I note that I don't know what the Central African Republic is, but I'm guessing that it's somewhere in Africa. I'm probably best off estimating that it has the average population of a state in Africa, but I don't know what this is either. It will be much smaller than the US population (P>.999), but that doesn't help me....much. I note that this fact in itself implies that I can form a probability distribution. My estimated probability of the Central African Republic being smaller than the US is .999, so I have .999 to distribute within the range 0>450,000,000 (4.5x10^8 is my estimate of the US population).

I don't think that I should use a hypothesis of complete ignorance here because I think that I would have a greater chance of hearing of it the more people it had, but this isn't very dependable considering that I don't follow politics that much. I also note that you may have made the name up, giving it a population of zero. But wouldn't that render the experiment invalid? I can't immediately see why. You're also posting this on April Fools, of all days, and we haven't had a joke yet, so I weight this option more than the others.

Yet we're trying to minimize error here, not pick the integer which we believe has the highest probability of being a correct answer. To take this possibility into account, I will multiply my guess of an average nation's population by .4.

What data can I use to make that guess. Well, I was at a Model United Nations conference once, and I thought that there were about 94 nations present. I suppose that there are about 40 nations not present in the UN, so let's run 6.5 billion/136. We get 46 million. I will multiply that number by .4 to get 18.7 million.

Reposted: put this in the wrong place the first time.