<html>
<head>
<meta http-equiv="Content-Type" content="text/html;
charset=windows-1252">
</head>
<body text="#000000" bgcolor="#FFFFFF">
<p>Jim,<br>
<br>
Yes. <br>
<br>
Chris Benham<br>
<br>
</p>
<div class="moz-cite-prefix">On 1/06/2019 9:45 pm, Faran, James
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:ee6293fa-7f6a-4312-8add-fa3288a8e099@email.android.com">
<meta http-equiv="Content-Type" content="text/html;
charset=windows-1252">
<meta content="text/html; charset=utf-8">
<div dir="auto">51 A>B>C>D
<div dir="auto">49 B>C>D>A</div>
<div dir="auto"><br>
</div>
<div dir="auto">Is A a better choice than B?</div>
<div dir="auto"><br>
</div>
<div dir="auto">1. Yes. Plurality demands it. Moreover, B beats
C and D on all ballots, so C and D can be ignored and the
pairwise race is all that's left.</div>
<div dir="auto"><br>
</div>
<div dir="auto">2. No. A is ranked bottom on 49% of ballots, B
ranked at least second on 100%, top on almost half.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Are C and D Irrelevant Alternatives?</div>
<div dir="auto"><br>
</div>
<div dir="auto">Jim Faran</div>
</div>
<div class="gmail_extra"><br>
<div class="gmail_quote">On Jun 1, 2019 5:28 AM, "C.Benham"
<a class="moz-txt-link-rfc2396E" href="mailto:cbenham@adam.com.au"><cbenham@adam.com.au></a> wrote:<br type="attribution">
</div>
</div>
<div>
<p>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>
</p>
<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>
25: C<br>
<p>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>
</p>
<p><br>
<br>
</p>
<div class="moz-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="yui_3_16_0_ym19_1_1559134455557_8273" dir="ltr"><span
id="yui_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="yui_3_16_0_ym19_1_1559134455557_8273" dir="ltr"><span><br>
</span></div>
<div id="yui_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="yui_3_16_0_ym19_1_1559134455557_8273" dir="ltr"><br>
</div>
<div id="yui_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="yui_3_16_0_ym19_1_1559134455557_8273" dir="ltr"><br>
</div>
<div id="yui_3_16_0_ym19_1_1559134455557_8273" dir="ltr">Toby</div>
<div class="qtdSeparateBR"
id="yui_3_16_0_ym19_1_1559134455557_8274"><br>
<br>
</div>
<div class="yahoo_quoted"
id="yui_3_16_0_ym19_1_1559134455557_8278"
style="display:block">
<div id="yui_3_16_0_ym19_1_1559134455557_8277"
style="font-family:Helvetica Neue,Helvetica,Arial,Lucida
Grande,sans-serif; font-size:13px">
<div id="yui_3_16_0_ym19_1_1559134455557_8276"
style="font-family:HelveticaNeue,Helvetica
Neue,Helvetica,Arial,Lucida Grande,Sans-Serif;
font-size:16px">
<div dir="ltr"
id="yui_3_16_0_ym19_1_1559134455557_8275"><font
id="yui_3_16_0_ym19_1_1559134455557_8279" size="2"
face="Arial">
<hr id="yui_3_16_0_ym19_1_1559134455557_8306"
size="1">
<b><span style="font-weight:bold">From:</span></b>
C.Benham <a class="moz-txt-link-rfc2396E"
href="mailto:cbenham@adam.com.au"
moz-do-not-send="true">
<cbenham@adam.com.au></a><br>
<b><span style="font-weight:bold">To:</span></b>
Toby Pereira <a class="moz-txt-link-rfc2396E"
href="mailto:tdp201b@yahoo.co.uk"
moz-do-not-send="true">
<tdp201b@yahoo.co.uk></a>; <a
class="moz-txt-link-rfc2396E"
href="mailto:cbenham@adam.com.au"
moz-do-not-send="true">
"cbenham@adam.com.au"</a> <a
class="moz-txt-link-rfc2396E"
href="mailto:cbenham@adam.com.au"
moz-do-not-send="true">
<cbenham@adam.com.au></a>; <a
class="moz-txt-link-rfc2396E"
href="mailto:election-methods@lists.electorama.com"
moz-do-not-send="true">
"election-methods@lists.electorama.com"</a> <a
class="moz-txt-link-rfc2396E"
href="mailto:election-methods@lists.electorama.com"
moz-do-not-send="true">
<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="y_msg_container"
id="yui_3_16_0_ym19_1_1559134455557_8383"><br>
<div id="yiv9431740989">
<div id="yui_3_16_0_ym19_1_1559134455557_8385">
<div id="yui_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="yiv9431740989yMail_cursorElementTracker_1558884457758">46:
A</div>
<div
id="yiv9431740989yMail_cursorElementTracker_1558884462587">44:
B>C</div>
<div
id="yiv9431740989yMail_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="yiv9431740989yqt2928960308"
id="yiv9431740989yqt29538">
<div class="yiv9431740989moz-cite-prefix">On
27/05/2019 3:38 am, Toby Pereira wrote:<br
clear="none">
</div>
</div>
</div>
<div class="yiv9431740989yqt2928960308"
id="yiv9431740989yqt91070">
<div>
<div style="color:#000; background-color:#fff;
font-family:Helvetica
Neue,Helvetica,Arial,Lucida
Grande,sans-serif; font-size:13px">
<div
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span
id="yiv9431740989yui_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="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span><br
clear="none">
</span></div>
<div
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span>A</span></div>
<div
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span><br
clear="none">
</span></div>
<div
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span
id="yiv9431740989yui_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="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span><br
clear="none">
</span></div>
<div
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span>A>B</span></div>
<div
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span><br
clear="none">
</span></div>
<div dir="ltr"
id="yiv9431740989yui_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="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span><br
clear="none">
</span></div>
<div
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4931">My vote could
also be:</span></div>
<div
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span><br
clear="none">
</span></div>
<div
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4929">A>B>C</span></div>
<div
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span><br
clear="none">
</span></div>
<div dir="ltr"
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span
id="yiv9431740989yui_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="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span><br
clear="none">
</span></div>
<div dir="ltr"
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span
id="yiv9431740989yui_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="yiv9431740989"
id="yiv9431740989yui_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"
moz-do-not-send="true">http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247</a></div>
<div dir="ltr"
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><br
clear="none">
</div>
<div dir="ltr"
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237">But
anyway, thank you for the link to the
calculator.</div>
<div dir="ltr"
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><br
clear="none">
</div>
<div dir="ltr"
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237">Toby</div>
<div
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4776"><br
clear="none">
</div>
<div
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4813"><br
clear="none">
</div>
<div class="yiv9431740989qtdSeparateBR"
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4243">
<br clear="none">
<br clear="none">
</div>
<div class="yiv9431740989yahoo_quoted"
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4264"
style="display:block">
<div
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4263"
style="font-family:Helvetica
Neue,Helvetica,Arial,Lucida
Grande,sans-serif; font-size:13px">
<div
id="yiv9431740989yui_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="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4261">
<hr size="1">
<b><span style="font-weight:bold">From:</span></b>
Chris Benham <a rel="nofollow"
shape="rect"
class="yiv9431740989moz-txt-link-rfc2396E"
target="_blank"
href="mailto:cbenhamau@yahoo.com.au"
moz-do-not-send="true">
<cbenhamau@yahoo.com.au></a><br
clear="none">
<b><span style="font-weight:bold">To:</span></b>
<a rel="nofollow" shape="rect"
class="yiv9431740989moz-txt-link-rfc2396E"
target="_blank"
href="mailto:tdp201b@yahoo.co.uk"
moz-do-not-send="true">
"tdp201b@yahoo.co.uk"</a> <a
rel="nofollow" shape="rect"
class="yiv9431740989moz-txt-link-rfc2396E"
target="_blank"
href="mailto:tdp201b@yahoo.co.uk"
moz-do-not-send="true">
<tdp201b@yahoo.co.uk></a>; <a
rel="nofollow" shape="rect"
class="yiv9431740989moz-txt-link-rfc2396E"
target="_blank"
href="mailto:cbenham@adam.com.au"
moz-do-not-send="true">
"cbenham@adam.com.au"</a> <a
rel="nofollow" shape="rect"
class="yiv9431740989moz-txt-link-rfc2396E"
target="_blank"
href="mailto:cbenham@adam.com.au"
moz-do-not-send="true">
<cbenham@adam.com.au></a>; <a
rel="nofollow" shape="rect"
class="yiv9431740989moz-txt-link-rfc2396E"
target="_blank"
href="mailto:election-methods@lists.electorama.com"
moz-do-not-send="true">
"election-methods@lists.electorama.com"</a> <a rel="nofollow"
shape="rect"
class="yiv9431740989moz-txt-link-rfc2396E"
target="_blank"
href="mailto:election-methods@lists.electorama.com"
moz-do-not-send="true">
<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="yiv9431740989y_msg_container"
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4268">
<br clear="none">
<div id="yiv9431740989">
<div
id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4267">
<div
id="yiv9431740989yui_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="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4859" target="_blank"
href="https://www.cse.wustl.edu/~legrand/rbvote/calc.html"
moz-do-not-send="true">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="yiv9431740989yui_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="yiv9431740989moz-cite-prefix"><br
clear="none">
On 27/05/2019 1:04 am, Toby
Pereira wrote:<br clear="none">
</div>
</div>
<div>
<div
id="yiv9431740989ymail_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="yiv9431740989yMail_cursorElementTracker_1558884457619"><br
clear="none">
</div>
<div
id="yiv9431740989yMail_cursorElementTracker_1558884457758">46:
A</div>
<div
id="yiv9431740989yMail_cursorElementTracker_1558884462587">44:
B>C</div>
<div
id="yiv9431740989yMail_cursorElementTracker_1558884480116">10:
C</div>
<div
id="yiv9431740989yMail_cursorElementTracker_1558884503906"><br
clear="none">
</div>
<div
id="yiv9431740989yMail_cursorElementTracker_1558884504072">Is
the same as:</div>
<div
id="yiv9431740989yMail_cursorElementTracker_1558884512155"><br
clear="none">
</div>
<div
id="yiv9431740989yMail_cursorElementTracker_1558884512327">46:
A>B=C</div>
<div
id="yiv9431740989yMail_cursorElementTracker_1558884536910">44:
B>C>A</div>
<div
id="yiv9431740989yMail_cursorElementTracker_1558884560941">10:
C>A=B</div>
<div
id="yiv9431740989yMail_cursorElementTracker_1558884616720"><br
clear="none">
</div>
<div
id="yiv9431740989yMail_cursorElementTracker_1558884616935">Presented
with these ballots, does this
change who you think the
winner should be?</div>
<div
id="yiv9431740989yMail_cursorElementTracker_1558884706281"><br
clear="none">
</div>
<div
id="yiv9431740989yMail_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="yiv9431740989yMail_cursorElementTracker_1558884772443"><br
clear="none">
</div>
<div
id="yiv9431740989yMail_cursorElementTracker_1558884772583">Toby</div>
<br clear="none">
<blockquote style="margin:0 0
20px 0">
<div
style="font-family:Roboto,sans-serif;
color:#6D00F6">
<div>On Sat, 25 May 2019 at
15:31, C.Benham</div>
<div><a rel="nofollow"
shape="rect"
class="yiv9431740989moz-txt-link-rfc2396E"
target="_blank"
href="mailto:cbenham@adam.com.au"
moz-do-not-send="true"><cbenham@adam.com.au></a>
wrote:</div>
</div>
<div style="padding:10px 0 0
20px; margin:10px 0 0 0;
border-left:1px solid
#6D00F6">
<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"
moz-do-not-send="true">
https://electorama.com/em </a>for list info<br clear="none">
</div>
</div>
</blockquote>
<div
id="yiv9431740989DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2"><br
clear="none">
<table style="border-top:1px
solid #D3D4DE">
<tbody>
<tr>
<td colspan="1"
rowspan="1"
style="width:55px;
padding-top:13px"><a
rel="nofollow"
shape="rect"
target="_blank"
href="http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient"
moz-do-not-send="true"><img
src="https://ipmcdn.avast.com/images/icons/icon-envelope-tick-green-avg-v1.png"
alt=""
style="width:46px;
min-height:29px"
moz-do-not-send="true"
width="46"
height="29"></a></td>
<td colspan="1"
rowspan="1"
style="width:470px;
padding-top:12px;
color:#41424e;
font-size:13px;
font-family:Arial,Helvetica,sans-serif;
line-height:18px">
Virus-free. <a
rel="nofollow"
shape="rect"
target="_blank"
href="http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient"
style="color:#4453ea" moz-do-not-send="true">
www.avg.com</a> </td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
<br clear="none">
<br clear="none">
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<br>
<br>
</div>
</div>
</div>
</div>
</div>
</blockquote>
</div>
</blockquote>
</body>
</html>