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Thanks for the proposal. That gets us somewhere already, although only for non-landlocked countries. Using the perimeter also opens us up to the coastline paradox.
I think that it might serve us better to consider them as distinct islands, to keep the measures comparable with landlocked countries.
Will you use the sea borders instead of the coastline to avoid the paradox?
You didn't really mention how this is all being tabulated. Just in theory? Do you have access to data sets or are you making them? The coastline paradox only really exists for smaller and smaller measuring devices. If for example your method is using satellite images of a given resolution, or another consistent measuring tool, the measurements should be comparable between country borders and therefore the error or the paradox should come out in the wash.
I would imagine using some sort of shapefile that I can run calculations in a scripted manner. So, in that case it will depend on the resolution of the shapefile.