TITLE: Mathematical modeling of voting/rating (e.g. political elections,  questions on MO, gadgets on amazon,...) 
QUESTION [6 upvotes]: 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.

REPLY [3 votes]: If there are no incentive problems (i.e. if everyone is honestly seeking the truth) then Aumann's Agree-to-Disagree Theorem tells you that if the voters are allowed to revise their votes after seeing the outcome, they can't ultimately disagree (at least if there is some objectively correct answer).  (And various results by people like Scott Aaronson suggest that the convergence to unanimity should be fast.)  
So if we see persistent non-unanimity in these votes (which, obviously, we do), and if we want to understand what's going on, we've got to ask exactly why Aumann's Theorem doesn't apply, and that's harder than it looks (see various papers of Robin Hanson for why the most obvious solutions fail).