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Let me articulate my line of thought.
Imagine that you're working for the ministry of transportation. We compare two countries. One country is significantly bigger than the other – for example we compare Germany (G) and Switzerland (S). There are much more trains in G, but almost the same percent delayed as in S (for ex. G - 6%, S5% trains delayed).
How to account for the size mathematically, if one's objective is to emphasise that even though there are nominally more % trains delayed in G, it is also significantly harder to maintain such a big and complicated system, so G's transp. net may be even better, definitely not worse than S'?
Also such a problem is quite relevant in the context of pandemic. I think it's harder to maintain 5% "rate ill" for USA than for some small country (all else equal): there are just more people, need more coordination and more efficient policies. It is not quite correct to compare "unweighted" rates. But which coefficient to use instead? How to represent this "size-hardness" relation mathematically?

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The very point of computing a percentage is to filter out the population size in order to make Germany and Switzerland comparable. So it does not make sense to move the population size back into a percentage, that defeats the purpose of a percentage. The difficulty you have is that you want to use one statistic for two competing purposes: filter the populationsize out and bring it back in again. That cannot work.

Instead you should when your report your results complement your percentages with the arguments you just made. If you can capture that in a number, then report both numbers.

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