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

[Forest Simmons]

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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20140430/265a81c4/attachment-0003.htm>