculations, I excluded states and provinces that only had one district, since no redistricting happens there. Canada’s map also uses simplified geography in certain coastal areas, which is nice because it keeps such natural features as winding seashores from having an outsize influence on the scores. U.S. coastal geography is somewhat simplified, too.

The numbers tell us that Canadian districts are considerably more compact than their U.S. counterparts, validating Trudeau’s comments. To help put the figures in concrete terms, the image below compares three Canadian districts at the median score of 42 with three U.S. districts with our median of 26. The U.S. ones are considerably more disjointed.


Median districts. (Christopher Ingraham)

It’s also fun to compare the least compact districts in each respective country. In Canada, it’s the district of Labrador in the province of Newfoundland and Labrador. It scores poorly not because of any redistricting process, but simply because it’s bounded by the ocean on one side and the winding provincial border on the other. Compare that with Maryland’s 3rd District: yes, parts of it border the Chesapeake Bay. But the majority of its boundaries are man-made, drawn by Maryland Democrats as part of their effort solidify their hold on power.


The least compact districts. (Christopher Ingraham)

It’s also instructive to compare how districts are drawn in densely populated areas in each country. Look, for instance, at the pleasantly well-ordered grid of districts around Toronto. Now contrast that with the snarl of districts in Chicago, drawn at the same scale.


Toronto vs. Chicago (Christopher Ingraham)

I’ll emphasize again that taken in isolation, these geometries wouldn’t tell us much about the respective redistricting processes in each country. It’s perfectly possible to draw nicely shaped districts that still disenfranchise voters, as Pennsylvania Republicans demonstrated this year.

However, the geometric differences become significant when you consider the process of their creation: The Canadian districts, drawn by independent commissions, are much more compact and visually coherent than their U.S. counterparts, which are mostly created by partisan actors.