[EM] MinLV(erw) Sorted Margins Elimination

[Forest Simmons]

On Sun, Jun 4, 2023, 11:03 PM C.Benham <cbenham at adam.com.au> wrote:

>
> 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".
>

Me too. I cannot make that kind of method (weakest link cycle breaking)
sufficiently burial resistant ... no matter how I define defeat strength.

My current thinking (based on geometrically motivated ballot sets) is that
non trivial top cycles are more likely to be artificial than sincere, and
the simplest, most likely mechanism (for creating promising cycles) is
unilateral burial or strategic truncation of the sincere CW by some faction.

And it seems to me if this guess is more or less accurate, our top
Condorcet design priority should be to "not reward the buriers" ... as
opposed to detecting a sincere signal in a noisy ballot set ... i.e. one
riddled by mistaken but sincere judgments ... the kind of ballot set where
weakest link cycle breaking would be indicated.

Forest



> 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 is 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
>>
>>
>>
>>
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