My point is that he hasn't given any reason to think that tax / person really is a better statistic for any purpose. I know that he says something that looks, in terms of sentence structure, like a reason, but there isn't actually any connecting logic there.

Mankiw's a clever chap, so let's give him the benefit of the doubt and try to see if there's any argument he might be hinting at. Perhaps it's something like this. "Higher taxes tend to reduce GDP. The way this works is that people will work less hard, or take less trouble to do more lucrative and presumably more valuable work, if their taxes are higher. The way this works is that people compare the effort they have to exert with the goods and services they can get, which assuming sensible exchange rates is basically the same thing as absolute income; so demotivation is, so to speak, a function of income; so to measure how demotivated our workers are by tax we should look at their taxes in absolute terms."

(I don't know whether that's what Mankiw has in mind, but it's the most plausible argument I can come up with that looks at all like what he said.)

I'll also mention another argument for measuring tax per person, which I don't think Mankiw hints at at all but which seems at least as persuasive as his argument: the purpose of taxation is to provide the people with benefits, typically somewhat evenly spread across the population or a substantial fraction of it; so the benefit provided per person is roughly a function of tax per person.

There seem to me to be several substantial problems with (what I'm guessing to be) Mankiw'sargument, and also with the other argument I mention above, even if we consider only "modern Western economies". Here are some:

1. The prices of goods and services are not at all constant across countries. Unfortunately, there also isn't any simple relationship between these prices and GDP, so it's not clear how to correct for this. (If relevant goods have prices perfectly constant across countries, demotivation is a function of tax per person. If they have prices exactly proportional to GDP, demotivation is a function of tax over GDP. Neither of these simple cases is common.)

2. Some particular goods, including some of great importance for the sort of demotivational effect I think he has in mind, have prices that correlate very strongly with GDP. Notably, houses tend to be more expensive in more affluent countries and cheaper in less affluent countries.

3. It's well established that most people care a lot about status, which goes along with relative income. So one particular and important "good", namely one's level of relative wealth, does in fact vary more or less in proportion to GDP. This observation is relevant to both arguments: the demotivational force of a given level of taxation will (in so far as it depends on status) be determined by tax / GDP rather than tax / population, and the cost of ensuring that no one is too poor in relative terms will also be determined by tax / GDP.

4. The diminishing marginal utility of money means that the richer a nation is, the more effective an average tax dollar is when spent on scalable things (e.g., infrastructure) or benefits for the worse-off, relative to the benefit it would have provided if it hadn't been taken in tax. (And, hence, also relative to the demotivational effect of taxing it.)