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Why get the lower bound: this means you systematically underestimate the items with fewer ratings. Also this formula assumes normal distribution.

There is another solution called 'True Bayesian Average' that is used on IMDB.com, for example. For the formula and the explanation how it works see here:

http://answers.google.com/answers/threadview/id/507508.html



It assumes that the aggregate outcome of a large number of Bernoulli trials (i.e. true/false; up/down; good/bad) are distributed binomially, which can be reasonably approximated by the Normal distribution when the number of trials is large. This is technically true, and works for HN-style voting.

This isn't true for Amazon ratings, since ranking something 1-5 isn't a Bernoulli trial. But the central limit theorem says that that the average of those ratings will be normally distributed (assuming that they're identically distributed and independent), so it can still work. The confidence interval is different, however.




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