[EM] Coombs method and typical RCV hybrid

[Forest Simmons]

Culi,

Great site!

And great first EM post.

Your "first minus last" score for each candidate is equivalent to what some
of us call the implicit fractional approval score, which is your score plus
the total number of ballots, all divided by two.

Yours is simpler for people that are comfortable with integer arithmetic.
The advantage of ours is that it is just the number of Top votes plus half
of the number of non-Bottom votes ... no possibility of getting negative
scores.

Now here is the best (IMHO) use of your suggested scores:

While more than one candidate remains, among these, eliminate the highest
score candidate that does not pairwise defeat the one with the lowest score.

Unlike the elimination method you suggested, this method, "Fractional
Implicit Approval Chain Climbing," FIACC, is monotonic, clone free, and
Banks efficient.

As long as equal rankings and truncations are allowed, we can confidently
(but humbly) affirm that FIACC is the best known "Universal Domain" method
with these three properties.

Universal Domain means RCV style ballots only.

A Banks candidate is one that stands at the head of a maximal chain of
candidates ordered by pairwise victory.

Every Banks candidate is also a Landau candidate, which means it has a
beatpath of two or fewer steps to any other candidate.

If a method is not Landau efficient, then (embarrassingly) sometimes it
will elect a candidate that is covered by some other candidate. This other
candidate has a valid complaint or Pareto dominance over the winner with
respect to pairwise wins, ties, and losses:

Candidate X covers Y iff it not only defeats Y, but also defeats every
candidate defeated by Y.

Of the well known methods, only Kemeny-Young and Copeland are Landau
efficient. But they both lack monotonicity, among other failings in
comparison with our simple FIACC method.

In particular, unlike Copeland, FIACC is highly resistant to Chicken and
Burial attacks.

And unlike K-Y, FIACC is computationally tractable, while K-Y is
non-polynomially hard.

I know that's a lot to digest ... but you can do it one bite at a time with
patience.

The method is simple ... and the three basic properties (monotonicity,
clone independence, and Condorcet efficiency) are easy to understamd.

It's only the Banks and Landau efficiency (that distiguish it from Ranked
Pairs, Schulze, River, etc) that are a challenge to fully appreciate.

To emphasize the simplicity of the method itself, I repeat the complete
definition here for reference:

While more than one candidate remains, among these, eliminate the highest
score candidate that does not pairwise defeat the one with the lowest score.

Assuming you know what "scores" we're talking about and what "pairwise
defeat" means, that procedure completely and unambiguously defines the
method.

Do you know anybody who can do the same for their favorite complete method
with the same unambiguous precision in fewer than twenty-five words?

[Copeland is not by itself a complete method, just like Condorcet is not a
complete method ... they require "completions" to resolve ubiquitous ties
and cycles.]

Once again, welcome, and thanks for your great first post to the EM list,
and invitation to your site.

-Forest

Forest



El sáb., 22 de ene. de 2022 12:03 p. m., <culitif at tuta.io> escribió:

> Hello all,
>
> I'm Culi, I'm a recent subscriber. Took a social choice theory in college
> and have wanted to make visualizations for electoral methods ever since. I
> recently finally got some time to create something like that!
>
> It's basically a tool that compares the outcome of an election in RCV,
> Coomb's RCV, and a third method which I have yet to find out the name of
> (I'd appreciate help with it). It's all explained more on the site, but
> basically it tries to take into account both first-choice and last-choice
> picks into deciding which candidate to drop every round.
>
> I'd love to someday expand the tool to show how a number of other
> single-winner electoral methods would result in the same election. I built
> a similar tool a while ago in Python but never got to deploy it. I only got
> so far as to simulate the election in FPTP, RCV, Borda Count, Coombs,
> Copeland, Quadratic Voting, and Contingent Vote.
>
> Now that I have web development skills I'd love to rebuild it and make it
> into an educational tool to let people compare different voting systems.
> I'd also love some day to code out some of the electoral methods discussed
> here on this mailing list!
>
> Anyways, here's what the site currently looks like (I'll have a better url
> later I promise). I'd love any feedback and suggestions for the name of the
> third voting method:
>
> https://elegant-shaw-2cb49a.netlify.app/votevote
>
> Best,
> Culi.
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
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