[EM] RCV Challenge

Fri Dec 24 22:49:34 PST 2021

Definitely simpler than my idea! And great rationale!

Arguably the simplest possible adequate method in this RCV category!

El vie., 24 de dic. de 2021 10:29 p. m., robert bristow-johnson <
rbj at audioimagination.com> escribió:

>
> I'm just a Condorcet guy.  Everyone's vote counts the same.  If a simple
> majority of voters agree that A is preferred to B, then when at all
> possible, B is not elected.  After that add whatever contingency you think
> best for the case of a cycle.  I, personally, believe that cycles will be
> very rare and perhaps the simplest process in lieu of a Condorcet winner
> would be the plurality winner of first-preference votes.  I know everyone
> will say that's the worst, most gameable Condorcet "completion process",
> but I think in a government election that the rules should be well known
> and well understood.
>
> (1) The candidate, defined as the Condorcet winner, is elected if the
> rankings on all of the ballots indicate that this one candidate defeats,
> with a simple majority of voter preferences, every other candidate when
> compared in turn with each other individual candidate. A selected candidate
> defeats another candidate by a simple majority when the number of ballots
> marked ranking the selected candidate higher than the other candidate
> exceeds the number of ballots marked to the contrary.
>
> (2) If no Condorcet winner exists in step (1), then the candidate with the
> plurality of first preferences is elected.
>
> Sorry to be so pedantic.
>
> > On 12/24/2021 12:44 AM Forest Simmons <forest.simmons21 at gmail.com>
> wrote:
> >
> >
> > Here's my simplest adequate public proposal in the RCV category:
> >
> >
> > While no candidate has been elected ... eliminate all of the candidates
> beaten pairwise by the lowest (remaining) implicit approval candidate L.
> > Then if L is the only remaining candidate, elect L, Else eliminate L.
> > EndWhile
> >
> > That's all there is to it except for a reminder of what "implicit
> approval" is, and what "pairwise defeat" means.
> >
> > The implicit approval of a candidate is the number of ballots on which
> it is ranked above at least one other candidate *before* any eliminations
> have been executed.
> >
> > Candidate X beats candidate Y pairwise iff X is ranked (strictly) ahead
> of Y on more ballots than not.
> >
> > This method satisfies all of the criteria that I outlined in the RCV
> Challenge (copied below). Note how seamlessly all of these compliances are
> met!
> >
> > [But just because I am giving all of this advanced information to EM
> list experts doesn't mean that any of it is appropriate for any explanation
> to the public ... it is not!
> >
> > I am warning you that you need to choose carefully how to explain this
> or any other method to members of the public. In general the less said the
> better ... beyond examples of counting ballots. As a general rule it is a
> big mistake to answer a question before they ask it.]
> >
> > And beyond the criteria we talked about last time, this method satisfies
> Independence from Smith Dominated Alternatives and is also Banks Efficient!
> >
> > A Banks candidate is one that stands at the head of a maximal chain that
> is totally ordered by the pairwise-beat/defeat relation. All Banks
> candidates have short beatpaths (two or fewer steps) to all candidates,
> which can be seen in the context of our method, because in that context
> every lower L candidate is beaten by the winner, and each of the remaining
> lower candidates is wiped out by one of the lower L's.
> >
> > In our context the totally ordered chain is the sequence of L's in the
> counting procedure that distinguishes the method from other RCV methods.
> >
> > One of the most important features of this method is its resistance to
> strategic attacks against Condorcet candidates. Without this essential
> feature a Condorcet method is "too soft on manipulators" to reliably elect
> the sincere/true Condorcet Winner.
> >
> > Most experts seem to agree that sincere Condorcet Candidates (CC's)
> exist in most public elections. But poorly crafted (and even some fairly
> adequate) methods sometimes allow manipulators to subvert (by insincere
> rankings) the sincere CC''s ballot status with impunity ... all to the
> manipulators' advantage and detriment of the CC.
> >
> > A couple of examples will clarify this point.
> >
> > 45 A>B (sincere is A>C)
> > 30 B>C
> > 25 C>A
> >
> > The sincere ballots show C to be the CW:
> > C beats A, 55 to 45, and C beats B, 70 to 30.
> >
> > But the insincere "burial" of C by the A faction changes C's pairwise
> victory over B into a defeat of C by B, 75 to 25.
> >
> > Most Condorcet methods, including Ranked Pairs, CSSD, and MinMax, reward
> this A faction gambit with victory for A.
> >
> > Even Benham elects A by eliminating C in its first round.
> >
> > So those methods are "soft on burial," at least in this case. How about
> our Banks efficient method? [We need a good name for it ... something less
> technical and more inspiring than IACC for "Implicit Approval Chain
> Climbing".]
> >
> > The implicit approval order in the sincere case is...
> > C 100
> > A 70
> > B 30
> >
> > L1 is B, which is eliminated during the first pass through the while
> loop.
> > L2 is A which is eliminated upon the second pass.
> > L3 is C, the last candidate standing.
> >
> > This is no surprise because a ballot Condorcet winner will always be the
> top member of any maximal chain totally ordered by the pairwise beat
> relation.
> >
> > Now the test ... how does it perform on the manipulated ballots? Is it
> soft on burial like the other better known methods?
> >
> > This time the implicit approval order is
> > B 75
> > A 70
> > C 55
> > L1 is C which takes out A with it in the first pass through the while
> loop leaving B as the winner.
> > The A faction burial plot backfired!
> >
> > We can plainly see why it back fired ... when C was relegated to the
> bottom of the implicit approval list by the A supporters, that
> automatically gave C an opportunity for revenge since the bottom approval
> candidate has first chance to take down all of the candidates it beats
> pairwise.
> >
> > Here's another common test case...
> >
> > 48 C
> > 28 A>B
> > 24 B (sincere is B>A)
> >
> > A is the sincere Condorcet winner, but the B faction's truncation of A
> changes A's victory over C, 52 to 48, to a defeat by C, 48 to 26.
> >
> > With the sincere Condorcet Candidate subverted, our chain climbing
> method starts with A = L1 at the bottom of the approval list ...
> > B 52
> > C 48
> > A 26
> >
> > Then L1 is A which takes out B with itself, and leaves L2=C as the
> winner. So B's gambit backfired.
> >
> > Meanwhile all of the above mentioned Condorcet winning votes (wv)
> methods reward the manipulator B.
> >
> > Benham, which is not a wv method agrees with our chain climbing method,
> but it has other problems, including non-monotonicity. However, if the
> method were to successfully avoid almost all attacks against sincere CC,s,
> the non-monotonicity would almost never be brought into play.
> >
> > I'm not saying that IACC makes manipulation backfire in every case ...
> but when the X faction beaten by the sincere Condorcet Winner W,
> insincerely relegates W to the bottom of the implicit approval list L1=W,
> that will backfire because in the very first pass through the while loop
> this candidate L1=W will take out X ... it's not just a mysterious
> coincidence.
> >
> > This is a brand new method that needs some serious testing .... but I
> don't know of any simpler RCV method with this much promise.
> >
> > That's my challenge to you!
> >
> > Best Wishes for the Holidays!
> >
> > -FWS
> >
> >
> > El jue., 23 de dic. de 2021 4:08 p. m., Forest Simmons <
> forest.simmons21 at gmail.com> escribió:
> > > Despite our best efforts, I'm not sure that we've yet seen or heard
> the best possible deterministic, Ranked Choice Voting proposals.
> > >
> > > In my next message I will submit the best public proposal that I can
> think of in that category (the category of Universal Domain ... i.e. based
> purely on Ranked Choice/Preference information ... equal rankings and
> truncations allowed). Of course, anybody can easily improve on any such
> method by coloring outside of the UD lines ... for example by use of
> explicit approval cutoffs, scores, grades, judgments, virtual candidates,
> and other devices for stratifying rank relations by relative
> importance/strength, as well as probabilities, random ballot drawings, etc.
> > >
> > > But let's temporarily put aside all of these power tools and see what
> we can accomplish with screwdriver, pliers, etc.
> > >
> > > The challenge is to make the method as simple as possible while
> complying with clone independence, monotonicity, and the other most basic
> criteria like Pareto, anonymity, neutrality, majority, etc.
> > >
> > > Simplicity is in the eye of the beholder ... hard to pin down, but you
> know it when you see it.... definitely not just a bunch of ad hoc rules
> cobbled together to patch up an out moded second rate method from
> yesteryear. The fewer seams, the better.
> > >
> > > Simplicity includes simplicity of data summary, simplicity of
> computation, simplicity of formulation/description, etc.
> > >
> > > One antonym of simplicity is complexity ... complexity of the basic
> idea/heuristic, logical complexity, computational complexity, etc.
> > >
> > > I look forward to seeing some of your favorite methods ... original or
> not. And don't worry if they do not completely comply with the ideal
> criteria I outlined above ... a really good, intuitively appealing, simple
> idea can be forgiven a small transgression or two .... and could become the
> germ for an even better method.
> > >
> > > I put simplicity ahead of familiarity because a simple idea can easily
> become familiar, so lack of familiarity is a temporary problem caused by a
> history of poor attention to civics education.
> > >
> > > This challenge is an opportunity for you to take one small step to
> help remedy that educational deficiency!
> > >
> > > Thanks!
> > >
> > > -Forest
> > ----
> > Election-Methods mailing list - see https://electorama.com/em for list
> info
>
> --
>
> r b-j . _ . _ . _ . _ rbj at audioimagination.com
>
> "Imagination is more important than knowledge."
>
> .
> .
> .
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
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