Suggest HN: Algorithm to guess population size from poll results

Hey, I'd like to share a little project idea I thought of a few months ago. I immediately liked it and felt like working on it, but I didn't have time. So I suggested it to a few of my friends, but they eventually didn't work on it either. So finally I'm posting it here, maybe someone here will do it, and if so I'd love to see the process and the result. It's like this: Make an algorithm that, given results of a poll, guesses the number of people in the population. For example: "According to the poll, 18.75% of people prefer jazz music, 43.75% of people prefer rock, and 37.5% don't care." The algorithm will probably guess that only 16 people were asked in the poll. Now I know, it's gonna get complicated, with probability distributions, rounding errors, heuristics, and whatnot. But I think it will be very interesting, and possibly there will scientific uses for this algorithm as well. Maybe this is a good subject for a paper. The first step would probably be to phrase and solve this problem mathematically. This will require good knowledge of probability. Then, developing an algorithm.