@Vectornaut: I think the problem is that what makes something "philosophical" is not at all rigorously defined. The Church-Turing thesis, for example, is a concrete mathematical conjecture, but because it's not phrased purely mathematically (because it applies to models of computing that have not yet been defined, such a definition would be tedious), people may think of it as philosophy. In general, I don't think it's fair to say that the process of coming up with a mathematical definition is "philosophical," even if prior to the definition philosophers were the only ones to discuss the topic.

Do you have any further links to mechanism design literature that addresses rating mechanisms specifically?

The reason I ask is because when I run a simulation in 10,000 dimensions with 10,000 trials, the mean is very close to the correct mean (about 40.82), but the standard deviation is very close to 0.24. It is also almost exactly 0.24 when I run the same simulation for $n$ merely a thousand, or for $n$ a hundred thousand. It is surprising to me that the variance should be so close to 1/2 over many different orders of magnitude, but if I take your analysis at face value the variance should go to zero, no?

Do you know the asymptotic variance of this distribution as $n \to \infty$?