[EM] RCV Challenge

[Forest Simmons]

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
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20211223/67f40f32/attachment-0001.html>