# [EM] STAR Challenge

Forest Simmons forest.simmons21 at gmail.com
Tue Jun 28 16:22:36 PDT 2022

```El mar., 28 de jun. de 2022 5:29 a. m., Kristofer Munsterhjelm <
km_elmet at t-online.de> escribió:

> On 28.06.2022 01:21, Forest Simmons wrote:
>
> > So we see that in public elections this (Banks!) method reduces to the
> > simple rule "Elect the lowest score candidate that defeats every higher
> > score candidate," which is another formulation of Score,Benham as well
> > as Ranked Pairs, River, and BeatPath,etc when defeat strength is
> > measured by winning score.
> >
> > Which of these equivalent formulations will be easiest to sell?
> >
> > I mention Banks only to add prestige to the method, and to show how to
> > generalize it to specialized, non-public elections that are likely to
> > have more interesting Smith structure (twisted prism, etc).
>
> Nice!
>
> I would lean towards the Benham phrasing, but that's probably because
> I've been considering how to tersely describe Benham lately:
>
> "A candidate defeats another if the former is ranked (rated) ahead of
> the latter on more ballots than vice versa.
>
> A candidate is undefeated if nobody (still in the running) defeats him.
>
> While there is no undefeated candidate, eliminate the Plurality (Range)
> loser.
>
> Elect the remaining undefeated candidate."
>
Excellent!

>
> Of course, with the first two sentences staying the same, you could
> replace the latter two sentences with:
>
> "Elect the lowest score candidate that defeats every higher score
> candidate",
>
> which is shorter but not as close to the mechanical procedure.
>

Your Benham formulation is much better psychologically. in particular, some
voters could get hung up on  "... elect the lowest score ..."  ...wondering
why lowest?

Also, (1) people are used to eliminations ... "How can it be a real voting
method without eliminations?"

And (2) they are more attuned to step-by-step procedures than
characterizations.

>
>
> If the jurisdiction is currently using Condorcet, or is the STAR method
> is intended as a first step to Condorcet proper, then "just do RP but
> with this defeat strength measure" might be more natural.
>

In any case, after defining the method ... as an aside ... "it turns out
that another way to find the exact same winner is Ranked Pairs, as long as
defeat strength is gauged by winning score rather than winning votes or
margins."

RP(winning score): Go down the list of candidates one-by-one in order of
decreasing score. When you get to candidate X, lock in all of the defeats
where X is the victor, unless that would contradict a previously locked in
defeat.
ETC.

>
> I guess you lose monotonicity

Actually RP(winning score) is perfectly monotone ... and so all of its
equivalent variants. The Banks efficient method is not equivalent, but does
elect the same candidate when Smith has fewer than four members ... as does
STAR when restricted to Smith (when Smith has fewer than four members).

because it's hard to get all of Banks,
> monotonicity, and polynomial runtime.

> -km
>

Another interesting method to consider is RP(losing score) where the defeat
weakness is the score of the defeated candidate ... i.e. the strength is
the reciprocal of the score of the pairwise loser.

This version of RP always elects the same candidate as Sequential Pairwise
Elimination where the agenda is the score order from lowest to highest.

Furthermore, in the case of #Smith<4, this method always elects the highest
score Smith member.

If I remember correctly, Score(Smith) had the highest VSE of all the
methods tested. And I bet the VSE of Score SPE would agree to several
decimal places, since even in the rare cases of #Smith>3, it is more likely
than not that Score(Smith) winner would also be the Score SPE winner, etc.

I'm not suggesting abandoning RP(winning score) for RP(losing acore); it
wouldn't be worth giving up your Benham formulation of RP(ws).

I haven't checked yet, but I'm guessing that RP(score margins) is another
description of Score Sorted Margins, which would be a great proposal, but
not as good psychologically as your Benham proposal.

-Forest

>
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