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I'm implementing a rating system to be used on my website, and I think the Bayesian average is the best way to go about it. Every item will be rated in six different categories by the users. I don't want items with only one high rating to shoot to the top though, which is why I want to implement a Bayesian system.

Here is the formula:

Bayesian Rating = ( (avg_num_votes * avg_rating) + (this_num_votes * this_rating) ) / (avg_num_votes + this_num_votes)

Because the items will be rated in 6 different categories, should I use the average of the sums of those categories as "this_rating" for the Bayesian system? For instance, take one item with two ratings (scale of 0-5):

Rating 1:
  Category A: 3
  Category B: 1
  Category C: 2
  Category D: 4
  Category E: 5
  Category F: 3
  Sum: 18

Rating 2:
  Category A: 2
  Category B: 3
  Category C: 3
  Category D: 5
  Category E: 0
  Category F: 1
  Sum: 14

Should "this_rating" be simply the average of the sums listed above? Is my thinking correct, or should a Bayesian system be implemented for each category as well (or is that overthinking it)?

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It depends on whether you want to wind up only with a cumulative rating of each object, or category-specific rating. Having a separate system in each category sounds more realistic, but your particular context might suggest otherwise. You could even do both a category-specific and overall rating!

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    $\begingroup$ I agree. Also, depending on the domain a weighted composite of categories might be a more appropriate index of an overall rating. $\endgroup$ – Jeromy Anglim Aug 19 '10 at 10:55
  • $\begingroup$ Thanks for the thoughts Aniko. I'll take a look at this in the next few days. $\endgroup$ – James Skidmore Aug 20 '10 at 6:18

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