Arrow's Result

Many of the concepts of economics have a certain resistance to popular explanation. Arnold Kling nominated Arrow's (Nobel winning) Impossibility Theorem as a particular challenge. Tyler Cowen, Alex Tabbarok, and Steve Landsburg each took up the challenge: you can find their stuff at the links - I found them all incomprehensibly cluttered with irrelevant details. The basic notion involved is that when several people set out to choose among a set of alternatives, it's impossible to find a voting system that aggregates individual preferences yet satisfies all of some specified and plausible seeming fair decision rules. This probably won't surprise anybody who has tried to cooperatively plan a Thanksgiving dinner.

As I said, I couldn't follow the reasoning in the links, but Wikipedia is pretty clear, and has both formal and informal statements of problem and proof. Tyler also links to this fairly simple yet detailed proof.

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