[EM] MinLV(erw) Sorted Margins Elimination

[C.Benham]

On 9/06/2023 9:31 pm, Kevin Venzke wrote:

> I think that max losing votes comes across as inherently non-monotone, since if a candidate
> X has two losing votes scores of 30 and 40, but then the latter is increased to 42 votes and
> the contest becomes a win, their max losing votes will drop from 40 to 30. It's then not
> clear how to guarantee that the decrease of this score is compensated for, in its effect, by
> the gain of a pairwise win.

Kevin,

Are talking about the  MinLV(erw) Sorted Margins Elimination method, and 
"max" instead of min is a typo?
If so, in the example I assume you mean the 30 (not the 40) is increased 
enough for it to stop being a loss.

It is very very rare for the Smith set to contain more than three 
members.  The members of the Smith set at some point
will be the only candidates left after the rest have been eliminated.  
Then it should be clear that X "gaining a pairwise win"
simply makes X the CW.

Chris

On 9/06/2023 9:31 pm, Kevin Venzke wrote:
> Hi Chris/Forest,
>
> Le lundi 5 juin 2023 à 01:03:25 UTC−5, C.Benham <cbenham at adam.com.au> a écrit :
>> 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.
> There was a concept of "pairwise Plurality" under which the problem is that B's maxPS is
> lower than the max opposition to B. So nothing to do with A. Similarly you could have
> "pairwise minimal defense" which says if you have a majority loss but no majority win, then
> you lose. It's considerably harder to meet than normal MD.
>
> B's maxPS is not actually less than A's minPS. The 45-40 above is based on MinLV's adjusted
> matrix.
>
> I think that minPS should always be understood to be zero, so that there isn't an inherent
> Clone-Winner issue with it.
>
> I think that max losing votes comes across as inherently non-monotone, since if a candidate
> X has two losing votes scores of 30 and 40, but then the latter is increased to 42 votes and
> the contest becomes a win, their max losing votes will drop from 40 to 30. It's then not
> clear how to guarantee that the decrease of this score is compensated for, in its effect, by
> the gain of a pairwise win.
>
>> 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.
> Yes, it was noticed as an aberration that methods accepted to satisfy Plurality would elect B.
>
> I've always implemented Plurality as checking against strict first preferences only.
>
> When you use WV, in fact MinMax still doesn't satisfy Plurality:
>
> 39: C
> 29: A>B
> 20: D>A>B
> 12: B>D>C
>
> D wins, agreeing with MMPO but basically nothing else.
>
> (Margins would elect A, which is allowed by Plurality, but is still a very unusual choice.
> To compare, generally MD methods elect B, and LNHarm methods pick C.)
>
> Kevin
> votingmethods.net