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

Fri May 2 00:46:28 PDT 2014

```Forest wrote:

> But this brings up another method:  Majority Enhanced MPO(tw), in
> analogy with Majority Enhanced Approval:
>
> Initiate a list L with the name of the candidate with the least
> MPO(tw).  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.

That doesn't seem to resist Burial as well as  MMLV(erw)M.  In this
example I gave in an earlier recent post:

> 34 A>B
> 17 C>A
> 16 B>C
> 31 B
> 02 B>C  (sincere is B or B>A)
>
> A is the sincere Condorcet winner (and a sincere Mutual Dominant Third
> winner).
>
> A>B>C>A.    MMLV(erw)  scores:  B49 > A34 > C17. The margin between
> adjacent candidates B and A (15)  is smaller than
> that between A and C (17), and A pairwise beats B, so Margins Sort
> first flips that order to give A>B>C with no candidate pairwise
> beating the next highest in the order, and so elects the candidate
> highest in this final order, A.
>
> C>A -17,   A>B -15,   B>C +32.      A has the weakest defeat and so wins.

MPO (tw) scores:   B51 > A66 > 83    B (the buriers' candidate)  has the
smallest PO(tw) score and is uncovered and so wins.

Likewise in another earlier example:

> 46 A
> 44 B>C (sincere is B or B>A)
> 05 C>A
> 05 C>B
>
> A>B 51-49,  B>C  44-10,  C>A 54-46.   MinMax (Losing Votes) scores:
> B49,  A46,  C10.

MPO(tw) scores:  B51 > A56 > C90

Again the Burier's candidate B wins with Forest's suggested " Majority
Enhanced MPO(tw)" method.  MMLV(erw)M elects A, and if all of 46A change
to A>B it still elects A.

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(tw), in
> analogy with Majority Enhanced Approval:
>
> Initiate a list L with the name of the candidate with the least
> MPO(tw).  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
>
>
>
>
> ----
> Election-Methods mailing list - seehttp://electorama.com/em  for list info

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