http://www.sjsu.edu/faculty/watkins/arrow.htm

The article above discusses Arrow’s Impossibility Theorem, which states that dictatorship is the only procedure for aggregating individual preferences to produce a complete, transitive group ranking that satisfies the two following conditions:
- Pareto principle: If all the individual rank A over B, then the group ranking must have A over B.
- independence of irrelevant alternatives (IIA): The group ranking between A and B cannot depend on how individuals rank a third option C.

This sounds like it has some depressing implications for the many group rating systems we use, whether it’s rating movies on IMDB or ranking web pages for relevance in a Google search. So why do these systems work? In practice, though the group rankings are not “perfect” - there are a lot of individuals to please, after all - they are generally pretty good. Most real-world cases are not as trivial as the three-alternative example demonstrated in class, and there are many, many more individuals who have preferences. Also, trends are likely to develop in the real world because certain alternatives are truly better than others, so most people agree on those particular rankings. Of course, there is a danger of erroneous trends appearing due to cascade effects. For example, if enough people give a bad movie a great rating on a website, other users are more likely to notice it and click on it just because it has a high rating.

The author mentions that there is one way around the Impossibility Theorem: if the alternatives (A, B, and so on) have some quantitative meaning and all individual rankings exhibit single-peakedness as discussed in class, then an aggregate ranking can be constructed that fulfills the conditions above.