After reading "How Not to Sort by Average Rating" (http://www.evanmiller.org/how-not-to-sort-by-average-rating.html), I was curious to know if there was the same thing for variables with more than two outcomes (0,1) or even continuous variables.
For example, how would you generalise the lower bound to the Amazon problem ? Clearly there are 5 outcomes (one for each number of star given by the user). What measure would you use to make the 4.5 stars with 2000 votes better rated that the 5 star with 2 votes ?
Also, it seems to me that this kind of problem could have a bayesian interpretation. I mean using the formula in "How not to sort" is not far from setting a prior in the distribution, maybe a Bernoulli with parameter inferred on the whole dataset / category the item belongs to ? Does anyone know a reference for this particular problem ?