Hmm that depends on the book and who posted the 1s and the 5s, you just described the ratings of every scientology book and every evolution book in amazon.
But I agree that while there is a decent chance that a book with lots of 5s and lots 1s will be of value, the chances that a book with straight 3s to be worth anything are pretty slim.
This is a dream of mine as well, but performance may be a problem. Custom functions mean no caching and arbitrary computational burden from each function.
It doesn't have to be totally custom. Just solicit a few representative types and allow all those. This also solves the problem of not everyone knowing how to write such a function, and dealing with user code running on the server.
Better yet, play around with lots of different sorting methods, and look for patterns in the sorting method used (s), the user's data and history (h), and the amount of money the user ends up spending ($).
Maximize $, and don't ask stupid questions like "Would you rather sort by variance, average rating, or Wilson score?"
(I'm pretty sure that's what Amazon is busy doing every day. They're positively brilliant at turning data into money.)
This only applies if you are using a sub-par database. While caching computationally heavy operations is not always a good choice (since they will need to get updated when more entries are added to the dataset), chances are you will have orders of magnitudes more lookups than writes and hence it makes sense to create a computed column and index the results (and hence cache them).
In the case of Amazon, perhaps the Associates Web Service APIs could allow the creation of tool allowing user-defined sorting functions. I've never used these APIs, but I found some details on them that lead me to think it would be possible. See http://aws.amazon.com/associates/#details
That said, asking honestly, are you entirely convinced of the mass appeal of user-defined (or user-selected) sorting algorithms? I find that the current algorithm usually gives fairly sane results.
Yes. And similarly, for sites like News.YC: I'd rather read a "2 points" comment with 100 upvotes and 99 downvotes, than something banal with one upvote.
Comments like that are frequently dogmatic assertions about down-the-middle controversial issues (like religion or politics) that draw knee-jerk up/down votes from the two ever-combative groups. The comments with one upvote can sometimes be hidden gems in an abandoned thread, or possibly one great comment among many others.
They can be. But if they are shallow, dogmatic assertions, they often (and should) go negative and stay negative.
I've seen lots of good, fair comments with strong opinions (whether I agree with them or not) go initially negative -- early downvotes from the anonymous censorious underemployed peanut gallery -- then creep back up to small positive values after a full day's cycle. Those are much better comments than any pandering +20 one-liner.