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

[Daniel Carrera]

On Sat, Jan 22, 2022 at 5:11 PM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> On 22.01.2022 21:33, Daniel Carrera wrote:
> > 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.
>
> It probably fails monotonicity, because it's X//Y and it's not Borda.
> The thing that makes Copeland//Borda monotone is that the pairwise
> matrix doesn't change when you remove candidates. But the number of
> first preferences for remaining candidates *does* change when candidates
> are eliminated.
>

I didn't think of that. I think that when I wrote Copeland//Plurality I was
really thinking of Copeland,Plurality --- i.e. keep the first preferences
as is, and pick the highest one that is in the Copeland set. No
redistribution. But changing to Copeland,Plurality just introduces new
problems (below).



> I would also guess that it would be pretty susceptible to strategy. It
> isn't cloneproof either because neither Copeland nor Plurality is.
>

Yeah, probably. For Copeland,Plurality you get the same spoiler effect as
Plurality.


> 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.
>
> I always find the core support argument kind of weird. If core support
> is the end-all be-all, then Plurality's your man. But clearly it isn't.
> On the other hand, IRV can elect a candidate who has only two first
> preferences, so the worst case (lack of) reliance on core support can be
> pretty bad -- and IRV can fail to elect the CW even when the CW has more
> initial first preferences than the IRV winner. So it doesn't really hold
> up.
>

Yeah. It's a weird argument. "We want enough Plurality to dismiss the CW
(sometimes), but not enough to elect the Plurality winner, oh and sometimes
we'll pick the 3rd or 4th highest Plurality candidate even if the CW is 2nd
because... I guess IRV just does that sometimes".

rbj made a point just an hour ago that Condorcet is a principle "if a
majority agrees that A > B, then B must not win", while IRV is an algorithm
without underlying ethic. It's the core principle of Condorcet that
convinces me that it is the embodiment of democracy in a multi-candidate
election.

Cheers,
--
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University
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