[EM] New Criterion

[Forest Simmons]

Date: Wed, 21 May 2014 19:19:21 +0930
> From: "C.Benham" <cbenham at adam.com.au>
> To: election-methods at lists.electorama.com
> Subject: Re: [EM] New Criterion
> Message-ID: <537C76A1.60105 at adam.com.au>
> Content-Type: text/plain; charset="iso-8859-1"; Format="flowed"
>
> > "for Benham, what if we count fractional (for equal rank top) as you
> > suggest when doing the IRV eliminations, but check at each step for a
> > pairwise beats all candidate in the usual way?"
>
> Forest,  That wouldn't be too bad.  But it seems to me that it would
> make Pushover strategizing less risky (than not allowing above-bottom
> equal-rankings) and since the method
> fails FBC  I didn't see sufficient justification for the extra complexity.
>
> > "In your example below, since B beats A pairwise 31 to zero and B
> > beats C 65 to 35, no IRV elimination step is required, so how equal
> > rank top is counted in this example does not seem to matter."
>
> Yes, Benham has less of a Pushover vulnerability problem than IRV.   I
> don't understand your other question.  Benham only checks for a single
> CW. "Symmetrically completing" pairwise
> contests can't make any difference to that.
>

True, symmetric completion wouldn't make any difference but I was wondering
if perhaps you intended counting 20 A=C as 10 A  and 10 C.

>
> A better example of my suggested way of getting extra "pushover
> resistance":
>
> 04: A=C  (sincere is A or A>B)
> 41 A
> 28 B>A
> 27 C>B
>
> B>A 55-45,    A>C 69-27,   C>B 31-28.   Top Preferences (erf):  A43 >
> C29 > B28
>
> B is the sincere CW (and so also the sincere Benham winner) and the
> sincere IRV winner. Benham and IRV elect A.
>
> My suggested variant looks at the order of candidates according to their
> TP(erf) scores and on seeing that A is higher in that order than C
> assigns the whole value of A=C ballots to A
> (and none of it to C) to give  A45 > B28 > C27 (purely for the purpose
> of the IRV component and not the pairwise component in Benham) and then
> eliminates C and elects B.
>

I'm glad that you have found a good way of allowing equal top ranking into
IRV and Benham, because without the possibility of equal top ranking it
would (more often) be impossible to find a semi-sincere Nash equilibrium
that preserved the sincere CW.

In that regard, if the sincere preferences are (according to one of your
suggestions)

45 A>B
28 B>A
27 C>B

wouldn't the following ballot set be a Nash equilibrium (including
deterrent for pushover) under both fractional and whole rules for equal top?

41 A>B
28 B>A
27 C=B

>
> Chris Benham
>
>
> On 5/21/2014 9:12 AM, Forest Simmons wrote:
> > Chris,
> >
> > for Benham, what if we count fractional (for equal rank top) as you
> > suggest when doing the IRV eliminations, but check at each step for a
> > pairwise beats all candidate in the usual way?
> >
> > In your example below, since B beats A pairwise 31 to zero and B beats
> > C 65 to 35, no IRV elimination step is required, so how equal rank top
> > is counted in this example does not seem to matter.
> >
> > Or is there some reason for doing a "symmetric completion" of equal
> > rankings for the pairwise contests as well?
> >
> > Forest
>
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