In reply to Nick Smith - UKC:
Ok, two ways to go about things to try and reduce the biases brought in by new voters (A) and malicious voting (B).
(
A) When contructing the 'histogram' for each picture, at the moment (or until recently) you weight every vote equally. You use likelyhood estimation here, but having thought about it more it's only really going help with voters who have made very very few votes. So, it's probably best to ignore this effect, except for when you derive the 'average' vote for deciding which number star you award the image, where you can weight each vote based on the number of votes made by that user, as you outlined above. See
http://en.wikipedia.org/wiki/Weighted_mean
So, if score is the final score of the image, vote[i] is what user i gave it, and n[i] is the number of votes user i has made across all the galleries, and N is the number of votes the image has received:
score = ( vote[1]*n[1] + vote[1]*n[1] + ... vote[N]*n[N] ) / ( n[1] + n[2] + ... n[N] )
(
B) More complicated. Each user, given they've voted sufficient times, has a mean vote and a distribution around this.
For instance, (just picking out of top 10 voters)...
Darkhorse tends to vote below 'average', call this #3:
I've voted for 730 photos, average vote 2.4.
(6% superb - 15% good - 22% average - 23% poor - 31% rubbish)
Some chap called Jon Read votes slightly above #3, but with a nice spread:
I've voted for 5,519 photos, average vote 3.3.
(8% superb - 33% good - 41% average - 13% poor - 2% rubbish)
whereas someone like Dave Yardley votes around #3 but very tightly around #3:
I've voted for 9,241 photos, average vote 3.2.
(0% superb - 27% good - 62% average - 9% poor - 0% rubbish)
So, you could use this information to contruct an expected model of a users voting. Firstly, you could address any bias in the voting where, crudely, a Darkhorse vote of #2 is the same as aDave Yardley #3, i.e. they both think the image is 'average' according to their voting behaviour.
Also, you could weight each vote (similar to above), but here if Darkhorse gave something a #5, (s)he must really like it, and the same, perhaps more so, if Dave Yardley gave something a #5, or a #1 he really hates it. Whereas if I gave something #5 superb, it should probably carry less weight as I'm more likely to dish #5s out.
This would end malicious voting overnight. However, it does assume that the average image on this site is worthy of #3.
It would be slightly tricky to adjust each vote, such that the distribution of votes you can see for each image reflects the weighted system rather than the original votes. We can correspond about the algoriths for this though.
Any use?