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That's not was Arrows theorem says at all. It just says that all (deterministic) voting systems can sometimes incentivise tactical voting. "Tiered" voting, whe

That's not was Arrows theorem says at all. It just says that all (deterministic) voting systems can sometimes incentivise tactical voting. "Tiered" voting, where we add up local majorities, is known as the tribe system in mathematical social choice theory and can be proven to be the worst possible in terms of making the individual vote matter.

qsort 5y ago
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 electoral mandate, and therefore almost any set of rules that's generally acceptable to the constituents is equally valid. Am I misunderstanding something? I'm not an expert on this at all.
- 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.
tialaramex 5y ago
I think you're talking about Gibbard–Satterthwaite theorem Arrow's Theorem doesn't care about "tactical voting", it's about the Impossibility of what appear to be intuitively reasonable fairness constraints on the outcome. Specifically you cannot have: unrestricted domain, non-dictatorship, Pareto efficiency, and independence of irrelevant alternatives Gibbard–Satterthwaite says if there are at least three candidates, then either one of them can't win, or some of the electorate should offer an insincere preference (ie tactical voting) to best achieve their goal. They're closely related, if you have proved Arrow then you can get to Gibbard–Satterthwaite from there, but they are not the same exact thing.
- thomasahle 5y ago
  Say you get rid of "independence of irrelevant alternatives", then I may influence the result by tactically ordering my candidates.

qsort 5y ago

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 electoral mandate, and therefore almost any set of rules that's generally acceptable to the constituents is equally valid. Am I misunderstanding something? I'm not an expert on this at all.

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.

tialaramex 5y ago

I think you're talking about Gibbard–Satterthwaite theorem Arrow's Theorem doesn't care about "tactical voting", it's about the Impossibility of what appear to be intuitively reasonable fairness constraints on the outcome. Specifically you cannot have: unrestricted domain, non-dictatorship, Pareto efficiency, and independence of irrelevant alternatives Gibbard–Satterthwaite says if there are at least three candidates, then either one of them can't win, or some of the electorate should offer an insincere preference (ie tactical voting) to best achieve their goal. They're closely related, if you have proved Arrow then you can get to Gibbard–Satterthwaite from there, but they are not the same exact thing.

thomasahle 5y ago
Say you get rid of "independence of irrelevant alternatives", then I may influence the result by tactically ordering my candidates.