How Not to Sort by Average Rating (2009)
Averages (even with the post's approach) still have the problem of not being "honest" in the game theory sense. For example, if something is rated 4 stars with 100 reviews, a reviewer who believes its true rating should be 3 stars is motivated to give it 1 star because that will move the average rating closer to his desired outcome. A look at rating distributions shows that this is in fact how many people behave.Median ratings are "honest" in this sense, as long as ties are broken arbitrarily rather than by averaging. Math challenge: is there a way of combining the desirable properties mentioned in the post with the property of honesty? I suspect there is but I haven't tried it.