[dhosek]

The dataset defines the countries as polygons. The perimeter of a polygon is well-defined.

Your argument that perimeter error nearly always increases the perimeter seems completely wrong to me. In a perfect snapshot of a coastline, the perimeter would be fractalized at the size of a grain of sand and would define a maximum perimeter. Any approximations would tend to smooth this out and reduce the perimeter.

But regardless of whether we can make a perfect measurement of a coastline, for the purposes of this calculation, we're looking at the country represented as a polygon on the surface of a sphere. Both the area and perimeter of such a polygon are well-defined quantities. If it makes you feel better, we can say that we're not determining the roundness of the country but the roundness of the representation of the country in the dataset (which is what the original story was also doing).

[nwallin]

Go look at Iceland on a map. Don't just imagine it in your head, actually look at it. Now look at a map of Jordan. Ask yourself which of these countries is more circular, and then ask yourself which of these countries your metric will tell you is more circular.

https://www.google.com/maps/place/Iceland

https://www.google.com/maps/place/Jordan/@31.25,34.9,7z