At the Student Union pub, the evening after our first Social Choice theory lecture with Amartya Sen, the Teaching Assistant lowered his voice to a whisper and told us the terrible story of 'He who must not be named'- a brilliant Bengali whose fundamental research extended Arrow's impossibility result to prove the non existence of cats. Like Godel's proof of God, it relied on the theory of ultrafilters which we ought not to mess with lest we meet a similar fate.
Just recently, the neighbor's cat has been jumping through the window and making disparaging meowing noises- possibly of a racist or sexist nature- and this has got we wondering. Is there a simple way to derive the same result as the too brilliant Bengali?
How about this?
Suppose there's a cat whose meows are always decodable as equivalent to the results of a perfect Social Choice rule. If the rule is impossible so is the cat. However, it is a plain fact of cat-person phenomenology that any cat offered the right incentives- tummy rubs and treats- produces a string of mewing noises decodable in the desired manner. Therefore all cats are impossible. Q.E.D.