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Re: [RangeVoting] Re: More on the reversal problem

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  • Stephen Unger
    I used what I understand to be the formal definition of Bucklin, not some abbreviated version (altho I am sure that, in actual use, various abbreviated
    Message 1 of 50 , Apr 1 7:51 AM
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      I used what I understand to be the formal definition of Bucklin, not
      some abbreviated version (altho I am sure that, in actual use, various
      abbreviated versions were employed). In that case, we operate with a full,
      standard ranking, with a single candidate for each rank. The reverse
      of a vote is simply the ranking written backwards, which is what a
      voter would do if the object was to order the candidates with the
      worst one first, etc. This is the most straightforward way of
      interpreting the various terms.

      No such failures occur with approval or score. In approval voting, for
      example, every candidate approved in the initial election is NOT
      approved in the reverse election, and vice versa. There is no "middle"
      group approved both ways.

      So Bucklin clearly fails the reversal test. The fact that the "middle
      votes are the same in both cases" is inherent in Bucklin. It explains,
      but does not justify, the mechanism of the failure. Note that, under
      Borda, which can be regarded as a restricted version of score,
      reversal is always handled properly.

      Reversal failures can be serious, even when they don't affect the
      winner, because, e.g., the difference between placing second or fourth
      may have real consequences for parties and candidates. Where a
      reversal failure occurs in a case where the candidates are not all
      bunched together, we have an example where at least one of two
      instances of elections is being seriously distorted.


      On Sun, 31 Mar 2013, Abd ul-Rahman Lomax wrote:

      > At 07:06 PM 3/31/2013, Stephen Unger wrote:
      >> Here is a simpler example of an election, where Bucklin fails the
      >> reversal test. In this case, if all votes are reversed, Bucklin
      >> generates the same winner. There are no ties encountered.
      >> 3 B>A>C
      >> 1 C>A>B
      >> 1 A>C>B
      >> 1 C>B>A
      >> The results are A=5, B=4, C=3
      >> When all votes are reversed, the results are A=5, C=4, B=3. Same
      >> winner.
      > That's because the middle votes are the same in both cases. Note that
      > this is a total corruption of Bucklin, *unless those middle votes are
      > actually *approvals.* Shown here is 2-rank Bucklin, and this is
      > really an Approval election. All Bucklin has done is to allow a
      > preference order for up to two candidates.
      > If voters have the preferences stated, and vote in an Approval
      > election, approving the middle rank, all of them, same result.
      > Reversible with no change. That's because of the voting power
      > expressed in the middle rank.
      > In the reversible elections previously shown, the *ballot* set was
      > the same with reversal. So of course it generated the same result!
      > Whatever a deterministic algorithm does with *the same ballot set*
      > must be the same. Isn't that some kind of basic criterion?
      > Ties simply confuse the issue. To my mind, a tie between candidates
      > is the election of a ballot set, to be resolved by whatever means are
      > established, it's outside the method itself. I.e., coin toss, size of
      > donation to the Town Slush Fund, whatever.
      > The election wasn't really *reversed.* The *preferences*, but the
      > ballot design was not reversed.
      > I.e., if the voter voted B>A (>C) on a Bucklin ballot, the reversal
      > of this would not be C>A (>B), it would be C > (A > B) That is,
      > approved is converted to not-approved, and vice-versa.
      > So when the votes are reversed, more accurately, i.e., more
      > completely (how is it "reversal" for the voter to approve A in both
      > directions?), C wins. C>B>A is the new reversed preference order, the
      > preference order reversal of A>B>C.
      > Basically, Stephen, you (and others expressing similar Bucklin votes)
      > did not actually reverse the votes. You *half* reversed them. You did
      > *not* make them into their opposites.
      >> A modified version, where different numbers of voters choose each
      >> ballot ordering, is below.
      >> 6 B>A>C
      >> 3 C>A>B
      >> 2 A>C>B
      >> 1 C>B>A
      >> The results are A=11, B=7, C=6.
      >> When all votes are reversed, the results are A=10, C=8, B=6. Same
      >> winner.
      > Running the complete reversal analysis, the reversal is again
      > complete through the preference order, C>B>A.
      > The "breakdown" is in assuming complete rank order Bucklin, which is
      > far, far, from how Bucklin is designed. if you have the voters all
      > approving their top two candidates, you get this supposed oddity. But
      > it's not odd at all. It's a result of the asymmetry of the method, as
      > used, naively, as in Bucklin where voters are *required* to all
      > approve two out of three candidates.
    • Abd ul-Rahman Lomax
      ... That would certainly be true, does not contradict what I wrote, and the concept of repeated voting with lowered approval cutoff was extensively discussed
      Message 50 of 50 , Apr 6 9:16 AM
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        At 08:12 AM 4/5/2013, Bruce Gilson wrote:
        >On Fri, Apr 5, 2013 at 9:38 AM, Abd ul-Rahman Lomax
        > > Bucklin appeared, in many analyses, to not pass reversal because of
        > > mindless ranking without regard for approval.
        > >
        > >
        >In fact, when Steven Brams discusses Bucklin in his book, *Mathematics and
        >Democracy*, mostly in conjunction with his nearly identical system called
        >"Fallback Voting," he makes it clear that only approved candidates are
        >ranked by the voter.
        >So at least one person outside this group has noted this.

        That would certainly be true, does not contradict what I wrote, and
        the concept of repeated voting with lowered approval cutoff was
        extensively discussed by students of approval voting.

        However, reviewing Mathematics and Democracy, I'm struck by what
        seems to be entirely missing from it: any consideration of repeated
        ballot, seeking an explicit majority, whether absolutely (Robert's
        Rules) or as a goal (i.e., runoff systems that terminate, usually on
        the second ballt, with a plurality result if a majority is not found
        -- or that *force* a majority by disallowing any other votes that for two).

        It's a glaring omission. It's not just Brams. The characteristics of
        runoff voting were widely ignored in voting systems discussions,
        including Bayesian Regret calculations that assumed the same voting
        electorate with the same preferences. I can think of no example of
        someone proposing runoff voting using an advanced voting system,
        until I started doing it, and that blind spot seems to have existed
        in the past.

        Strangely, the actual behavior of runoff voting and how it differed
        from IRV was either ignored, or was *explained* by some deficiency in
        turnout, or manipulability by monied interests, ignoring the actual
        situations. Yet Robert's Rules of Order is totally aware of the
        problem of *not* holding a real runoff, using IRV. Their concern is
        not abstract, they are parliamentarians. They also criticize IRV for
        center squeeze, and their own preferential voting process *still
        seeks a true majority or the election must be repeated.*

        Almost by accident, in Arizona (it wasn't an accident, we have a man
        on the ground there, who did yeoman work), we may be getting
        Approval/Runoff, with a mandatory top two runoff. Technically, of
        course, this is Top Two RAnge, which outperforms Range in simulations
        with realistic voting patterns. We can probably do better, but this
        is very good to start! (I've suggested that Bucklin for the primary,
        at least, is an obvious move.)

        (Pure Range with *accurate and commensurable* utility expression is,
        by definition, optimal for summed social utility. But there are few
        ways to get that expression. Interestingly, an inconvenient runoff
        election does push results toward absolute utility, because if the
        choices are not greatly different in utility, the voter has less
        motivation to vote, hence expressed votes will tend to have higher
        preference strength behind them.)

        Reading over Brams I see that PAV is essentially what I've proposed,
        but I've suggested a true hybrid ballot that allows equal ranking.
        He's suggested, essentially, a ranked ballot with an explicit
        approval cutoff. I've simply suggested using a Range ballot with
        midrange as explicit approval cutoff. That allows ranking within the
        approved and disapproved sets, yet the "sincere" ballot is easy to
        vote, except for the *intrinsic difficulty*, deciding how to
        categorize the candidates, which gets tougher when there are three or
        more. (And there are always, in fact, many, if write-ins are
        allowed.) Runoff systems make the decision in the primary a bit
        easier, approval becomes a binary decision: would I prefer the
        election of this candidate to a runoff being held?)

        Brams also mentions voting after a series of pre-election polls. If
        we assume that the polls are accurate, this is essentially repeated
        ballot, but based on a sample instead of the full electorate.
        However, that assumption can be a problem!

        If, instead of a poll, it's a real election, in a runoff system
        primary, we can be reasonably confident that a majority result is
        real! Multiple majorities are a problem, but the hybrid ballots I've
        suggested can find ways of making that choice, if it's considered
        excessively inconvenient to refer it to the voters in a runoff.

        (Polls should not simply collect favorite information, that will
        distort them. Range polls are much better, that's been obvious for
        some time. A Range 2 poll -- +/-, default 0 -- showed what
        vote-for-one polls could not show, true relative position of
        candidates, and strength of support and opposition.)
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