We need to make choices in our life and so we need to compare(=rate) things what is good what is bad. Question: are there some mathematical models which may capture features of some kind of voting/ratings systems ?
More precisely I want to have some model where there is some "ideal choice" (e.g. experts estimation of quality of question on MO) and result of real voting - which might be different. The model should help us to understand how to make ratings more close to "ideal choice". The possible application which I keep in mind is user's ratings of gadgets at amazon (or other sites), with the hope to improve it taking into account something like user's "reputation"...
Another application - current science journals play the role of "rating agencies"
- papers published at "Annals" = stamp of great quality. Assume journals will disappear. Can we create a kind of crowd-sourcing rating which will be close to current journal based rating system ?
There are many votings systems - political elections, ratings of questions on stackoverflow, user's ratings of gadgets sold at amazon.com,... Of course, all of them have different features, however it might be that there are certain simple ideas which might be relevant for understanding how all these things work... To understand this: are there simple ideas or there are not? if there are - what are them ? is the gist of this question.
The question is very vague and so any comment is welcome.