<html><head></head><body><div style="color:#000; background-color:#fff; font-family:Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:13px"><div id="yui_3_16_0_ym19_1_1559492825887_5603"><span>Chris</span></div><div id="yui_3_16_0_ym19_1_1559492825887_5603"><span><br></span></div><div id="yui_3_16_0_ym19_1_1559492825887_5603"><span id="yui_3_16_0_ym19_1_1559492825887_5707">Yes, that does seem reasonable. For A to positionally dominate B, I take it that means that for every rank position (above last) A has more of that rank or higher than B. A does look the more reasonable winner than B in your scenario.</span></div><div id="yui_3_16_0_ym19_1_1559492825887_5603"><span><br></span></div><div id="yui_3_16_0_ym19_1_1559492825887_5603"><span>Toby</span></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1559492825887_5604"><br><br></div><div class="yahoo_quoted" id="yui_3_16_0_ym19_1_1559492825887_5608" style="display: block;"> <div style="font-family: Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 13px;" id="yui_3_16_0_ym19_1_1559492825887_5607"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 16px;" id="yui_3_16_0_ym19_1_1559492825887_5606"> <div dir="ltr" id="yui_3_16_0_ym19_1_1559492825887_5605"> <font size="2" face="Arial" id="yui_3_16_0_ym19_1_1559492825887_5609"> <hr size="1"> <b><span style="font-weight:bold;">From:</span></b> C.Benham <cbenham@adam.com.au><br> <b><span style="font-weight: bold;">To:</span></b> Toby Pereira <tdp201b@yahoo.co.uk>; "cbenham@adam.com.au" <cbenham@adam.com.au>; "election-methods@lists.electorama.com" <election-methods@lists.electorama.com> <br> <b><span style="font-weight: bold;">Sent:</span></b> Saturday, 1 June 2019, 10:28<br> <b><span style="font-weight: bold;">Subject:</span></b> Re: [EM] Losing Votes (equal-ranking whole)<br> </font> </div> <div class="y_msg_container" id="yui_3_16_0_ym19_1_1559492825887_5613"><br><div id="yiv3120586576">
<div id="yui_3_16_0_ym19_1_1559492825887_5612">
<div id="yui_3_16_0_ym19_1_1559492825887_5611">Toby,<br>
<br>
I didn't coin the Plurality criterion, and I do somewhat prefer
your suggested alternative wording. To take account of equal-top
ranking being<br>
allowed, I would specify the fractional interpretation of "number
of ballots ranking A as the first preference". The original
coiner of the criterion<br>
was operating on the assumption that no equal-ranking would be
allowed (except at the bottom implied by truncation which would be
allowed) <br>
and perhaps also that no-one would needlessly mark a candidate
strictly bottom when they could just truncate.<br>
<br>
I think in part the criterion is tailor-made for voters accustomed
to and content with plurality voting, and after some new election
on ballots<br>
that allow voters to rank the candidates is used, they want to
know why B won while their favourite candidate A was voted (alone)
in first place<br>
on more ballots than B was voted above bottom. And I like the
criterion because I agree that there can't be a good enough
answer. <br>
<br>
A standard (and possible criterion) I like says that if A both
positionally dominates and pairwise beats B then B can't win. That
implies Plurality.<br>
</div>
<div dir="ltr">35: A<br clear="none">
</div>
<div dir="ltr" id="yui_3_16_0_ym19_1_1559492825887_5746">10: A=B<br clear="none">
</div>
<div dir="ltr" id="yui_3_16_0_ym19_1_1559492825887_5745">30: B>C<br clear="none">
</div>
25: C<br>
<div id="yui_3_16_0_ym19_1_1559492825887_5827">Here no ballots vote A or B below equal-top. A has more top (or
first) place votes than B so positionally dominates and pairwise
beats B.<br>
Do you think B is an acceptable winner?<br>
<br>
Chris Benham<br>
</div>
<div><br>
<br>
</div>
<div class="yiv3120586576moz-cite-prefix">On 29/05/2019 10:37 pm, Toby Pereira
wrote:<br>
</div>
<blockquote type="cite">
<div style="color:#000;background-color:#fff;font-family:Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:13px;">
<div id="yiv3120586576yui_3_16_0_ym19_1_1559134455557_8273" dir="ltr"><span id="yiv3120586576yui_3_16_0_ym19_1_1559134455557_8307">I don't have a
definite answer to the question of equally ranked ballots,
and to me I suppose it's still an open question exactly what
the best way forwards is, even if you make a good argument
against margins.</span></div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1559134455557_8273" dir="ltr"><span><br>
</span></div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1559134455557_8273" dir="ltr">I don't
have an example where the plurality criterion bars from
winning the candidate that I think should have won. Looking at
the definition on the Wikipedia: "If the number of ballots
ranking A as the first preference is greater than the number
of ballots on which another candidate B is given any
preference, then A's probability of winning must be no less
than B's.", it's more that I would disagree with the
terminology "given any preference."</div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1559134455557_8273" dir="ltr"><br>
</div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1559134455557_8273" dir="ltr">If the
definition was "If the number of ballots ranking A as the
first preference is greater than the number of ballots on
which another candidate B is ranked anything other than last
or joint last (either explicitly or through implication on a
truncated ballot), then A's probability of winning must be no
less than B's." then I'd be less critical of it. I think the
way it's worded implies an approval cut-off even if in
practice it makes no difference.</div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1559134455557_8273" dir="ltr"><br>
</div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1559134455557_8273" dir="ltr">Toby</div>
<div class="yiv3120586576qtdSeparateBR" id="yiv3120586576yui_3_16_0_ym19_1_1559134455557_8274"><br>
<br>
</div>
<div class="yiv3120586576yahoo_quoted" id="yiv3120586576yui_3_16_0_ym19_1_1559134455557_8278" style="display:block;">
<div style="font-family:Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:13px;" id="yiv3120586576yui_3_16_0_ym19_1_1559134455557_8277">
<div style="font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif;font-size:16px;" id="yiv3120586576yui_3_16_0_ym19_1_1559134455557_8276">
<div dir="ltr" id="yiv3120586576yui_3_16_0_ym19_1_1559134455557_8275">
<font id="yiv3120586576yui_3_16_0_ym19_1_1559134455557_8279" size="2" face="Arial">
<hr id="yiv3120586576yui_3_16_0_ym19_1_1559134455557_8306" size="1">
<b><span style="font-weight:bold;">From:</span></b>
C.Benham <a rel="nofollow" class="yiv3120586576moz-txt-link-rfc2396E" ymailto="mailto:cbenham@adam.com.au" target="_blank" href="mailto:cbenham@adam.com.au"><cbenham@adam.com.au></a><br>
<b><span style="font-weight:bold;">To:</span></b>
Toby Pereira <a rel="nofollow" class="yiv3120586576moz-txt-link-rfc2396E" ymailto="mailto:tdp201b@yahoo.co.uk" target="_blank" href="mailto:tdp201b@yahoo.co.uk"><tdp201b@yahoo.co.uk></a>;
<a rel="nofollow" class="yiv3120586576moz-txt-link-rfc2396E" ymailto="mailto:cbenham@adam.com.au" target="_blank" href="mailto:cbenham@adam.com.au">"cbenham@adam.com.au"</a> <a rel="nofollow" class="yiv3120586576moz-txt-link-rfc2396E" ymailto="mailto:cbenham@adam.com.au" target="_blank" href="mailto:cbenham@adam.com.au"><cbenham@adam.com.au></a>;
<a rel="nofollow" class="yiv3120586576moz-txt-link-rfc2396E" ymailto="mailto:election-methods@lists.electorama.com" target="_blank" href="mailto:election-methods@lists.electorama.com">"election-methods@lists.electorama.com"</a>
<a rel="nofollow" class="yiv3120586576moz-txt-link-rfc2396E" ymailto="mailto:election-methods@lists.electorama.com" target="_blank" href="mailto:election-methods@lists.electorama.com"><election-methods@lists.electorama.com></a> <br>
<b><span style="font-weight:bold;">Sent:</span></b>
Sunday, 26 May 2019, 20:19<br>
<b><span style="font-weight:bold;">Subject:</span></b>
Re: [EM] Losing Votes (equal-ranking whole)<br>
</font> </div>
<div class="yiv3120586576y_msg_container" id="yiv3120586576yui_3_16_0_ym19_1_1559134455557_8383"><br>
<div id="yiv3120586576">
<div id="yiv3120586576yui_3_16_0_ym19_1_1559134455557_8385">
<div id="yiv3120586576yui_3_16_0_ym19_1_1559134455557_8384">Toby,<br clear="none">
<br clear="none">
If you try to give that calculator a truncated
ballot it will just turn it into the sort of
ballot you like.<br clear="none">
<br clear="none">
How do you think equally-ranked ballots should be
counted in a pairwise comparison? A half-vote to<br clear="none">
each or zero to both?<br clear="none">
<br clear="none">
So you can't actually point to any election
example where the Plurality criterion bars from
winning the candidate <br clear="none">
that you think should have won?<br clear="none">
</div>
<div id="yiv3120586576yMail_cursorElementTracker_1558884457758">46:
A</div>
<div id="yiv3120586576yMail_cursorElementTracker_1558884462587">44:
B>C</div>
<div id="yiv3120586576yMail_cursorElementTracker_1558884480116">10:
C</div>
<div>Returning to this, are you happy with B
winning? And if not, why not?<br clear="none">
<br clear="none">
Chris Benham<br clear="none">
<br clear="none">
</div>
<div class="yiv3120586576yqt2928960308" id="yiv3120586576yqt29538">
<div class="yiv3120586576moz-cite-prefix">On
27/05/2019 3:38 am, Toby Pereira wrote:<br clear="none">
</div>
<blockquote type="cite"> </blockquote>
</div>
</div>
<div class="yiv3120586576yqt2928960308" id="yiv3120586576yqt91070">
<div>
<div style="color:#000;background-color:#fff;font-family:Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:13px;">
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237"><span id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4290">By unranked
candidates, I meant the ones that had not
had any sort of "vote" - the ones not
explicitly listed by the voter. If there are
three candidates in an election, A, B, and
C, I might like A but absolutely hate the
others. My vote might simply be:</span></div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237"><span><br clear="none">
</span></div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237"><span>A</span></div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237"><span><br clear="none">
</span></div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237"><span id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4394">On the other
hand, while I might still absolutely hate B
and C, I might still hate C more. So my vote
might be:</span></div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237"><span><br clear="none">
</span></div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237"><span>A>B</span></div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237"><span><br clear="none">
</span></div>
<div dir="ltr" id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237">But
just because I have ranked B on my ballot,
this should not be taken as any sort of
endorsement of B or a vote "for" B. <span><br clear="none">
</span></div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237"><span><br clear="none">
</span></div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237"><span id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4931">My vote could
also be:</span></div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237"><span><br clear="none">
</span></div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237"><span id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4929">A>B>C</span></div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237"><span><br clear="none">
</span></div>
<div dir="ltr" id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237"><span id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4502">Does adding C on
the end mean that I have in some sense voted
for C? I don't think there would actually be
any methods where adding C on the end would
have any effect on how the winner is
calculated, but the plurality criterion
would presumably in theory find it
acceptable to do so.</span></div>
<div dir="ltr" id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237"><span><br clear="none">
</span></div>
<div dir="ltr" id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237"><span id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4505">But this is more
a philosophical objection to the assumptions
implicit in the plurality criterion than an
an objection to the results that a method
obeying the criterion would produce in
practice. But anyway, I put my thoughts
about the plurality criterion a while ago
(as did Juho) here: </span><a rel="nofollow" shape="rect" class="yiv3120586576" id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4693" target="_blank" href="http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247">http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247</a></div>
<div dir="ltr" id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237"><br clear="none">
</div>
<div dir="ltr" id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237">But
anyway, thank you for the link to the
calculator.</div>
<div dir="ltr" id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237"><br clear="none">
</div>
<div dir="ltr" id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4237">Toby</div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4776"><br clear="none">
</div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4813"><br clear="none">
</div>
<div class="yiv3120586576qtdSeparateBR" id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4243"><br clear="none">
<br clear="none">
</div>
<div class="yiv3120586576yahoo_quoted" id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4264" style="display:block;">
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4263" style="font-family:Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:13px;">
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4262" style="font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif;font-size:16px;">
<div dir="ltr" id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4261">
<font id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4289" size="2" face="Arial"> </font>
<hr size="1"> <b><span style="font-weight:bold;">From:</span></b>
Chris Benham <a rel="nofollow" shape="rect" class="yiv3120586576moz-txt-link-rfc2396E" ymailto="mailto:cbenhamau@yahoo.com.au" target="_blank" href="mailto:cbenhamau@yahoo.com.au"><cbenhamau@yahoo.com.au></a><br clear="none">
<b><span style="font-weight:bold;">To:</span></b>
<a rel="nofollow" shape="rect" class="yiv3120586576moz-txt-link-rfc2396E" ymailto="mailto:tdp201b@yahoo.co.uk" target="_blank" href="mailto:tdp201b@yahoo.co.uk">"tdp201b@yahoo.co.uk"</a>
<a rel="nofollow" shape="rect" class="yiv3120586576moz-txt-link-rfc2396E" ymailto="mailto:tdp201b@yahoo.co.uk" target="_blank" href="mailto:tdp201b@yahoo.co.uk"><tdp201b@yahoo.co.uk></a>;
<a rel="nofollow" shape="rect" class="yiv3120586576moz-txt-link-rfc2396E" ymailto="mailto:cbenham@adam.com.au" target="_blank" href="mailto:cbenham@adam.com.au">"cbenham@adam.com.au"</a>
<a rel="nofollow" shape="rect" class="yiv3120586576moz-txt-link-rfc2396E" ymailto="mailto:cbenham@adam.com.au" target="_blank" href="mailto:cbenham@adam.com.au"><cbenham@adam.com.au></a>;
<a rel="nofollow" shape="rect" class="yiv3120586576moz-txt-link-rfc2396E" ymailto="mailto:election-methods@lists.electorama.com" target="_blank" href="mailto:election-methods@lists.electorama.com">"election-methods@lists.electorama.com"</a>
<a rel="nofollow" shape="rect" class="yiv3120586576moz-txt-link-rfc2396E" ymailto="mailto:election-methods@lists.electorama.com" target="_blank" href="mailto:election-methods@lists.electorama.com"><election-methods@lists.electorama.com></a>
<br clear="none">
<b><span style="font-weight:bold;">Sent:</span></b>
Sunday, 26 May 2019, 18:08<br clear="none">
<b><span style="font-weight:bold;">Subject:</span></b>
Re: [EM] Losing Votes (equal-ranking
whole)<br clear="none">
</div>
<div class="yiv3120586576y_msg_container" id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4268"><br clear="none">
<div id="yiv3120586576">
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4267">
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4266">Toby,<br clear="none">
<br clear="none">
You would like this old online
ranked-ballot voting calculator:<br clear="none">
<br clear="none">
<a rel="nofollow" shape="rect" id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4859" target="_blank" href="https://www.cse.wustl.edu/~legrand/rbvote/calc.html">https://www.cse.wustl.edu/~legrand/rbvote/calc.html</a><br clear="none">
<br clear="none">
What do you think are the "false
premises" that the Plurality
criterion is based on??? It was
coined with the assumption<br clear="none">
that voters could only strictly
rank from the top however many
candidates they wish, and those
not truncated had in<br clear="none">
some sense been "voted for". It
says that if A has more
first-place votes than B has any
sort of votes then B can't win.<br clear="none">
No explicit mention of "unranked
candidates".<br clear="none">
<br clear="none">
(Adapting it to ballots that allow
equal-ranking at the top,?? "first
preferences" refers to
first-preference score on the <br clear="none">
ballots symmetrically completed,
at least at the top, ballots).<br clear="none">
</div>
<div id="yiv3120586576yui_3_16_0_ym19_1_1558893123363_4878">To
sensibly claim that it is a
"mistake" for an algorithm to do
(or apparently "assume")
something, I think you need to <br clear="none">
point to something wrong with an
actual result of it doing so.<br clear="none">
<br clear="none">
My answer to your question is no.
<br clear="none">
</div>
<div>Chris Benham<br clear="none">
<br clear="none">
</div>
<div class="yiv3120586576moz-cite-prefix"><br clear="none">
On 27/05/2019 1:04 am, Toby
Pereira wrote:<br clear="none">
</div>
<blockquote type="cite"> </blockquote>
</div>
<div>
<div id="yiv3120586576ymail_android_signature">I
think it's a mistake to assume
some sort of approval of a ranked
candidate. If it's not explicitly
part of a method then you should
not infer it. As far as I'm
concerned:</div>
<div id="yiv3120586576yMail_cursorElementTracker_1558884457619"><br clear="none">
</div>
<div id="yiv3120586576yMail_cursorElementTracker_1558884457758">46:
A</div>
<div id="yiv3120586576yMail_cursorElementTracker_1558884462587">44:
B>C</div>
<div id="yiv3120586576yMail_cursorElementTracker_1558884480116">10:
C</div>
<div id="yiv3120586576yMail_cursorElementTracker_1558884503906"><br clear="none">
</div>
<div id="yiv3120586576yMail_cursorElementTracker_1558884504072">Is
the same as:</div>
<div id="yiv3120586576yMail_cursorElementTracker_1558884512155"><br clear="none">
</div>
<div id="yiv3120586576yMail_cursorElementTracker_1558884512327">46:
A>B=C</div>
<div id="yiv3120586576yMail_cursorElementTracker_1558884536910">44:
B>C>A</div>
<div id="yiv3120586576yMail_cursorElementTracker_1558884560941">10:
C>A=B</div>
<div id="yiv3120586576yMail_cursorElementTracker_1558884616720"><br clear="none">
</div>
<div id="yiv3120586576yMail_cursorElementTracker_1558884616935">Presented
with these ballots, does this
change who you think the winner
should be?</div>
<div id="yiv3120586576yMail_cursorElementTracker_1558884706281"><br clear="none">
</div>
<div id="yiv3120586576yMail_cursorElementTracker_1558884706524">This
isn't a defence of margins by me
or an argument against anything
else in your post, but I think the
plurality criterion, by talking
about unranked candidates, is
based on false premises.</div>
<div id="yiv3120586576yMail_cursorElementTracker_1558884772443"><br clear="none">
</div>
<div id="yiv3120586576yMail_cursorElementTracker_1558884772583">Toby</div>
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<blockquote style="margin:0 0 20px 0;">
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<div>On Sat, 25 May 2019 at
15:31, C.Benham</div>
<div><a rel="nofollow" shape="rect" class="yiv3120586576moz-txt-link-rfc2396E" ymailto="mailto:cbenham@adam.com.au" target="_blank" href="mailto:cbenham@adam.com.au"><cbenham@adam.com.au></a>
wrote:</div>
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<div dir="ltr">There are several
Condorcet algorithms that
decide the winner by <br clear="none">
</div>
<div dir="ltr">weighing "defeat
strengths" and they<br clear="none">
</div>
<div dir="ltr">are all
equivalent to MinMax when
there are no more than 3
candidates.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">The ones I have
in mind that are equal or very
nearly equal in merit are <br clear="none">
</div>
<div dir="ltr">River, Schulze,
Ranked Pairs, Smith//MinMax.<br clear="none">
</div>
<div dir="ltr">In public
political elections they are
very very unlikely to give <br clear="none">
</div>
<div dir="ltr">different
winners. River and
Smith//MinMax seem to me<br clear="none">
</div>
<div dir="ltr">to be the easiest
to understand and explain and
use. The other two are <br clear="none">
</div>
<div dir="ltr">perhaps a bit
more elegant and have their<br clear="none">
</div>
<div dir="ltr">enthusiastic
supporters.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">This is to make
the case that measuring
pairwise defeat strength by
the <br clear="none">
</div>
<div dir="ltr">number of votes
on the losing side with
above-bottom<br clear="none">
</div>
<div dir="ltr">equal-ranking
contributing a whole vote to
each side (and otherwise as <br clear="none">
</div>
<div dir="ltr">with normal
Winning Votes) is much better
than either<br clear="none">
</div>
<div dir="ltr">Winning Votes or
Margins.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">The case for
Losing Votes(erw) against
Margins is that it (in common
<br clear="none">
</div>
<div dir="ltr">with WV) it meets
the Plurality criterion and
the Non-Drastic<br clear="none">
</div>
<div dir="ltr">Defense
criterion.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">The case for
Losing Votes(erw) against
Winning Votes is that it meets
<br clear="none">
</div>
<div dir="ltr">the Chicken
Dilemma criterion and that is
much less likely<br clear="none">
</div>
<div dir="ltr">to fail to elect
a positionally dominant
uncovered candidate. (I don't
<br clear="none">
</div>
<div dir="ltr">see how it can
fail to elect such a candidate
in the 3-candidate case.)<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">For those who
think that Margins might be
acceptable:<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">46: A<br clear="none">
</div>
<div dir="ltr">44: B>C<br clear="none">
</div>
<div dir="ltr">10: C<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">A>B 46-44
(margin=2), B>C 44-10
(margin=34), C>A 54-46
(margin=8).<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Using Losing
Votes (erw) as the measure of
defeat strength, the weakest <br clear="none">
</div>
<div dir="ltr">defeat is the one
with the most votes on the
losing side.<br clear="none">
</div>
<div dir="ltr">That is the
C>A defeat so MinMax drops
that and A wins. Conversely
the <br clear="none">
</div>
<div dir="ltr">strongest defeat
is the one with the fewest
votes on the<br clear="none">
</div>
<div dir="ltr">losing side. That
is the B>C defeat so River
and Ranked Pairs lock <br clear="none">
</div>
<div dir="ltr">that. The second
strongest is the A>B defeat
so those methods<br clear="none">
</div>
<div dir="ltr">also lock that.
All but one candidate has been
thereby disqualified so B <br clear="none">
</div>
<div dir="ltr">wins, or we
ignore the third pairwise
defeat because that<br clear="none">
</div>
<div dir="ltr">makes a cycle, so
give a final order A>B>C
and A wins.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">To meet both of
the Plurality criterion and
the Chicken Dilemma <br clear="none">
</div>
<div dir="ltr">criterion A must
win.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Winning Votes
elects C, violating Chicken
Dilemma (which it has to do to
<br clear="none">
</div>
<div dir="ltr">meet the
previously fashionable Minimal
Defense criterion).<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Margins elects B.
This fails the Plurality
criterion because A has more <br clear="none">
</div>
<div dir="ltr">exclusive
first-place votes than B has
any sort of above-bottom<br clear="none">
</div>
<div dir="ltr">votes. It is also
an egregious and outrageous
failure of Later-no-Help <br clear="none">
</div>
<div dir="ltr">(assuming that if
all the ballots just vote for
one candidate we<br clear="none">
</div>
<div dir="ltr">elect the
plurality winner).<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">To anyone who is
remotely positionally or
strategically minded or has <br clear="none">
</div>
<div dir="ltr">any common sense
and isn't blind to everything
except the<br clear="none">
</div>
<div dir="ltr">Margins pairwise
matrix, B is clearly the
weakest candidate and a <br clear="none">
</div>
<div dir="ltr">completely
unacceptable winner.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">35: A<br clear="none">
</div>
<div dir="ltr">10: A=B<br clear="none">
</div>
<div dir="ltr">30: B>C<br clear="none">
</div>
<div dir="ltr">25: C<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">A>B 45-40
(erw, "normally" 35-30,
margin=5), B>C 40-25
(margin=15), <br clear="none">
</div>
<div dir="ltr">C>A 55-45
(margin=10).<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Voted at least
equal-top (or Top Ratings)
scores: A45, B40, C25.<br clear="none">
</div>
<div dir="ltr">Voted above
bottom (or Approval) scores:
A45, B40, C55<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">An old Kevin
Venzke example. B is neither
the most top-rated candidate <br clear="none">
</div>
<div dir="ltr">or the most
approved candidate and is<br clear="none">
</div>
<div dir="ltr">pairwise-beaten
and positionally dominated by
A (the most top-rated).<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Winning Votes and
Margins both elect the clearly
weakest candidate, B.<br clear="none">
</div>
<div dir="ltr">Losing Votes(erw)
elects A.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">For those who
prefer to have a method comply
with Minimal Defense (which <br clear="none">
</div>
<div dir="ltr">says that if on
more than half the ballots<br clear="none">
</div>
<div dir="ltr">C is voted above
A and A no higher than
equal-bottom then A can't win)
<br clear="none">
</div>
<div dir="ltr">rather than
Chicken Dilemma another method<br clear="none">
</div>
<div dir="ltr">I prefer to WV is
Smith//Approval which here
elects C.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">25: A>B<br clear="none">
</div>
<div dir="ltr">26: B>C<br clear="none">
</div>
<div dir="ltr">23: C>A<br clear="none">
</div>
<div dir="ltr">26: C<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">C>A 75-25
(margin=50), A>B 48-26
(margin=22), B>C 51-49
(margin=2).<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Voted at least
equal-top (or Top Ratings)
scores: C49, B26, A25.<br clear="none">
</div>
<div dir="ltr">Voted above
bottom (or Approval) scores:
C75, B51, A48.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">C is an
overwhelmingly positionally
dominant uncovered candidate.
<br clear="none">
</div>
<div dir="ltr">Margins and
Losing Votes elect C.<br clear="none">
</div>
<div dir="ltr">WV and IRV elect
B.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Now say we change
4 of the 26 C ballots to
A>C, thereby making C a bit
<br clear="none">
</div>
<div dir="ltr">weaker.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">25: A>B<br clear="none">
</div>
<div dir="ltr">26: B>C<br clear="none">
</div>
<div dir="ltr">23: C>A<br clear="none">
</div>
<div dir="ltr">22: C<br clear="none">
</div>
<div dir="ltr">04: A>C<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">C>A 71-29
(margin=42), A>B 52-26
(margin=26), B>C 51-49
(margin=2).<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Voted at least
equal-top (or Top Ratings)
scores: C45, B26, A29.<br clear="none">
</div>
<div dir="ltr">Voted above
bottom (or Approval) scores:
C75, B51, A52.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">The weakening of
C has caused WV and IRV to
change from B to C, now <br clear="none">
</div>
<div dir="ltr">agreeing with LV
and Margins.<br clear="none">
</div>
<div dir="ltr">Assuming the
change was from sincere to
insincere, those very lucky <br clear="none">
</div>
<div dir="ltr">and/or very well
informed 4 voters<br clear="none">
</div>
<div dir="ltr">have pulled off a
Push-over strategy.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">This is a failure
of Mono-raise-delete (more
obvious if we reverse the <br clear="none">
</div>
<div dir="ltr">order of the two
situations), which<br clear="none">
</div>
<div dir="ltr">is one of
Woodall's mononicity criteria
that he says is incompatible <br clear="none">
</div>
<div dir="ltr">with Condorcet.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Nonetheless in
this case C is still the
positionally dominant
uncovered <br clear="none">
</div>
<div dir="ltr">candidate and
Losing Votes (erw)<br clear="none">
</div>
<div dir="ltr">and Margins both
still elect C.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Steve Eppley's
old example to illustrate (I
think his) Non-Drastic <br clear="none">
</div>
<div dir="ltr">Defense
criterion, which says that if<br clear="none">
</div>
<div dir="ltr">on more than half
the ballots B is voted no
lower than equal-top and <br clear="none">
</div>
<div dir="ltr">above A then A
can't win.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">46: A>C
(sincere may be A>B)<br clear="none">
</div>
<div dir="ltr">10: B>A<br clear="none">
</div>
<div dir="ltr">10: B>C<br clear="none">
</div>
<div dir="ltr">34: C=B (the
"defenders", sincere may be
C>B)<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">B>A 54-46
(m=8), A>C 56-44 (m=12),
C>B (80-54 erw, "normally"
46-20, m=26).<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Voted at least
equal-top (or Top Ratings)
scores: B54, A46, C34.<br clear="none">
</div>
<div dir="ltr">Voted above
bottom (or Approval) scores:
B54, A56, C90.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">B is the only
candidate top-rated on more
than half the ballots. More <br clear="none">
</div>
<div dir="ltr">than half the
voters voted B<br clear="none">
</div>
<div dir="ltr">above A and B not
lower than equal-top. Margins
and Losing Votes <br clear="none">
</div>
<div dir="ltr">without my
recommended<br clear="none">
</div>
<div dir="ltr">"above-bottom
equal-ranking whole" bit elect
A, violating the <br clear="none">
</div>
<div dir="ltr">Non-Drastic
Defense criterion.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Losing Votes
(erw) and WV elect B.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">If anyone has
some counter-examples where
they think that Winning Votes
<br clear="none">
</div>
<div dir="ltr">does better than<br clear="none">
</div>
<div dir="ltr">Losing Votes
(erw), I'd be interested in
seeing them.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Chris Benham<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<br>
<div dir="ltr">----<br clear="none">
</div>
<div dir="ltr">Election-Methods
mailing list - see <a rel="nofollow" shape="rect" target="_blank" href="https://electorama.com/em">https://electorama.com/em
</a>for list info<br clear="none">
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