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

[Forest Simmons]

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.

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
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>
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