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Do user ratings of products — games, films, books, restaurants, etc. — tend to follow any particular distributions? If so, what form do they commonly take? Are there public data sources that show these distributions (e.g. for Amazon books, Netflix movies, etc.)?

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About the only general thing you could say is "multinomial". –  Glen_b Feb 22 at 21:56
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Here is a useful article on the topic: cacm.acm.org/magazines/2009/10/… –  Hibernating Feb 22 at 22:28
    
@Hibernating: Interesting. That article seems to argue that the J shape is the result of underreporting and other undesirable factors, implying that products, in fact, have some different underlying distribution of "actual" qualities. Is there any evidence for this? What is the shape of the distribution of product quality (certainly not symmetric, I would expect). –  raxacoricofallapatorius Feb 22 at 22:40

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up vote 2 down vote accepted

Here's a post from the YouTube blog that, anecdotally, I think is fairly representative of star ratings systems online generally.

As you can see, it's a J-curve.

Here are some further examples from different sectors, with the graphs reproduced here:

ratings distributions

The biggest relevant dataset I'm aware of was the one Netflix released for the Netflix Prize competition – however it has since been removed due to a privacy lawsuit. You may however be able to find copies of it online.

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