# [EM] New Criterion

Forest Simmons fsimmons at pcc.edu
Tue May 20 16:42:56 PDT 2014

```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>
> To: election-methods at lists.electorama.com
> Subject: Re: [EM] New Criterion
> 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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