# [EM] Is this another formulation of Benham's new method?

Thu May 1 07:26:50 PDT 2014

```Forest,
> Is Condorcet(MaxPO(tw)) equivalent to Condorcet(MinLV(eq rank
> whole))?  If so the margins versions would be equivalent too.
>
> "PO" stands for "Pairwise Opposition,"  and "tw" for "Truncation
> Whole," which means that if two candidates are truncated together on a
> ballot they are both counted in opposition to each other.

It looks like yes.

35 A>B
25 B
40 C

C > A  40-35,    A>B 35-25,   B>C 60-40.      MinMax (Losing Votes)
scores:  C40 > A35 > B25.   (Margins Sort keeps this order).

Forest's suggested  "truncation whole" version:
C>A 65-60,    A>B 75-65,   B>C 60-40.        Max Pairwise Opposition
(truncation whole) scores:  C60 < A65 < B75 .

The smaller a candidate's Max PO score the better for it.   I'll look at

Chris Benham

On 5/1/2014 6:05 AM, Forest Simmons wrote:
> Is Condorcet(MaxPO(tw)) equivalent to Condorcet(MinLV(eq rank
> whole))?  If so the margins versions would be equivalent too.
>
> "PO" stands for "Pairwise Opposition,"  and "tw" for "Truncation
> Whole," which means that if two candidates are truncated together on a
> ballot they are both counted in opposition to each other.
>
> With this convention the Pairwise Opposition (tw) from candidate A
> against candidate B is the number N of ballots on which A is ranked
> strictly above B plus the number of ballots on which A and B are
> truncated together.
>
> With the equal rank whole convention, the LV strength of the defeat of
> B by A is the number M of ballots on  which B is ranked (but not
> truncated!) above or equal to A.
>
> Careful consideration reveals N+M is a constant, namely the total
> number of ballots, since no case was left out or counted more than once.
>
> This suggests a formulation of Benham's new method that we could call
> MPO(tw) Sorted Pairwise Margins. in analogy to Approval Sorted
> Pairwise Margins.
>
> List the candidates in order of MPO(tw) scores, and then adjust the
> list by reversal of adjacent pairs that are out of pairwise defeat
> order taking into account how close they are in their scores.
>
> I believe that the above discussion shows that this formulation is
> equivalent to Benham's MaxMinLV(erw) Margins method.
>
> The truncation whole (tw) convention forces MMPO(tw) to comply with
> Plurality.  The pairwise sorting feature makes it comply with Smith.
>
> But this brings up another method:  Majority Enhanced MPO(tv), in
> analogy with Majority Enhanced Approval:
>
> Initiate a list L with the name of the candidate with the least
> MPO(tv).  Then while there is any candidate that covers all of the
> candidates listed, from among such candidates add to the list the name
> of the one with the least MPO(tw). Elect the last candidate added to
> the list.
>
> Forest
>
>
>
>
> ----
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