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View Diary: How to Repair the Voting System: Sec. Debra Bowen's Answer (302 comments)

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    For the non-nerds: "the Gibbard-Satterthwaite theorem" shows that there is no election system without some possibility for voting strategy in some cases.

    Gibbard's proof is better, because it works from first principles to show that in any "voting game" with three or more candidates, there is no single dominant strategy that gets best achievable results no matter what everyone else does. It is clearly inspired by Arrow's theorem, but it doesn't use it explicitly.

    Satterthwaite explicitly uses Arrow's theorem in his proof, so his proof only applies to ordinal ("comparative") voting systems like plurality or IRV, and not to cardinal ("evaluative") voting systems like approval or MJ.

    Most people talk as if they're the same theorem, so you won't get that by "reading up" unless you mean reading the original papers. (I find Gibbard's to be better-written; it's nice to read those old math papers which don't use notation as a crutch for poor writing.)

    More recent work has shown that there is still a semi-loophole in Gibbard's theorem. Any voting system must have strategy, but (as long as you stick to simple game theory and don't bring in crazy partial-information models) for some of them, including Approval and (by my unpublished proof) Majority Judgment, it is possible to have no dishonest strategy. So if you prefer A over B over C, you might have to think strategically about approving A and B or just A, but you can entirely discount voting for B but not A.

    Senate rules which prevent any reform of the filibuster are unconstitutional. Therefore, we can rein in the filibuster tomorrow with 51 votes.

    by homunq on Thu Nov 08, 2012 at 08:29:55 AM PST

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