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

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  •  Perfect abstract voting is provably impossible (1+ / 0-)
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    homunq

    By Arrow's impossibility theorem, no ranked voting system can ever be designed to satisfy all requirements.  To crib from the wikipedia article:

    In short, the theorem states that no rank-order voting system can be designed that satisfies these three "fairness" criteria:

    1. If every voter prefers alternative X over alternative Y, then the group prefers X over Y.
    2. If every voter's preference between X and Y remains unchanged, then the group's preference between X and Y will also remain unchanged (even if voters' preferences between other pairs like X and Z, Y and Z, or Z and W change).
    3. There is no "dictator": no single voter possesses the power to always determine the group's preference.

    Approval voting doesn't fall under Arrow's, but falls under another impossibility theorem.

    Stepping back, though, I think approval voting is a reasonable way to go, and it's simpler than the instant-runoff voting systems that many cities are moving to for mayoral elections.

    contraposition.org - thoughts on energy, the environment, and society.

    by barath on Thu Nov 08, 2012 at 07:37:26 AM PST

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    •  Yeah, but do you know why Gibbard's theorem... (0+ / 0-)

      ...is better than Satterthwaite's? Or did you think they were the same thing?

      Seriously. I'm as big an elections-math nerd as anyone (I'm currently applying for a PhD in it), but as a practical matter, it is possible to solve the problems with our election system. Approval voting doesn't get us there 100%, but it is a HUGE step in the right direction, and it's simple. So confusing people with talk of Arrow's Theorem is not I think the best tactic.

      (I'm being rhetorical, but I actually do have an answer for the question above.)

      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 07:48:51 AM PST

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      •  I won't argue. (0+ / 0-)

        Feel free to explain, because it's been many years since I read up about those.

        contraposition.org - thoughts on energy, the environment, and society.

        by barath on Thu Nov 08, 2012 at 07:58:18 AM PST

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        •  OK here goes (0+ / 0-)

          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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