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He shows the flaws of both examples but only gives a solution to the first one. How does one nicely sort a rating scale like Amazon's that does have more than "yes" and "no"?


I don't know offhand how the Wilson thing generalizes. The simple Bayesian posterior mean one I mentioned yesterday is pretty simple: suppose you have a1,a2,...,ak ratings with 1,2,...,k stars; then the posterior mean number of stars is [(1+a1).1 + (1+a2).2 + ... + (1+ak).k] / [(1+a1) + (1+a2) + ... + (1+ak)]. (Of course the denominator can be written more briefly, but I think it's clearer that way.) Equivalently, you just calculate the average star count, but you add in a bunch of fictitious reviews, one with each possible number of stars. Once again, by adjusting the number of each kind of fictitious review you can (e.g.) make less-reviewed items do better or worse relative to more-reviewed ones; by changing the coefficients that are 1,2,...,k above you can (e.g.) make a 5-star review more than 5/4 as good as a 4-star one; etc.




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