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<p><font size="4">Thanks. Do you think that it is possible to make
such an example without a sub-cycle?<br>
<br>
Because if not I am not overly perturbed. If you don't have a
ready answer I'll get around to<br>
thinking more about it myself.<br>
<br>
We have the option of solving the clone problem by making it a
one-at-time elimination method:<br>
use it find the lowest-ordered candidate, then eliminate that
candidate and repeat and so on until<br>
one remains.<br>
<br>
(But of course that makes it more complex and possibly stuffs up
mono-raise.)<br>
<br>
In your first matrix it was the diagonal row of "500"s that
confused me. I was expecting it to be blanks<br>
or zeroes.<br>
<br>
Chris<br>
</font></p>
<pre
style="white-space: pre-wrap; color: rgb(0, 0, 0); font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;"><font
size="4"> </font></pre>
<p><font size="4"><br>
<br>
</font></p>
<blockquote type="cite"><font size="4"><b
style="color: rgb(0, 0, 0); font-family: "Times New Roman"; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: normal; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;">Joshua
Boehme</b><span
style="color: rgb(0, 0, 0); font-family: "Times New Roman"; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: normal; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;"><span> </span></span><a
href="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"
title="[EM] "Margin Sorted Minimum Losing Votes (equal rated whole)" candidate in poll"
style="font-family: "Times New Roman"; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: normal;">joshua.p.boehme
at gmail.com</a><br
style="color: rgb(0, 0, 0); font-family: "Times New Roman"; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: normal; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;">
<i
style="color: rgb(0, 0, 0); font-family: "Times New Roman"; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: normal; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;">Fri
Apr 12 04:16:24 PDT 202<b>4</b></i></font>
<hr
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<pre
style="white-space: pre-wrap; color: rgb(0, 0, 0); font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;"><font
size="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:
><i> Joshua,
</i>><i>
</i>><i> I am finding this pairwise matrix confusing and hard to understand.
</i>><i>
</i>><i> Is there any chance we can see the original ballot set?
</i>><i>
</i>><i> Chris Benham</i></font></pre>
</blockquote>
<blockquote type="cite">
<pre
style="white-space: pre-wrap; color: rgb(0, 0, 0); font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;"><font
size="4">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.</font></pre>
</blockquote>
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