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

[Chris Benham]

Thanks. Do you think that it is possible to make such an example without 
a sub-cycle?

Because if not I am not overly perturbed. If you don't have a ready 
answer I'll get around to
thinking more about it myself.

We have the option of solving the clone problem by making it a 
one-at-time elimination method:
use it find the lowest-ordered candidate, then eliminate that candidate 
and repeat and so on until
one remains.

(But of course that makes it more complex and possibly stuffs up 
mono-raise.)

In your first matrix it was the diagonal row of "500"s that confused me. 
I was expecting it to be blanks
or zeroes.

Chris



> *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=%3C0829ef7b-1d7f-4c1c-8d7a-8b19f9ec3f1b%40gmail.com%3E>
> /Fri Apr 12 04:16:24 PDT 202*4*/
> ------------------------------------------------------------------------
> 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/
> 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.
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