I don't propose to try answering the question (assuming it's a valid one), since to do so in a serious way would take time and be complicated. I'll content myself with saying that I think the US today is a pretty damn good country, and I think there are large numbers of non-Americans throughout the world who also think that; and I'd expect it, as one of the world's long-standing liberal democracies, to rank highly against non-democracies both past and present in any ranking exercise undertaken by people who knew what they were doing and were historically knowledgeable and reasonably impartial. What I'm interested in, however, is a post by Glenn Greenwald in which he waxes indignant about the proposition that America is the greatest country in world history, picked up by him from a tweet of Charles Cooke's saying that it is. You can find Cooke's reply to Greenwald here, but it doesn't really take up the point that is of interest to me: namely, one of the means by which Greenwald attempts to discredit the belief in American superiority. He argues from probabilities. Thus:
[T]here are 179 countries on the planet. The probability that you will happen to be born into The Objectively Greatest One, to the extent there is such a thing, is less than 1%.
[I]f you extend the claim to the Greatest Country that Has Ever Existed in All of Human History, then the probability is minute...
These observations Greenwald offers by way of impugning 'the thought process behind this formulation' (that is, the claim for America's historical superiority); and it's not the only reference he makes to the thought processes of those who support the claim.
Greenwald should have given more careful attention to his own critical thought processes before launching this little beauty on the world.
Probability calculations are made relative to what one knows, or thinks one knows, and what one doesn't. And the claim that America is the greatest country isn't generally made as a proposition of pure chance within the relevant statistical field. Imagine, for an analogy, someone saying that Donald Bradman was the greatest Test batsman of all time. It would not be apt to reply: 'Gosh, given the very large number of Test batsmen there have been, what are the chances of just Bradman having been the greatest ever?' The claim is based on some knowledge about Bradman's batting relative to that of other Test batsmen. It is not a stab in the dark.
OK, the analogy is imperfect because there are some fairly definitive indices of what constitutes outstanding batsmanship in cricket. What constitutes a great country is more open to argument. So let's consider the following analogy instead. If I say that Jane Austen (or Charles Dickens) is the greatest English novelist, I'm not just making a wild bet, at odds of several thousands to one, on her (or his) being so. It's a judgement based on having read the work of the writer in question and also read some reasonable quantity of the output of other English novelists, plus a certain amount of critical opinion etc, and arrived at the ranking in that way. Of course, the judgement might be disputed, or even wrong; there might be an English novelist I haven't read who I would find, if I did, to be superior.
But this issue isn't about someone's failure to consider the odds of just any old country, X, in a field of n countries, being the best ever. A person who truly believes that America is the greatest believes it on the basis of knowledge which they have, or think they have, about that country's qualities relative to the comparable and contrasting qualities of other countries.