[EM] Copeland//Plurality --- can it beat IRV?

[Forest Simmons]

El dom., 23 de ene. de 2022 12:23 a. m., Forest Simmons <
forest.simmons21 at gmail.com> escribió:

> Here's a very simple, seamlessly Condorcet compliant method with an IRV
> flavor... but instead of eliminating the candidate with the fewest first
> place votes at each step, it eliminates the candidate with the poorest
> showing in any "matchup" among the remaining candidates:
>
> While there remain two or more candidates, eliminate the one with the
> fewest votes in any matchup among those remaining candidates. Then elect
> the sole survivor.
>
> If at any stage two or more candidates tie for fewest votes, look at
> second fewest, etc until the tie is broken. Beyond that start comparing max
> opposing votes, etc. This tie breaker hierarchy is easy to justify, easy to
> execute, and as decisive as all get out!
>
> This method cannot eliminate the CW because the candidate with the fewest
> votes will have fewer votes than the CW in their matchup, and perhaps even
> fewer in some other matchup.
>
> It is so omputationally simple that a small child can do it manually,
> given a copy of the pairwise matrix:
>
> Let k be the row containing the smallest entry in the entire matrix. [Too
> hard for a small child to find?] Cross out both row k and column k. [Kids
> like this kind of work.] Repeat until only one entry remains. Elect the
> candidate whose row is not crossed out.
>
> Not monotonic, but only because Sequential Elimination methods in general
> are non-monotonic.
>
> If we want IRV flavor, it's probably gonna have to be non-monotonic.
>
> This method is due to Benham's modification of a non-Condorcet method
> whose name slips my mind at the moment.
>
The name might be "Gross Loser Elimination"

The Gross Loser is the candidate that comes closest to being skunked in a
pairwise matchup.

Elect the candidate that remains after repeatedly eliminating the Gross
Loser.

Eleven words ... perhaps the best possible RCV method that can be defined
so unambiguously and succinctly.

No need to mention Smith, but the fact remains it always elects a Smith
member.

Here's a classic example of Chicken Defense:

49 C
26 A>B
25 B (sincere B>C)

B subverts the sincere CW (A) by a chicken defection that creates a cycle

A>B>C>A

RP, Schulze, MinMax, River, etc reward the defector by breaking the cycle
at the A>B step, which is the weakest majority (26 to 25), allowing the
defector to win with impunity.

Benham and Gross Loser both eliminate B first (for different reasons) and
leave C as the winner, disappointing the defector.

Benham eliminates B because it has the fewest first place votes, while GL
eliminates B because it only musters 25 votes against A .. it is the Gross
Loser.

Benham is a hybrid of IRV and Condorcet patched together with duct tape and
baling wire, while GL accomplishes the same thing simply and seamlessly.

It seems too good to be true, but sometimes simple really is the best!



> El sáb., 22 de ene. de 2022 12:33 p. m., Daniel Carrera <
> dcarrera at gmail.com> escribió:
>
>> Hi guys,
>>
>> As you know, like many of you I am dismayed that so many election reform
>> advocates are promoting IRV, apparently thinking that it is the only or the
>> best alternative to FPTP. So once again I'm trying to think of methods that
>> might appeal to an existing IRV advocate, to see if I can get them to ditch
>> IRV and pick something that is actually good. In the past you've seen me
>> ask about BTR-IRV, Benham, Smith[//,,]IRV, etc. So let me present another
>> idea:
>>
>> What about Copeland//Plurality?
>>
>> 1) The method is incredibly easy:  "Among the candidates that win the
>> most head-to-head matches, pick the one with the most first votes."
>> (yes, I'm setting it so the score for ties is zero)
>>
>> 2) I'm pretty sure that the method is Smith efficient and monotone.
>>
>> 3) For an IRV advocate it might have better intuitive appeal than other
>> alternatives because it has that Plurality component that some of them
>> want. I've read IRV advocates say that IRV > Condorcet because the winning
>> candidate should have strong 1st-place support. I can't imagine any reason
>> why that would possibly be true, but it means that an X//Plurality method
>> might appeal to them.
>>
>> Can anyone help me figure out what properties Copeland//Plurality would
>> have? Does it have any major downsides that I should know about? It's hard
>> to see how it could go very wrong.
>>
>> Cheers,
>> --
>> Dr. Daniel Carrera
>> Postdoctoral Research Associate
>> Iowa State University
>> ----
>> Election-Methods mailing list - see https://electorama.com/em for list
>> info
>>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20220127/731b783f/attachment.html>