[EM] MinLV(erw) Sorted Margins Elimination

[C.Benham]

On 5/06/2023 9:16 am, Forest Simmons wrote:
> 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.
>
> 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?

I and/or Kevin Venzke may have mentioned it in passing.  The example is 
originally from Kevin.

I agree that is a good criterion  and should be a strong standard. I 
quite a while ago rejected the idea
that the best Condorcet methods were those that focused purely on 
"defeat strengths" with a view to
simply "break the cycle at its weakest link".

> Also B is Ranked on fewer ballots (40) than A is ranked Top (45) so 
> Plurality requires B to lose as well.
>
The Plurality criterion was coined by Douglas Woodall, who only 
discussed ballots with strict ranking from
the top with truncation allowed.  So it says that that B isn't allowed 
to win if B is voted above bottom on fewer
ballots than A is voted alone above all others.

So it generally accepted that Winning Votes meets the ("normal", 
original)  Plurality criterion.

Chris Benham

>
>
> On Thu, May 4, 2023, 1:25 AM C.Benham <cbenham at adam.com.au> wrote:
>
>
>
>
>     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
>
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20230605/99937c05/attachment-0001.htm>