[EM] MinLV(erw) Sorted Margins Elimination

[Forest Simmons]

On Thu, May 4, 2023, 1:25 AM C.Benham <cbenham at adam.com.au> wrote:

>
> I made a strange mistake in the working out of my first example (but not
> the result).  Below it is corrected.
>
> (I actually first made the mistake in 2016 and I soon noticed it then and
> posted a corrected version, but what I posted last month
> was mostly copied from the initial uncorrected post. )
>
> Chris Benham
>
>
> My favourite method that meets both Condorcet and Chicken Dilemma is 'Min
> Losing-Votes (equal-ranking whole) Sorted Margins Elimination':
>
> *Voters rank from the top whatever number of candidates they like.
> Equal-ranking and truncation are allowed.
>
> For the purpose of determining candidates' pairwise scores:
>
> a ballot that votes both X and Y above no other (remaining) candidates
> contributes nothing to X's pairwise score versus Y and vice versa,
>
> a ballot that ranks X and Y equal and above at least one (remaining)
> candidate contributes a whole vote to X's pairwise score versus Y and vice
> versa,
>
> a ballot that ranks X above Y contributes a whole vote to X's pairwise
> score versus Y and nothing to Y's  pairwise score
> versus X.
>
> Give each candidate X a score equal to X's smallest losing pairwise score.
>
> Initially order the candidates from highest-scored to lowest scored. If
> any adjacent pair is out-of-order pairwise, then swap
> the out-of-order pair with the smallest score-difference. If there is a
> tie for that then swap the tied pair that is lowest in
> the order. Repeat until no adjacent pair is pairwise out-of-order, and
> then eliminate the lowest-ordered candidate.
>
> Repeat (disregarding any pairwise scores with eliminated candidates) until
> one candidate  remains. *
>
> Some examples:
>
> 46 A>B
> 44 B>C (sincere is B or B>A)
> 05 C>A
> 05 C>B
>
> A>B 51-49,    B>C  90-10,    C>A 54-46.
>
> MinLV(erw)  scores: B49 > A46 > C10.
>
> Both adjacent pairs (B>A and A>C) are pairwise out of order. The B>A
> score-difference is the smallest of the two
> (3 versus 36) so we first swap that order to give
>
> A49 > B51 > C10
>
> Now neither pair of adjacent candidates is pairwise out of order so C is
> eliminated and A wins.
>
> Winning Votes, Margins,  MMPO elect the Burier's candidate.
>
> 25 A>B
> 26 B>C
> 23 C>A
> 26 C
>
> C>A  75-25,    A>B  48-26,   B>C  51-49.
>
> MinLV(erw) scores:   C49 > B26 > A25.
>
> Both adjacent pairs (C>B and B>A) are pairwise out-of-order. The B-A score
> difference is by
> far the smallest, so we swap  the B>A order to give
>
> C > A > B.   That order is final and C wins.  C is the most top ranked and
> the most above-bottom ranked
> candidate.  WV, MMPO,  IRV, Benham elect B.
>
> 35 A
> 10 A=B
> 30 B>C
> 25 C
>
> C>A  55-45,     A>B  45-40 (note 10A=B effect),   B>C 40-25.
>

I noticed that A has more losing votes (45) than B has wining votes (40).

It seems to me that this fact (by itself) should disqualify B.

Also B is Ranked on feet ballots (40) than A is ranked Top (45) so
Plurality requires B to los as well.

So how about this as a tournament versión of Plurality:

If B's maxPairwiseSuppoft is less than A's minPS, then B should not win.

Anybody ever proposed this Criterion before?

>
>
> MinLV(erw) scores:   A45 > B40 > C25.  Neither adjacent pair is pairwise
> out-of-order  so the order is final
> and A wins.
>
> A both pairwise-beats and positionally dominates B, but WV, Margins, MMPO
> all elect B.
>
> Chris Benham
>
>
>
>
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