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<p>Joshua,<br>
<br>
<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;">In an A versus B comparison, since A's "winning votes" are the ones for A, A's "losing votes" would be the ones for B.</pre>
</blockquote>
A's ("winning" or "losing") votes are only votes for A. In an A
versus B comparison, the votes for A are "losing" if A loses that
pairwise contest and "winning" if A wins it.<br>
<br>
The votes for B in that contest are not "A's losing votes". It
might be ok English to call them "A's *opposing* votes", but
no-one mentioned anything like that.<br>
<br>
<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;">If B did *worse* against C (B beats C by less than 4), B becomes the winner under this method.
</pre>
</blockquote>
<br>
That would be an example of the failure of Mono-raise that I
mentioned. The methods that all behave like MinMax when there are
just 3 candidates all meet it.<br>
<br>
BTW, Gross Loser Elimination (or any Winning Votes method) can't
function with only a "margin matrix". The gross scores are
needed.<br>
<br>
Chris<br>
<br>
<br>
<br>
<blockquote type="cite"><b
style="color: rgb(0, 0, 0); font-family: "Times New Roman"; font-size: medium; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; 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-size: medium; 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; 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%20Poll%20on%20voting-systems%2C%0A%20to%20inform%20voters%20in%20upcoming%20enactment-elections&In-Reply-To=%3C8516d62a-9f4a-4390-a5b8-8673bb1a9fbb%40gmail.com%3E"
title="[EM] Poll on voting-systems, to inform voters in upcoming enactment-elections"
style="font-family: "Times New Roman"; font-size: medium; 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; white-space: normal;">joshua.p.boehme
at gmail.com</a><br
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<i
style="color: rgb(0, 0, 0); font-family: "Times New Roman"; font-size: medium; 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; white-space: normal; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;">Sat
Apr 20 04:15:16 PDT 2024</i><span
style="color: rgb(0, 0, 0); font-family: "Times New Roman"; font-size: medium; 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; 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>
<p
style="color: rgb(0, 0, 0); font-family: "Times New Roman"; font-size: medium; 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; white-space: normal; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;"><br>
</p>
<hr
style="color: rgb(0, 0, 0); font-family: "Times New Roman"; font-size: medium; 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; white-space: normal; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;">
<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;">In an A versus B comparison, since A's "winning votes" are the ones for A, A's "losing votes" would be the ones for B. Eliminating the candidate with the worst pairwise defeat is completely unambiguous, though.
Interestingly this doesn't always resolve a three-way cycle in the typical way (margin matrix is row candidate over column candidate)...
A B C
A 0 2 -4
B -2 0 6
C 4 -6 0
C gets eliminated, leaving A as the winner over B. Most methods would break A's weak win over B and make B the winner.
If B did *worse* against C (B beats C by less than 4), B becomes the winner under this method.
On 4/20/24 04:05, Chris Benham wrote:
><i>
</i>><i> Joshua,
</i>><i>
</i>><i> The wording is correct and the English seems plain to me.
</i>><i>
</i>><i> You just keep eliminating the candidate that has (among remaining candidates) the worst (as measured by losing votes) pairwise loss.
</i>><i>
</i>><i> 49 A
</i>><i> 24 B
</i>><i> 27 C>B
</i>><i>
</i>><i> A>C 49-27, C>B 27-24, B>A 51>49</i></pre>
</blockquote>
<br>
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