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I really don't understand why so many people seem to be impressed with Arrow's theorem. It seems to me that it only demonstrates that it's impossible to do some
by gweinberg 5y ago
I really don't understand why so many people seem to be impressed with Arrow's theorem. It seems to me that it only demonstrates that it's impossible to do something you clearly don't want to do in the first place.
Imagine you have a voting public whose preferences are (roughly) 1/3 prefer A > B > C, 1/3 prefer B > C > A, and 1/3 C > A > B. Fisrt off, it's quite obvious that there is no real "right" thing to do, whichever candidate wins, roughly 2/3 of the electorate would prefer one of the others. Fine as far as it goes. But let's say there are slightly more A > B > C, and A is declared the winner. Arrow seems to think it is a bug that only people's knowledge of B allows A to defeat C, but obviously it's a feature.
- mdp2021 5y agoDisambiguation. If 34% (or even 49%) claiming A>B>C made A the winner, 66% (large majority, or even 51%, simple majority) explicitly claimed that C>A ... That «roughly 2/3 of the electorate would prefer one of the others» means that whatever candidate is chosen (say, A), the large majority states that a single different candidate (in this case, C) is better than the winner. There is clearly a paradox.
- deleted 5y ago[deleted]