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I thought the standard interpretation of Arrow's theorem was that if no voting system satisfies the hypotheses, then there is no such thing as an objective elec

• tialaramex 5y ago
  It's crucial especially in practice for something in the real world like US gerrymandering, to remain aware that Arrow is talking about the hypothetical worst case. This isn't "No system can work" it's "No system will always work". If out of 5000 voters, 4985 voters prefer Alice to anybody else, 10 prefer Bob and only 5 prefer Charlie; Arrow does not mean Bob and Charlie can tell their voters "See, nobody knows who really won". Alice won. Overwhelmingly the voters prefer Alice. Arrow has nothing interesting to tell us about this scenario. But if only 2400 prefer Alice, 1800 prefer Bob and 800 prefer Charlie, it gets trickier and Arrow starts to appear on the horizon. After all, what if every one of those Charlie supporters hates Alice and would rather have voted for Bob than see Alice win? We can try to improve our system to try to ensure we get this case right, but Arrow proves that we can't ever do a good enough job for every such case. Especially in the case of US election it's worth remembering that if you only have two candidates, Arrow doesn't actually apply at all. A straight-forward majority works fine if all you wanted to do was decide whether the Red or Blue team wins.