I really like the Wikipedia introduction to the article on Mechanism Design which describes it as taking: "an objectives-first approach to designing economic m

I really like the Wikipedia introduction to the article on Mechanism Design which describes it as taking: "an objectives-first approach to designing economic mechanisms or incentives, toward desired objectives, in strategic settings, where players act rationally. Because it starts at the end of the game, then goes backwards, it is also called reverse game theory." Also, I think you are overstating Arrow's Impossibility Theorem. It only applies to voting systems where voters can rank candidates, and where the result of the election is desired to be a consistent community-wide ranking of all the candidates.