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<p>Dan, <br>
<br>
The new short version of your paper I also find opaque. Earlier
you agreed with Andrew that <br>
<br>
<blockquote type="cite">It seems like the short version is that
the winner is the candidate with the smallest sum of SQUARES of
non-victories (defeats plus ties) against their opponents.</blockquote>
<br>
And then you told me that in this example<br>
<br>
46 A<br>
44 B>C<br>
10 C<br>
<br>
your K-count method elects A.<br>
<br>
C>A 54-46, A>B 46-44, B<C 44-10<br>
<br>
Each candidate has only one "non-victory". So then I take it
then, using Andrew's version the winner is C, because squaring
the pairwise non-victory scores of C44, B46, A54 doesn't change
their order and C's is the smallest.<br>
<br>
Obviously one of us has it wrong.<br>
<br>
Chris<br>
<br>
<br>
</p>
<div class="moz-cite-prefix">On 20/05/2025 8:58 am, Daniel Kirslis
via Election-Methods wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAFFnmiartw1c57xpp8D7ksqF5PRCqDjNK4zbCdbKJgcn4pZY+w@mail.gmail.com">
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<div dir="ltr">Hi Chris,
<div><br>
</div>
<div>Yes, that is correct. I have created a simplified version
of the paper that attempts to explain the method in the most
concise possible way. It's only two pages: <a
href="https://drive.google.com/file/d/1F_I2ZBUKXKbmcS-uSvMAf_gNdNO8m0GB/view?usp=drive_link"
moz-do-not-send="true" class="moz-txt-link-freetext">https://drive.google.com/file/d/1F_I2ZBUKXKbmcS-uSvMAf_gNdNO8m0GB/view?usp=drive_link</a></div>
<div><br>
</div>
<div>It skips over a lot of the background that explains why I
view this as a compromise between the Borda count and
Condorcet methods and just focuses on explaining the method
itself. Once you see how the plotting works, it is like Bocce
Ball - closest to the target ball wins.</div>
<div><br>
</div>
<div>Thank you for your engagement on this. I should have
started with this version of the paper!</div>
</div>
<br>
<div class="gmail_quote gmail_quote_container">
<div dir="ltr" class="gmail_attr">On Mon, May 19, 2025 at
12:32 PM Chris Benham via Election-Methods <<a
href="mailto:election-methods@lists.electorama.com"
moz-do-not-send="true" class="moz-txt-link-freetext">election-methods@lists.electorama.com</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote"
style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div>
<blockquote type="cite">
<div style="font-family:Arial,sans-serif;font-size:14px"><br>
</div>
<div style="font-family:Arial,sans-serif;font-size:14px">It
seems like the short version is that the winner is the
candidate with the smallest sum of SQUARES of
non-victories (defeats plus ties) against their
opponents.</div>
</blockquote>
<div><br>
I take that these numbers you are squaring are the
candidate's opposing and tying vote scores, and not simply
the number of such results. Is that right? <br>
<br>
Because otherwise that would often be very indecisive,
like Copeland.<br>
<br>
<br>
On 19/05/2025 1:40 am, Andrew B Jennings (elections) via
Election-Methods wrote:<br>
</div>
<blockquote type="cite">
<div style="font-family:Arial,sans-serif;font-size:14px">Hi
Dan,</div>
<div style="font-family:Arial,sans-serif;font-size:14px"><br>
</div>
<div style="font-family:Arial,sans-serif;font-size:14px">Great
paper. Thank you for posting!</div>
<div style="font-family:Arial,sans-serif;font-size:14px"><br>
</div>
<div style="font-family:Arial,sans-serif;font-size:14px">It
seems like the short version is that the winner is the
candidate with the smallest sum of SQUARES of
non-victories (defeats plus ties) against their
opponents.</div>
<div style="font-family:Arial,sans-serif;font-size:14px"><br>
</div>
<div style="font-family:Arial,sans-serif;font-size:14px">Taking
the square root and dividing can make it meaningful by
scaling it to [0,1] or [0,s] (where s is the number of
voters), but doesn't change the finish order.</div>
<div style="font-family:Arial,sans-serif;font-size:14px">
<div> </div>
<div> </div>
</div>
<div style="font-family:Arial,sans-serif;font-size:14px"><br>
</div>
<div style="font-family:Arial,sans-serif;font-size:14px">It
does seem like an interesting attempt to "square the
circle" (great pun) and compromise between Borda and
Condorcet. I hadn't realized that Borda and Minimax are
minimizing the one-norm and infinity-norm in the same
geometric space. The two-norm certainly seems like it
should be explored.</div>
<div style="font-family:Arial,sans-serif;font-size:14px"><br>
</div>
<div style="font-family:Arial,sans-serif;font-size:14px">I
would love to see the proof of non-favorite-betrayal.</div>
<div style="font-family:Arial,sans-serif;font-size:14px"><br>
</div>
<div style="font-family:Arial,sans-serif;font-size:14px">Best,</div>
<div style="font-family:Arial,sans-serif;font-size:14px"><br>
</div>
<div style="font-family:Arial,sans-serif;font-size:14px">~
Andy</div>
<div> On Thursday, May 15th, 2025 at 4:25 PM, Daniel
Kirslis via Election-Methods <a
href="mailto:election-methods@lists.electorama.com"
target="_blank" moz-do-not-send="true"><election-methods@lists.electorama.com></a>
wrote:<br>
<blockquote type="cite">
<div dir="ltr">
<div>
<div>Hello!</div>
<div><br>
</div>
<div>I am a newcomer to this mailing list, so
please forgive me if this message violates any
norms or protocols that the members of this list
adhere to. </div>
<div><br>
</div>
<div>I have recently developed a novel method for
tabulating ranked-choice elections that attempts
to reconcile the concerns of Borda and
Condorcet. I believe that it maintains the
simplicity and mathematical elegance of the
Borda count while incorporating Condorcet's
concern with pairwise dominance. Intuitively, it
can be understood as ordering candidates by how
close they come to being unanimously selected
when plotted in Cartesian coordinate space. Here
is a link to the paper:</div>
<div><a rel="noreferrer nofollow noopener"
href="https://drive.google.com/file/d/152eNheS2qkLHJbDvG4EwW3jdO4I_NwcX/view?usp=sharing"
target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">https://drive.google.com/file/d/152eNheS2qkLHJbDvG4EwW3jdO4I_NwcX/view?usp=sharing</a></div>
</div>
<div><br>
</div>
<div>Given its simplicity, I have been very
surprised to discover that this method has never
been proposed before. I am hoping that some of you
all will take a look at the paper and share your
comments, questions, and critiques. Ultimately, it
is my hope that ranked-choice voting advocates can
arrive at a consensus about the best method for
RCV and thus strengthen efforts to adopt it and
deliver much needed democratic improvements. But
even if you don't find the system itself
compelling, you may find the method of plotting
electoral outcomes elucidated in the paper to be
useful for the analysis of other electoral
systems.</div>
<div><br>
</div>
<div>Thank you!</div>
<div><br>
</div>
<div>-Dan</div>
</div>
</blockquote>
<br>
</div>
<br>
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