[EM] New Criterion

[C.Benham]

> "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.

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.

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
>
>
>
>
>     Date: Wed, 21 May 2014 03:53:38 +0930
>     From: "C.Benham" <cbenham at adam.com.au <mailto:cbenham at adam.com.au>>
>     To: election-methods at lists.electorama.com
>     <mailto:election-methods at lists.electorama.com>
>     Subject: Re: [EM] New Criterion
>     Message-ID: <537B9DAA.4030406 at adam.com.au
>     <mailto:537B9DAA.4030406 at adam.com.au>>
>     Content-Type: text/plain; charset="iso-8859-1"; Format="flowed"
>
>     Forest,
>
>     I've been meaning to remind you: for  IRV and  Benham   (and
>     Woodall and
>     similar) I'm strongly opposed to allowing voters to do any
>     equal-ranking
>     apart from truncating because it makes Push-over strategizing much
>     less
>     risky and more likely to succeed.
>
>     Two versions of ER-IRV have been discussed, one where an A=B ballot
>     gives a "whole vote" to each and one where it gives half a vote to
>     each,
>     i.e,
>     ER-IRV(whole) and  ER-IRV(fractional).   The problem I referred to is
>     much worse for the former and so I consider the latter to less bad.
>
>     But if we insist on allowing above-bottom equal-ranking and don't
>     mind a
>     lot of extra complexity, I have this suggestion:
>
>     *Before each elimination, order the candidates according to their
>     ER-IRV(fractional), (so that among continuing candidates a ballot that
>     equal-top
>     ranks n candidates give 1/n of a vote to each).
>
>     Then assign each of the ballots that equal-top rank more than one
>     candidate to whichever of them is highest in that order.
>
>     Then eliminate the candidate with the fewest ballots assigned to hir.*
>
>     34 A=B
>     31 B
>     35 C
>
>     So in this example of Forest's, to create the initial order the 34 A=B
>     ballots give half a vote each to A and B, to give the scores
>     B (31+17=48) > C35 > A17.
>
>     B is above A in this order, so all of the A=B ballots are assigned
>     to B.
>     This gives the scores B65 > C35 > A0.  A has the lowest score so
>     A is eliminated and B wins.
>
>     Chris  Benham
>
>
>
>
>
>
> ----
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