very interesting, Zalim: "... the main source of the paradox is that preferences are not cardinal. if there were an absolute measure of utility (perhaps something what teh communists say, like everyone shoud prefer this to that..), the problem would not arise. say X=1 and Y=2 and Z=3 and that the numbers represent absolute utilities for everyone in society..." - I don't think having a cardinal preference Necessarity guarantees a solution. - When you assign numbers to x, y and z, I think you are confusing preferences with utility. Now, granted they are very closely related, but they are not the same. Perhaps, you wanted to say x yields a utility(whatver the heck that is) of 1 and so on. This still does not solve the paradox. The problem is that people have different preferences, a.k.a. in your parlance, it yields different levels of utility to different people. So say, if x > y and y > z for person1, s/he gets utils of 3, 2 and 1 from x, y and z respectively. We have now rephrased the paradox, but paradox it remains. - Ok, if one person says everyone should prefer A to B (perhaps because s/he prefers A to B) then that person is a "dictator" in Arrow's world. And that is precisely his impossibility - it is impossible to find a consistent method of picking the best alternatives (when they number more than 3) without a dictator. (of course his work has a lot of bells and whistles.) But some might wish to state it as a POSSIBILITY result though : It is possible to find a consistent method of picking the best alternative if there is a dictator. Basically, if you want a consistent method, you've got to have a dictator.