[EM] "Margin Sorted Minimum Losing Votes (equal rated whole)" candidate in poll

[Joshua Boehme]

I manually tweaked a margin matrix from an existing example I keep on hand. In case you find it easier to think in those terms (I do), here it is...

     A   B    C    D    E
A   0  50  -30  -30  -30
B -50   0   20   20   20
C  30 -20    0  100 -300
D  30 -20 -100    0  200
E  30 -20  300 -200    0

The original emails defined the method in terms of votes cast for each candidate, so I restated it in those terms (and added enough votes to make it feasible). With completely ordered ballots, I think it doesn't matter which of those two bases you apply the method to.


Here's one set of ballots that produces those pairwise comparisons and has C, D, and E as clones on every ballot:

35   ABCDE
450  BADEC
115  CDEAB
200  CEDAB
175  ECDAB
25   BECDA


On 4/12/24 05:05, Chris Benham wrote:
> Joshua,
> 
> I am finding this pairwise matrix confusing and hard to understand.
> 
> Is there any chance we can see the original ballot set?
> 
> Chris Benham
> 
> 
> 
> 
>> *Joshua Boehme*joshua.p.boehme at gmail.com <mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20%22Margin%20Sorted%20Minimum%20Losing%20Votes%20%28equal%20rated%20whole%29%22%0A%20candidate%20in%20poll&In-Reply-To=%3C14996a2d-f932-4966-91bb-318241c74e08%40gmail.com%3E>
>> /Thu Apr 11 23:58:28 PDT 2024/
>>
>>
>> ------------------------------------------------------------------------
>> If I'm understanding this correctly, this method isn't always cloneproof. Consider the following pairwise matrix (entries are row candidate over column candidate)...
>>
>>       A   B   C   D   E
>> A 500 525 485 485 485
>> B 475 500 510 510 510
>> C 515 490 500 550 350
>> D 515 490 450 500 600
>> E 515 490 650 400 500
>>
>> The initial ordering is:
>>
>>     A   B   D   E   C
>> 485 475 450 400 350
>>
>> which is pairwise correct so we don't switch any candidates.
>>
>>
>> If you drop D and E, which are clones of C, you get:
>>
>>     C   A   B
>> 490 485 475
>>
>> which is also pairwise correct.
> 
> 
>