[EM] Poll, preliminary ballots

[Closed Limelike Curves]

Yep. So, @Richard, the VoteFair guy <electionmethods at votefair.org>, we can
decompose IIA failures for (almost) all methods into IIA failures =
Condorcet cycles + Condorcet inefficiency.

I think a better metric for measuring how badly a system fails IIA, rather
than the raw count, is a metric based on changes in winner quality
when some other candidate drops out. (Probably the worst-case fall in
utility?)

On Fri, Apr 19, 2024 at 3:51 AM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> On 2024-04-19 01:44, Richard, the VoteFair guy wrote:
> > On 4/18/2024 1:17 PM, Kristofer Munsterhjelm wrote:
> >  > There doesn't need to be a fixed proportion of failures, does there?
> >
> > You are correct.
> >
> > What I'm taking into account are two factors:
> >
> > * How deeply down into the pairwise counts does the method look?
> >
> > * How convoluted is the counting process?
> >
> > The Schulze method looks very deeply into the pairwise counts.  However,
> > its counting process is so convoluted that it's very difficult to
> > comprehend.
> >
> > I suspect that that convolution causes lots of IIA failures.
>
> I'm not sure, since the elegance of an object doesn't need to relate to
> the simplicity of the algorithm that finds them. E.g. it's very easy to
> say what a prime number is, but a polynomial time deterministic
> algorithm to determine if a number is prime can be quite complex.
>
> >
> > Research is needed to measure failure rates.
> >
> > I really don't know what those measurements will reveal.
> >
> > Interestingly, Yee diagrams serve as a simple way to measure some IIA
> > failure rates.  They clearly reveal the IIA failures of IRV.
> >
> > We need something even better to identify and measure the failure rates
> > of better counting methods.
> >
> > The graph I generated and referred to is just a beginning.  We need lots
> > more research that measures failure RATES.  Just looking at
> > pass-versus-fail checkboxes is not looking deep enough.
>
> Here's a simple result for IIA.
>
> Define an election under a method M as failing IIA if:
>         - The original winner according to M is X, and
>         - It is possible to remove one or more candidates who aren't X, so
> that
> the winner instead becomes some other candidate Y.
>
> Then, for a Condorcet method, an election fails IIA iff it has no
> Condorcet winner. Remove every candidate in the cycle, except for the
> one who beats X pairwise, and then that candidate is the Y who wins.
>
> For a non-Condorcet method, if it works like majority rule when there
> are only two candidates, the election fails IIA either if there's no CW,
> or if there is a Condorcet winner that the method doesn't elect.
>
> In either case, you just remove everybody except the current winner and
> a candidate who beats him pairwise.
>
> So here for Condorcet methods, the IIA rate is simply the rate of non-CW
> elections under the election distribution in question (impartial
> culture, spatial, etc). It is not affected by other properties like
> monotonicity, reversal symmetry, clone dependence, or even LIIA.
>
> And the rate for non-Condorcet methods depends directly on how often
> they fail Condorcet, and not on other properties either.
>
> -km
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>
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