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3-rank Bucklin (by Lomax) = MCA (by Benham)

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  • WarrenS
    well Abd... what with allowing rank-equalities and forcing there to be 3 ranks only, you ve changed what I thought of as Bucklin voting more into something
    Message 1 of 12 , Feb 2, 2010
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      well Abd... what with allowing rank-equalities and forcing there to be 3 ranks only,
      you've changed what I thought of as "Bucklin" voting more into something else. Which is fine, but perhaps it now ought to be called "Lomax" voting.

      Anyway, the rules are:
      I: your vote: give a score in {1,2,3} to every candidate, higher scores better.

      II: examining only the "3" scores: if some candidate has a majority, he wins.

      III: examining only the "2"and "3" scores: whoever has the most wins.

      (right?).

      I point out that this voting system happens (far as I can tell) to be equivalent to Chris Benham's "MCA" system which he was touting at one point and which performs quite well,
      maybe better than range voting, on IEVS Bayesian Regret tests.

      Benham viewed it as approval voting but with 2 levels of approval -- regular or high approval. The candidate with the most high-approvals wins if gets >50%, else the usual
      approval-voting-winner wins.

      So I guess with two of you inventing it at least somewhat independently, it must have something going for it. Maybe you ought to fight it out with each other about how great it is... :)
    • Abd ul-Rahman Lomax
      ... Nope. It s simply Bucklin with a couple of tweaks, less than you think. In Duluth Bucklin, 3 ranks. First rank, only one vote was allowed. Same for second
      Message 2 of 12 , Feb 2, 2010
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        On Feb 2, 2010, at 5:44 PM, "WarrenS" <wds@...> wrote:

        > well Abd... what with allowing rank-equalities and forcing there to
        > be 3 ranks only,
        > you've changed what I thought of as "Bucklin" voting more into
        > something else. Which is fine, but perhaps it now ought to be
        > called "Lomax" voting.

        Nope. It's simply Bucklin with a couple of tweaks, less than you
        think. In Duluth Bucklin, 3 ranks. First rank, only one vote was
        allowed. Same for second rank. Third rank, voters could "also approve"
        as many as they liked.

        I've merely suggested that there is no good reason to *prohibit*
        overvotes.

        > Anyway, the rules are:
        > I: your vote: give a score in {1,2,3} to every candidate, higher
        > scores better.
        >
        > II: examining only the "3" scores: if some candidate has a majority,
        > he wins.
        >
        > III: examining only the "2"and "3" scores: whoever has the most wins.
        >
        > (right?).

        No. Count first rank. If majority, done. If not, count second rank and
        add. If majority (of ballots, not now "votes"), done. Repeat final
        round if necessary.

        If plurality win allowed, winner is candidate with most votes. That's
        how it was done over ninety years ago.

        My innovation, beyond suggesting what becomes Instant Runoff Approval,
        is to use the method as the primary in top two runoff, requiring a
        majority. I'll set aside the interesting issue of runoff rules.

        > I point out that this voting system happens (far as I can tell) to
        > be equivalent to Chris Benham's "MCA" system which he was touting at
        > one point and which performs quite well,
        > maybe better than range voting, on IEVS Bayesian Regret tests.

        Fascinating. Do you realize the implications?

        > Benham viewed it as approval voting but with 2 levels of approval --
        > regular or high approval. The candidate with the most high-
        > approvals wins if gets >50%, else the usual
        > approval-voting-winner wins.

        It can get even better. Bucklin is indeed an approval method. Iy
        becomes even more so with equal ranking allowed in all ranks. But the
        ballot is almost a Range 4 ballot. The rating of 1 is missing; this
        rating would allow expressing two disapproved classes. As I'd do it, a
        primary would not use rating 1 to determine a winner, but that rating
        could be used to determine runoff candidates. A condorcet winner
        should be in a runoff, don't you think?

        And how about the Range winner?

        While the primary plurality winner might be different, I'm not sure it
        would worth tossing that in to the runoff. But because write-ins
        should be allowed in runoffs (closer to Robert's Rules' no
        eliminations), a advanced method should be used in the runoff. Could
        be Bucklin again, plurality win allowed, 2-rank enough, I'd say.

        It's hard to model repeated balloting, but Bucklin does simulate it
        much better than IRV.
        >

        > So I guess with two of you inventing it at least somewhat
        > independently, it must have something going for it. Maybe you ought
        > to fight it out with each other about how great it is... :)

        I think of my tweaks on Bucklin to be very simple and obvious, but
        perhaps that's because of my experience with parliamentary procedure.
        Iterated voting was largely overlooked in searching for the ideal
        deterministic method.

        Yet runoff voting is the most common and well-established reform. It
        has two obvious problems.

        Center Squeeze and special elections. But a preferential method in the
        primary could *reduce* runoffs. And Bucklin largely fixes Center
        Squeeze, unlike the faux reform, IRV.

        Hence an obvious political strategy. Fix top-two runoff, but right,
        this time, with American Preferential Voting.

        And Count All the Votes.

        It may not start with that Range 4 ballot, but it could get there,
        it's a small step.

        Note that a two- round system could produce Range winners and still
        satisfy the Majority Crierion. That's quite a trick, I'd say.
      • WarrenS
        ... --yeah, well does the repeat final round as necessary actually make any difference? Can you give election examples where your rules give different winner
        Message 3 of 12 , Feb 2, 2010
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          > Nope. It's simply Bucklin with a couple of tweaks, less than you
          > think. In Duluth Bucklin, 3 ranks. First rank, only one vote was
          > allowed. Same for second rank. Third rank, voters could "also approve"
          > as many as they liked.
          >
          > I've merely suggested that there is no good reason to *prohibit*
          > overvotes.
          >
          > > Anyway, the rules are:
          > > I: your vote: give a score in {1,2,3} to every candidate, higher
          > > scores better.
          > >
          > > II: examining only the "3" scores: if some candidate has a majority,
          > > he wins.
          > >
          > > III: examining only the "2"and "3" scores: whoever has the most wins.
          > >
          > > (right?).
          >
          > No. Count first rank. If majority, done. If not, count second rank and
          > add. If majority (of ballots, not now "votes"), done. Repeat final
          > round if necessary.

          --yeah, well does the"repeat final round as necessary" actually make any difference?
          Can you give election examples where your rules give different winner than the rules just stated? (Maybe it is obvious, but I may be confused so it isn't?)

          > Implications?

          --yes, does sound promising. Maybe we should make a web page about MCA
          as a start. [It also sounded promising back (quite a while ago) when I had IEVS-tested Benham's thing, and I said so back then, but nobody paid much attention at the time.]
        • Abd ul-Rahman Lomax
          ... Should say, repeat process with final round if no majority found in second round. Look, the method is described in Brown v. Smallwood, you host a copy.
          Message 4 of 12 , Feb 2, 2010
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            At 10:16 PM 2/2/2010, you wrote:

            > > No. Count first rank. If majority, done. If not, count second rank and
            > > add. If majority (of ballots, not now "votes"), done. Repeat final
            > > round if necessary.
            >
            >--yeah, well does the"repeat final round as necessary" actually make
            >any difference?
            >Can you give election examples where your rules give different
            >winner than the rules just stated? (Maybe it is obvious, but I may
            >be confused so it isn't?)

            Should say, "repeat process with final round if no majority found in
            second round." Look, the method is described in Brown v. Smallwood,
            you host a copy. Take a look. Actual election, with votes shown.

            If those rules are the same as you stated, fine. But what you stated was

            > > Anyway, the rules are:
            > > I: your vote: give a score in {1,2,3} to every candidate, higher
            > > scores better.
            > >
            > > II: examining only the "3" scores: if some candidate has a majority,
            > > he wins.
            > >
            > > III: examining only the "2"and "3" scores: whoever has the most wins.
            > >
            > > (right?).

            You left out the final round. In your model, this would be "examining
            only the 1, 2, and 2 scores." In other words, all the approvals end
            up being counted if it goes to the third round.

            The old bugaboo about multiple majorities is bogus, for the most
            part. Basically, we should be so lucky! The tendency is to come up
            with majority failure, not multiple majorities, because lots of
            voters will truncate. But my guess is that Bucklin could eliminate
            over half of the runoffs, and would make better runoff choices (even
            if "top two," but better than that could be done.)

            Oh, I realize one more thing. You didn't allow truncation, the way
            you stated it, voters were not, and should not be, required to rank
            all candidates. And there were three explicit ranks, and the third
            rank is still an approval vote for the candidates marked, so there is
            a fourth rank, represented by "no mark." Look, it's simpler to state
            it they way that it was done originally. Three-rank ballot. First
            rank, second rank, third rank. Vote for none (if you like,) for one
            or none in first rank, one or none in second rank, and as many as you
            like, or none, in third rank.

            And if you vote for one candidate in two ranks, it can only count in
            one rank. Which one I'll leave to future generations, but a decent
            rule is possible. I'm also suggesting that you could leave the second
            rank unused but vote in the third rank, if you want. It will give you
            a little more later-no-harm protection, if that floats your boat.

            In Oklahoma they actually used a range-like process, I think that
            first rank was one full vote, second rank was a half vote, and third
            rank was 1/3 vote. Problem is, they required full ranking or the
            ballot was tossed. That's what got the law tossed.

            (If I were going to do range analysis on the ballots, I'd use 1 vote
            first rank, 3/4 vote second rank, 1/2 vote third rank. And, of
            course, I'd allow "overvoting" to your heart's content. Most people
            won't do it, most people won't need to do it, but it does no harm and
            allows, really, more accurate ranking or rating. (i.e., if a voter
            really has little preference between candidates, it's more accurate
            to rank them equally than to pick a ranking.)

            > > Implications?
            >
            >--yes, does sound promising. Maybe we should make a web page about MCA
            >as a start. [It also sounded promising back (quite a while ago)
            >when I had IEVS-tested Benham's thing, and I said so back then, but
            >nobody paid much attention at the time.

            I suspect you didn't adequately study Bucklin.
          • WarrenS
            ... -- http://www.rangevoting.org/BrownSmallwood.html well those rules did not permit equal rankings and voters did not (& could not) score all candidates.
            Message 5 of 12 , Feb 3, 2010
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              --- In RangeVoting@yahoogroups.com, Abd ul-Rahman Lomax <abd@...> wrote:
              >
              > At 10:16 PM 2/2/2010, you wrote:
              >
              > > > No. Count first rank. If majority, done. If not, count second rank and
              > > > add. If majority (of ballots, not now "votes"), done. Repeat final
              > > > round if necessary.
              > >
              > >--yeah, well does the"repeat final round as necessary" actually make
              > >any difference?
              > >Can you give election examples where your rules give different
              > >winner than the rules just stated? (Maybe it is obvious, but I may
              > >be confused so it isn't?)
              >
              > Should say, "repeat process with final round if no majority found in
              > second round." Look, the method is described in Brown v. Smallwood,
              > you host a copy. Take a look. Actual election, with votes shown.

              -- http://www.rangevoting.org/BrownSmallwood.html

              well those rules did not permit equal rankings and voters did not (& could not)
              score all candidates. But I think your point is, with the BvS rules, scores of "1"
              could act in a candidate's favor (whereas, with MCA, they never act in
              favor of a candidate) and actually there were 4 possible
              scores for a candidate, 3,2,1, and "unscored" in decreasing order.

              In those ways, these rules differ from Benham's MCA.


              > Oh, I realize one more thing. You didn't allow truncation, the way
              > you stated it, voters were not, and should not be, required to rank
              > all candidates. And there were three explicit ranks, and the third
              > rank is still an approval vote for the candidates marked, so there is
              > a fourth rank, represented by "no mark." Look, it's simpler to state
              > it they way that it was done originally. Three-rank ballot. First
              > rank, second rank, third rank. Vote for none (if you like,) for one
              > or none in first rank, one or none in second rank, and as many as you
              > like, or none, in third rank.

              --ok, that is quite different from MCA. (And not as desirable as MCA,
              would be my guess. Forbidding equal rankings at top is unlearning the whole lesson of
              approval voting.)

              > In Oklahoma they actually used a range-like process, I think that
              > first rank was one full vote, second rank was a half vote, and third
              > rank was 1/3 vote. Problem is, they required full ranking or the
              > ballot was tossed. That's what got the law tossed.

              > I suspect you didn't adequately study Bucklin.

              --well... IEVS also tried Bucklin and it was not as good as MCA if I recall right,
              but that was doing Bucklin using strict rank order votes.
              In any event, it might be good to make a web page about MCA and its properties
              (assuming you=Lomax now like MCA, or perhaps you dislike it and prefer your thing).

              MCA I think will do better in terms of Bayesian Regret (just a guess at this point) and it seems simpler.
            • Abd ul-Rahman Lomax
              ... Read again. Page 496. It s just as I stated. Equal ranking was allowed in two ranks, one explicit, i.e., the third rank, and the other, of course, the
              Message 6 of 12 , Feb 3, 2010
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                At 12:01 PM 2/3/2010, WarrenS wrote:

                > > Should say, "repeat process with final round if no majority found in
                > > second round." Look, the method is described in Brown v. Smallwood,
                > > you host a copy. Take a look. Actual election, with votes shown.
                >
                >-- http://www.rangevoting.org/BrownSmallwood.html
                >
                >well those rules did not permit equal rankings and voters did not (&
                >could not)
                >score all candidates.

                Read again. Page 496. It's just as I stated. Equal ranking was
                allowed in two ranks, one explicit, i.e., the third rank, and the
                other, of course, the implicit bottom ranking for candidates not
                ranked in the first three ranks. As to the third rank, "vote for all
                other candidates which you wish to support in the third column."

                Thus, if you wanted, you could vote antiplurality. You can score all
                candidates, i.e., freely place candidates in the three express ranks
                and the implicit bottom rank. The express ranks are all approvals, "support."

                > But I think your point is, with the BvS rules, scores of "1"
                >could act in a candidate's favor (whereas, with MCA, they never act in
                >favor of a candidate) and actually there were 4 possible
                >scores for a candidate, 3,2,1, and "unscored" in decreasing order.

                That's correct. But if we are going to talk "scores" with some
                relation to Range, I'd say that the method allowed scores of 4, 3, 2,
                0 for all candidates.

                Yes, equal ranking was not allowed in first and second ranks. To me,
                it's not terribly important to allow equal ranking in the first two
                ranks, but there is no reason to toss ballots which do it, and no
                reason to prohibit it. It's an option that would only be used by
                voters with no significant preference between two candidates. It does
                mean that there would have to be a separate count of all the legal
                ballots, the basis for the majority.

                >In those ways, these rules differ from Benham's MCA.

                I'm sure.

                > > Oh, I realize one more thing. You didn't allow truncation, the way
                > > you stated it, voters were not, and should not be, required to rank
                > > all candidates. And there were three explicit ranks, and the third
                > > rank is still an approval vote for the candidates marked, so there is
                > > a fourth rank, represented by "no mark." Look, it's simpler to state
                > > it they way that it was done originally. Three-rank ballot. First
                > > rank, second rank, third rank. Vote for none (if you like,) for one
                > > or none in first rank, one or none in second rank, and as many as you
                > > like, or none, in third rank.
                >
                >--ok, that is quite different from MCA. (And not as desirable as MCA,
                >would be my guess. Forbidding equal rankings at top is unlearning
                >the whole lesson of
                >approval voting.)

                But, of course, that's why I propose allowing equal rankings at all
                levels. Truncation *must* be allowed, forbidding it was always a Bad Idea.


                > > In Oklahoma they actually used a range-like process, I think that
                > > first rank was one full vote, second rank was a half vote, and third
                > > rank was 1/3 vote. Problem is, they required full ranking or the
                > > ballot was tossed. That's what got the law tossed.
                >
                > > I suspect you didn't adequately study Bucklin.
                >
                >--well... IEVS also tried Bucklin and it was not as good as MCA if I
                >recall right,
                >but that was doing Bucklin using strict rank order votes.

                Yes. Not realistic.

                >In any event, it might be good to make a web page about MCA and its properties
                >(assuming you=Lomax now like MCA, or perhaps you dislike it and
                >prefer your thing).

                It's worth looking at.

                >MCA I think will do better in terms of Bayesian Regret (just a guess
                >at this point) and it seems simpler.

                Remember, my real proposal is to use Bucklin as a primary in a runoff
                system where a majority is not found. This is very difficult to
                simulate, but it's possible it could be tried. To accurately simulate
                it, one would have to take a large set of voters, call them the
                "electorate," and assume that they turn out to vote in a major
                election. The Bucklin election is local, but they are there already,
                so they will vote. However, the runoff turnout would then need to be
                simulated. Voters with low preference between runoff candidates won't
                turn out to vote! This can be expected to shift results toward Range.

                Attention should be paid to the runoff choice. "top two" may not be
                the best. top three could be adequate, if the runoff also Bucklin,
                two-rank ballot is probably adequate (we can neglect write-ins for
                the sim.) It's also possible, and should be tried, to have the runoff
                be between other possible winners: Range and Condorcet, perhaps.

                How the votes are translated into rankings is important. As with
                approval used in a runoff situation, realistic voting strategy must
                be used. Simply determining rank order and voting it that way isn't
                enough with approval! And Bucklin is an approval method.

                Using an unrealistic simulation can produce unrealistic results.

                In the end, it will probably be necessary to see actual election
                results, combined perhaps with poll data, to get a good sense of how
                a method actually performs. Warren, would you have expected that with
                nonpartisan elections, IRV would imitate plurality?

                The error of prior simulations may have been in assuming that voters
                follow issue space distance. In fact, some sort of vague standard
                like "popular positive image" may be at work, combined with
                individual preferences for a single candidate. In any case, it seems
                that if there are three candidates with A, B, and C voters preferring
                each in first rank, then (A>B>C)/(A>C>B) = (B/C), roughly, among the
                A voters who do not truncate. As to the preference for B over C, the
                A voters are a sample from the whole population, excepting their
                first preference for A, they are otherwise the same .... at least
                those who add additional preferences! So if A is eliminated, B and C
                continue to stand in the same relationship. It then follows that the
                first round leader will go on to win. Plurality.

                I'd imagine that in very close elections, this might flip. But I
                haven't seen one yet. Just remember: nonpartisan elections. This is
                clearly not the case with partisan elections.

                By the way, big reform in many places was nonpartisan elections!
              • Jan Kok
                Thanks, Abd and Warren, for this wonderful discussion about Bucklin. ... If equal rankings are allowed, there are situations where voters could be tempted to
                Message 7 of 12 , Feb 3, 2010
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                  Thanks, Abd and Warren, for this wonderful discussion about Bucklin.

                  On Wed, Feb 3, 2010 at 7:29 PM, Abd ul-Rahman Lomax <abd@...> wrote:
                  > Yes, equal ranking was not allowed in first and second ranks. To me,
                  > it's not terribly important to allow equal ranking in the first two
                  > ranks, but there is no reason to toss ballots which do it, and no
                  > reason to prohibit it. It's an option that would only be used by
                  > voters with no significant preference between two candidates.

                  If equal rankings are allowed, there are situations where voters could
                  be tempted to rank two or more candidates in first place, even if they
                  have "significant" preference between them:

                  Suppose the X faction of voters likes candidates A and B and dislikes C.
                  The Y faction likes B and C and dislikes A.
                  The Z faction likes A and C and dislikes B.

                  (For a practical example, A might be on the left, B might be centrist,
                  and C on the right, but some characteristic of B strongly turns off
                  the Z faction such that they would prefer either of A or C over B.)

                  Then each faction has an incentive to "approve" their two preferred
                  candidates, and two or even three of the candidates could get a
                  majority of votes.

                  In such a scenario, if there was also a no-hope candidate N in the
                  race, a voter who preferred N over the others would have an incentive
                  to rank N and at least one of the major candidates in first place.

                  I think what I've shown is that ER-Bucklin is strategically equivalent
                  to Approval (well, in the above scenario it is).

                  What if multiple first choices are disallowed? That version of Bucklin
                  fails FBC (Favorite Betrayal Criterion). Suppose the candidates are A,
                  B and C. 2 voters prefer A first and B second. 5 voters prefer B first
                  and at least 2 of them vote C second. 6 voters prefer C first, period.
                  If the A supporters vote A first, the result is C wins. But if they
                  betray their favorite and vote B first, then they get a better outcome
                  for themselves - B wins.
                • Abd ul-Rahman Lomax
                  ... It s up to the voters to decide if preferences are significant enough to require separate ranking. As far as I m concerned, if the voters can improve
                  Message 8 of 12 , Feb 3, 2010
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                    At 12:57 AM 2/4/2010, Jan Kok wrote:
                    >If equal rankings are allowed, there are situations where voters could
                    >be tempted to rank two or more candidates in first place, even if they
                    >have "significant" preference between them:

                    It's up to the voters to decide if preferences are significant enough
                    to require separate ranking. As far as I'm concerned, if the voters
                    can improve expected results by multiple approvals, that helps the
                    method perform better, and it's only a problem if they do it
                    stupidly. And stupid voting is always a problem, there is no way around it.

                    >Suppose the X faction of voters likes candidates A and B and dislikes C.
                    >The Y faction likes B and C and dislikes A.
                    >The Z faction likes A and C and dislikes B.
                    >
                    >(For a practical example, A might be on the left, B might be centrist,
                    >and C on the right, but some characteristic of B strongly turns off
                    >the Z faction such that they would prefer either of A or C over B.)
                    >
                    >Then each faction has an incentive to "approve" their two preferred
                    >candidates, and two or even three of the candidates could get a
                    >majority of votes.

                    You have not explained why they would not vote, in Bucklin,
                    sincerely, i.e., preserving significant preferences. Nothing has been
                    said in this example about the election expectations, and, remember,
                    the default vote is a bullet vote for the favorite. If this is a good
                    primary election in a runoff system, with three candidates, and
                    Bucklin, the issue will not be voting for more than one in first
                    rank, which was what I was talking about.

                    The "some characteristic of B" would be very rare. The situation
                    described is quite abnormal.

                    >In such a scenario, if there was also a no-hope candidate N in the
                    >race, a voter who preferred N over the others would have an incentive
                    >to rank N and at least one of the major candidates in first place.

                    Maybe. Thin. I wouldn't do it, myself. It conceals my preference for
                    N. But if there was some hope that my vote could cause a majority to
                    appear in first rank, maybe. Except that this is actually
                    contradicted by the conditions.

                    >I think what I've shown is that ER-Bucklin is strategically equivalent
                    >to Approval (well, in the above scenario it is).

                    Sure. It is Approval, with simulation of repeated voting with lowered
                    approval cutoff, as determined by the voters. Repeated voting in
                    Approval is considered quite good as a system, there's been a fair
                    amount of study of this. It's like repeated voting with vote-for-one,
                    just more efficient.

                    (Sometimes people confuse repeated voting with runoff voting. The
                    latter eliminates candidates, though if write-ins are allowed on the
                    ballot, they aren't exactly eliminated, they are merely deprecated a
                    bit. The voters, if they want to, can overcome that.)


                    >What if multiple first choices are disallowed? That version of Bucklin
                    >fails FBC (Favorite Betrayal Criterion). Suppose the candidates are A,
                    >B and C. 2 voters prefer A first and B second. 5 voters prefer B first
                    >and at least 2 of them vote C second. 6 voters prefer C first, period.
                    >If the A supporters vote A first, the result is C wins. But if they
                    >betray their favorite and vote B first, then they get a better outcome
                    >for themselves - B wins.

                    Let's look at this.

                    2: A>B>C
                    5: B>C>A (not the vote pattern, the preferences)
                    6: C

                    As voted:
                    2: A>B
                    3: B
                    2: B>C
                    6: C

                    Sure. The A voters, in a very close election, can improve the outcome
                    by voting A=B. This is an example where equal ranking first rank
                    could be desirable, if these voters can anticipate it. Favorite
                    Betrayal would not exist if equal ranking is allowed. In any system
                    which only counts first preferences first, and which only allows one
                    first preference vote, Favorite Betrayal obviously going to be a
                    rational strategy, if the voter has sufficient knowledge. That's an
                    argument for approval voting at all ranks.

                    Basically, A is an irrelevant candidate, the prospect of betraying A
                    only exists because of this presence. Imagine two irrelevant
                    candidates, both preferred by the voter. With no multiple approvals
                    allowed in third rank, imagine three irrelevant candidates. The voter
                    can't vote sincerely without making the vote irrelevant. Equal
                    ranking obviously allows handling more candidates....

                    I don't think that the A supporters would do it. They would be
                    tossing away the first place votes for their favorite, A, showing
                    support, which is important to voters, in favor of a speculative
                    benefit. Again *how much of a benefit is it*?

                    What would we get from Range? Again, the shortcomings of election
                    scenarios that don't state utilities. Votes are not interpretable,
                    really, without preference strength being expressed. Suppose the
                    votes above have these utilities behind them:

                    2: A, 4 - B, 3
                    3: B, 4 - C, 1
                    2: B, 4 - C, 2
                    6: C, 4

                    Totals:
                    A: 8
                    B: 26
                    C: 31

                    The reason that the A voters have the strategic opportunity is that,
                    with the B voters, they can form a majority in the first round, and
                    this is quite what they might do with plurality. Any compromise that
                    can find a majority immediately can prevail. I'll point out that
                    because of write-in voting, there are always compromises routinely
                    made in first preference, people don't even bother putting their
                    absolute favorite in first preference, if he or she isn't on the
                    ballot and known to be a serious write-in candidate!

                    C is likely the SU winner here, but I can't be sure, and I can't
                    evaluate the voting strategy of the A voters without understanding
                    the utilities behind the votes. It looks like the A voters improve
                    the outcome, but *how much* is always the question.
                  • Jameson Quinn
                    ... I think that in this regard, MCA (two approved ranks) is better than the Lomax proposal (three approved ranks). Let s assume that in practice all races
                    Message 9 of 12 , Feb 4, 2010
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                      > > But I think your point is, with the BvS rules, scores of "1"
                      > >could act in a candidate's favor (whereas, with MCA, they never act in
                      > >favor of a candidate) and actually there were 4 possible
                      > >scores for a candidate, 3,2,1, and "unscored" in decreasing order.
                      >
                      > That's correct. But if we are going to talk "scores" with some
                      > relation to Range, I'd say that the method allowed scores of 4, 3, 2,
                      > 0 for all candidates.
                      >
                      >
                      I think that in this regard, MCA (two approved ranks) is better than the
                      Lomax proposal (three approved ranks). Let's assume that in practice all
                      races will have either 2 or 3 frontrunners. In an effective 2-way race, the
                      large majority of voters will disapprove exactly one of the two, so there
                      will be a CW and either of these systems will find it. In a 3-way race, some
                      voters will focus their vote on 3-way strategy (an important concern if
                      there happens not to be a CW), while others may be "distracted" by the
                      presence of their favorite minor candidate. There are two possibilities:
                      either MCA and 3-rank-equals-allowed-Bucklin will give the same results, or
                      the strategic voters will somehow gain an extra advantage over the
                      unstrategic voters in the latter system. I'd say that in both cases, the
                      simpler MCA is probably superior.

                      To be more concrete: I suspect that most well-informed voters will not use
                      the middle approved ranking, because they don't want to be the first to
                      "compromise" their true preference. For such people, the extra ranking is
                      only adding useless complexity.

                      The exception would be minor-candidate voters in a three-major-candidate
                      race (with a vote like X>A>B>>C). If pressed into only 2 approval
                      categories, these voters would choose either X=A>B>>C or X>A=B>>C. Since
                      their vote for X is only symbolic, their (reasoned) choice between the
                      latter possibilities actually gives the system more information to work with
                      and should result in less Bayesian regret. Also, note that such voters are,
                      by definition, significantly less than 25% of the electorate, and only in
                      three-major-candidate races.

                      In other words: assuming that elections with 4 major (nonclone) candidates
                      will be vanishingly rare, why do you need more than 3 ranking levels? (Even
                      the Rumanian case, with possibly 4 candidates in a Condorcet cycle, is
                      consistent with two of those four being near-clones. And with equality
                      allowed, near-clones are no problem. They'll never be so perfect as to cause
                      a two-way tie.)

                      On the other hand, I do like Lomax's proposal of having a runoff if majority
                      is not attained in one round. Runoffs are a tough sell, though - as FairVote
                      has proven, rightly or wrongly, avoiding runoffs is a big selling point of
                      voting reform.

                      Finally, as for Jan Kok's point: "I think what I've shown is that ER-Bucklin
                      is strategically equivalent
                      to Approval (well, in the above scenario it is)." That's essentially the
                      whole point of MCA. If all voters are well-informed about win probabilities
                      and strategic, MCA and approval should give the same results. However, MCA
                      allows one to continue to get those results with more human-like voters -
                      that is, ones with a sketchier knowledge of win probabilities and a less
                      coldbloodedly-rational approach to strategy. Since, in this formulation, the
                      point is to make correct strategic decisions easier for the voter, adding
                      further complexity - 3 levels of approval as in Lomax's proposal - is IMO
                      one step too far.

                      Jameson Quinn


                      [Non-text portions of this message have been removed]
                    • Abd ul-Rahman Lomax
                      ... Not necessarily a good assumption in nonpartisan races in nonpartisan elections. ... The limitation of two ranks puts a severe limitation on voters who
                      Message 10 of 12 , Feb 4, 2010
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                        At 01:01 PM 2/4/2010, Jameson Quinn wrote:

                        >I think that in this regard, MCA (two approved ranks) is better than the
                        >Lomax proposal (three approved ranks). Let's assume that in practice all
                        >races will have either 2 or 3 frontrunners.

                        Not necessarily a good assumption in nonpartisan races in nonpartisan
                        elections.

                        > In an effective 2-way race, the
                        >large majority of voters will disapprove exactly one of the two, so there
                        >will be a CW and either of these systems will find it.

                        The limitation of two ranks puts a severe limitation on voters who
                        want to express a clear preference for a minor candidate, or maybe
                        two minor candidates, and still cast an effective vote. Three ranks
                        allow the voter to do this with little risk. (In another example, it
                        was shown that there is some risk, and it would always be up to the
                        voter to determine what is more important.) If there *are* going to
                        be two ranks, then approval voting is pretty important for both ranks.

                        The assumption about "the large majority of voters" is probably
                        false. Most voters, in stable situations (not the first one or two
                        elections where preferential voting is allowed, before voters figure
                        out the implications), will vote for one. Has to do with voting psychology.

                        > In a 3-way race, some
                        >voters will focus their vote on 3-way strategy (an important concern if
                        >there happens not to be a CW), while others may be "distracted" by the
                        >presence of their favorite minor candidate. There are two possibilities:
                        >either MCA and 3-rank-equals-allowed-Bucklin will give the same results, or
                        >the strategic voters will somehow gain an extra advantage over the
                        >unstrategic voters in the latter system. I'd say that in both cases, the
                        >simpler MCA is probably superior.

                        I'm not arguing against MCA at this point.

                        >To be more concrete: I suspect that most well-informed voters will not use
                        >the middle approved ranking, because they don't want to be the first to
                        >"compromise" their true preference. For such people, the extra ranking is
                        >only adding useless complexity.

                        This doesn't match actual experience. What was seen in the Grand
                        Junction election described here is that a few voters, fairly
                        clearly, did not use the second rank, but used the third, but it's
                        also true that most voters did use the second rank. That percentage,
                        in some elections, would decline, sometimes greatly, but so too would
                        the third rank. Three ranks, in a properly designed system, allows
                        more effective voter expression, quite similar to Range. Equal
                        ranking should be allowed at all ranks.

                        But if it is not, Bucklin is still a stunning improvement over both
                        plurality and top two runoff, the latter particularly if used as a
                        primary, thus avoiding *some* runoffs. How many runoffs are avoided
                        is up to the voters! Add more lower preferences, avoid more runoffs,
                        add fewer, sticking to your guns, see more runoffs.

                        >The exception would be minor-candidate voters in a three-major-candidate
                        >race (with a vote like X>A>B>>C). If pressed into only 2 approval
                        >categories, these voters would choose either X=A>B>>C or X>A=B>>C. Since
                        >their vote for X is only symbolic, their (reasoned) choice between the
                        >latter possibilities actually gives the system more information to work with
                        >and should result in less Bayesian regret.

                        That's only true if equal ranking isn't allowed. The reality is that
                        in seriously contested elections with more than two serious
                        candidates, almost all will go to the third round, and the lucky
                        thing will be if a majority is found.

                        > Also, note that such voters are,
                        >by definition, significantly less than 25% of the electorate, and only in
                        >three-major-candidate races.

                        The spoiler effect involves often less than 10% of voters. Should we
                        neglect it, then? Remember, as well, the importance of the incubator
                        effect, and the reasons why voters would want to vote for their
                        favorite minor candidate. It's important to them. Coerce them into
                        suppressing their expression, they will not respond well.

                        >In other words: assuming that elections with 4 major (nonclone) candidates
                        >will be vanishingly rare, why do you need more than 3 ranking levels?

                        San Francisco. 23 candidates on the ballot, plus some registered write-ins.

                        >(Even
                        >the Rumanian case, with possibly 4 candidates in a Condorcet cycle, is
                        >consistent with two of those four being near-clones. And with equality
                        >allowed, near-clones are no problem. They'll never be so perfect as to cause
                        >a two-way tie.)

                        I'd use three-rank Bucklin in primaries. I'd use two-rank in runoffs.

                        >On the other hand, I do like Lomax's proposal of having a runoff if majority
                        >is not attained in one round. Runoffs are a tough sell, though - as FairVote
                        >has proven, rightly or wrongly, avoiding runoffs is a big selling point of
                        >voting reform.

                        Big error, actually. Runoff voting is a very old, sustained reform.
                        The key, I believe, is to provide means of *reducing* runoffs,
                        because it is quite possible from some primary results to predict the
                        runoff result well. There are attempts at this, such as requiring a
                        runoff when the winner has less than 40% of the vote. Bucklin would
                        work for this, for sure. Range/Bucklin would be even better,
                        collecting better data from voters. I.e., Range ballot, sliding
                        approval scale, one click per round, down to minimum approval. But
                        full counting if needed to make the best runoff selection. And I
                        still highly support allowing write-ins in runoffs, it's a way for
                        voters to fix unanticipated problems, and when the problems are bad
                        enough, they can definitely do it, they have actually done it.

                        >Finally, as for Jan Kok's point: "I think what I've shown is that ER-Bucklin
                        >is strategically equivalent
                        >to Approval (well, in the above scenario it is)." That's essentially the
                        >whole point of MCA. If all voters are well-informed about win probabilities
                        >and strategic, MCA and approval should give the same results. However, MCA
                        >allows one to continue to get those results with more human-like voters -
                        >that is, ones with a sketchier knowledge of win probabilities and a less
                        >coldbloodedly-rational approach to strategy. Since, in this formulation, the
                        >point is to make correct strategic decisions easier for the voter, adding
                        >further complexity - 3 levels of approval as in Lomax's proposal - is IMO
                        >one step too far.

                        The complexity is quite minor, and it appears that difficulty of
                        understanding the method was not an issue when Bucklin was used. It's
                        still *voting*, i.e., you are not ranking candidates in a popularity
                        contest to produce a social ordering, you are voting for candidates,
                        any Bucklin vote is a vote of support. Used in a runoff system, that
                        is absolutely true for the first round. You can save your
                        hold-your-nose and choose the sweetest-lemon for the runoff, if you
                        like, or stay home while you pack for your flight out.

                        Bucklin, as it were, negotiates for you, according to a control file,
                        your ballot, that determines how hard you will stick to your
                        favorite, or how ready you are to accept a compromise. If it is
                        Bucklin/Runoff, you will want to provide better information so that
                        your favorite does end up in the runoff, and, ideally, the second
                        best is also there, it's safer. That is why I'd want to add a
                        disapproved rank that is still above complete rejection. It could
                        allow for better runoff choices.

                        Voters are going to vote "strategically," and the idea that some
                        voting system is going to prevent it or discourage it is actually
                        guaranteed to cause dislike of ideal voting systems.
                      • Abd ul-Rahman Lomax
                        ... According to the sources I ve looked at, this was proposed, not by Chris, but by Forest Simmons, in 2002. In any case, it is Bucklin with equal ranking
                        Message 11 of 12 , Feb 4, 2010
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                          At 05:44 PM 2/2/2010, WarrenS wrote:
                          >I point out that this voting system happens (far as I can tell) to
                          >be equivalent to Chris Benham's "MCA" system which he was touting at
                          >one point and which performs quite well,
                          >maybe better than range voting, on IEVS Bayesian Regret tests.
                          >
                          >Benham viewed it as approval voting but with 2 levels of approval --
                          >regular or high approval. The candidate with the most
                          >high-approvals wins if gets >50%, else the usual
                          >approval-voting-winner wins.
                          >
                          >So I guess with two of you inventing it at least somewhat
                          >independently, it must have something going for it. Maybe you ought
                          >to fight it out with each other about how great it is... :)

                          According to the sources I've looked at, this was proposed, not by
                          Chris, but by Forest Simmons, in 2002.

                          In any case, it is Bucklin with equal ranking allowed. This is an
                          obvious improvement on Bucklin, quite equivalent to a similar
                          improvement of Plurality by allowing equal ranking top as well as bottom.

                          Two-rank Bucklin is still Bucklin, merely less flexible and less able
                          to handle large candidate counts. Remember, some prominent Bucklin
                          applications allowed unlimited voting in the third rank, so that
                          concept was already established; thus of the three explicit and one
                          implicit rank, two already allowed multiple votes. I see no reason at
                          all for prohibiting them in the top two ranks as well, it was, I
                          believe, just habit, thinking of the alternative votes as tacked onto
                          Plurality. There is no longer any reason to prevent those "overvotes."

                          Basically, Bucklin does make them less necessary, but where a voter
                          really wants to give top ranking to more than one candidate, why not?
                          As I've noted, there can be some issues with regard to future ballot
                          position and public campaign financing, but if a voter really has a
                          serious preference in that way, maybe it's good that they make a
                          choice! The rules could handle it. (For some purposes, then,
                          "overvotes" would result in fractional votes as indicated. But not
                          for the purposes of determining the winner, which would dilute the
                          votes and make it quite disadvantageous to cast them, it would be
                          more effective to rank them!)

                          My sense is that, with Bucklin/ER, few voters would actually overvote
                          in the top rank, they would only do it if their preference was minor,
                          *given the circumstances.* But, as was apparently noted, allowing it
                          (less important with a three-rank system than with a two-rank one)
                          could avoid tossing meaningful votes, which is what no-overvoting
                          rules do if the voter is not physically prevented (as by a voting
                          machine, for example) from casting an invalid vote.

                          Essentially, Warren, what's worth looking at is systems that simulate
                          sequential balloting, a real simulation, not a phony one like IRV. No
                          eliminations, but voting patterns that converge on an optimal
                          solution. In theory, Range produces an optimal solution and the
                          problems are purely practical, i.e., will voters vote so as to make
                          the system perform optimally? Bucklin analysis of a Range ballot
                          strikes me as providing a limited later-no-harm protection, and
                          putting this into a system that seeks majority approval, *real
                          approval*, with a runoff as needed, would encourage strategic voting
                          that is also easy and reasonably true to actual preferences.

                          That a system that with a few tweaks could match Range voting in IEVS
                          performance might exist, that was, in essence, proposed and used
                          widely a century ago, I find totally remarkable. There are and were
                          valid arguments against Bucklin, but they seem to have to do with
                          misunderstandings and misapplications.

                          An example is that San Francisco election where, allegedly, only 3%
                          of voters added lower preferences. The significance of that is
                          completely dependent on the election conditions! After all, suppose
                          there were only two candidates plus write-ins! Just how many lower
                          preferences would we expect? 3% could be *high*! But having that
                          second rank would allow voters who wanted to write in a preferred
                          candidate to actually do that and still participate in the real
                          election. That's important. But in the Bucklin elections I've seen,
                          where we have actual vote counts, the proportion of additional
                          rankings was far, far higher. People used them. How long that would
                          continue, I don't know. But some level of usage would remain, and
                          that level would help avoid a spoiler effect, and when there is a
                          serious three-way race, the method could handle it without major
                          center squeeze damage.
                        • WarrenS
                          ... --yeah, well, it d be good to find out the actual election data, then. It ought to be possible. Especially for Clay, who actually lives in San Francisco
                          Message 12 of 12 , Feb 5, 2010
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                            > An example is that San Francisco election where, allegedly, only 3%
                            > of voters added lower preferences. The significance of that is
                            > completely dependent on the election conditions! After all, suppose
                            > there were only two candidates plus write-ins!

                            --yeah, well, it'd be good to find out the actual election data, then.
                            It ought to be possible. Especially for Clay, who actually lives in San Francisco and could visit archives :)

                            With at least 30 US cities & Towns that adopted Bucklin voting, the data must be out there
                            at least 50 to 100 elections worth; but we for the most part do not have it. And I'm suspicious of some of the data we do have since I suspect it was selected partially to prove points and exhibit interesting behavior, not to be typical.
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