A   B   C   D   E

 A   B   D   E   C

 C   A   B

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.

 A   B    C    D    E

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. > > >