The method described here is simple because it's only looking at the mean of the belief about each item; it uses the prior belief as a way either to sandbag new items or to give them a bump. I tend to advocate methods that take into account the variance of the belief in order to minimize the risk of showing bad stuff at the top of the heap.

I have a newer article (not mentioned here) that ranks 5-star items using the variance of the belief. It ends up yielding a relatively simple formula, or at least a formula that doesn't require special functions. Like the OP I use a Dirichlet prior, but then I approximate the variance of the utility in addition to the expected utility:

http://www.evanmiller.org/ranking-items-with-star-ratings.ht...

The weakness of the approach (as well as the OP) is that it doesn't really define a loss function for decision-making (i.e. doesn't properly account for the costs of an incorrect belief), which one might argue is the whole point of being a Bayesian in the first place. In practice it seems that using a percentile point on the belief ends up approximating a multi-linear loss function, but I haven't worked out why that is.