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<p>Toby,<br>
<br>
If you try to give that calculator a truncated ballot it will just
turn it into the sort of ballot you like.<br>
<br>
How do you think equally-ranked ballots should be counted in a
pairwise comparison? A half-vote to<br>
each or zero to both?<br>
<br>
So you can't actually point to any election example where the
Plurality criterion bars from winning the candidate <br>
that you think should have won?<br>
</p>
<div id="yiv0773282891yMail_cursorElementTracker_1558884457758">46:
A</div>
<div id="yiv0773282891yMail_cursorElementTracker_1558884462587">44:
B>C</div>
<div id="yiv0773282891yMail_cursorElementTracker_1558884480116">10:
C</div>
<p>Returning to this, are you happy with B winning? And if not, why
not?<br>
<br>
Chris Benham<br>
<br>
</p>
<div class="moz-cite-prefix">On 27/05/2019 3:38 am, Toby Pereira
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:2003510133.9980742.1558894121968@mail.yahoo.com">
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<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_1558893123363_4237"><span
id="yui_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="yui_3_16_0_ym19_1_1558893123363_4237"><span><br>
</span></div>
<div id="yui_3_16_0_ym19_1_1558893123363_4237"><span>A</span></div>
<div id="yui_3_16_0_ym19_1_1558893123363_4237"><span><br>
</span></div>
<div id="yui_3_16_0_ym19_1_1558893123363_4237"><span
id="yui_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="yui_3_16_0_ym19_1_1558893123363_4237"><span><br>
</span></div>
<div id="yui_3_16_0_ym19_1_1558893123363_4237"><span>A>B</span></div>
<div id="yui_3_16_0_ym19_1_1558893123363_4237"><span><br>
</span></div>
<div id="yui_3_16_0_ym19_1_1558893123363_4237" dir="ltr">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>
</span></div>
<div id="yui_3_16_0_ym19_1_1558893123363_4237"><span><br>
</span></div>
<div id="yui_3_16_0_ym19_1_1558893123363_4237"><span
id="yui_3_16_0_ym19_1_1558893123363_4931">My vote could also
be:</span></div>
<div id="yui_3_16_0_ym19_1_1558893123363_4237"><span><br>
</span></div>
<div id="yui_3_16_0_ym19_1_1558893123363_4237"><span
id="yui_3_16_0_ym19_1_1558893123363_4929">A>B>C</span></div>
<div id="yui_3_16_0_ym19_1_1558893123363_4237"><span><br>
</span></div>
<div id="yui_3_16_0_ym19_1_1558893123363_4237" dir="ltr"><span
id="yui_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 id="yui_3_16_0_ym19_1_1558893123363_4237" dir="ltr"><span><br>
</span></div>
<div id="yui_3_16_0_ym19_1_1558893123363_4237" dir="ltr"><span
id="yui_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
href="http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247"
id="yui_3_16_0_ym19_1_1558893123363_4693" class=""
moz-do-not-send="true">http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247</a></div>
<div id="yui_3_16_0_ym19_1_1558893123363_4237" dir="ltr"><br>
</div>
<div id="yui_3_16_0_ym19_1_1558893123363_4237" dir="ltr">But
anyway, thank you for the link to the calculator.</div>
<div id="yui_3_16_0_ym19_1_1558893123363_4237" dir="ltr"><br>
</div>
<div id="yui_3_16_0_ym19_1_1558893123363_4237" dir="ltr">Toby</div>
<div id="yui_3_16_0_ym19_1_1558893123363_4776"><br>
</div>
<div id="yui_3_16_0_ym19_1_1558893123363_4813"><br>
</div>
<div class="qtdSeparateBR"
id="yui_3_16_0_ym19_1_1558893123363_4243"><br>
<br>
</div>
<div class="yahoo_quoted"
id="yui_3_16_0_ym19_1_1558893123363_4264" 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_1558893123363_4263">
<div style="font-family: HelveticaNeue, Helvetica Neue,
Helvetica, Arial, Lucida Grande, Sans-Serif; font-size:
16px;" id="yui_3_16_0_ym19_1_1558893123363_4262">
<div dir="ltr" id="yui_3_16_0_ym19_1_1558893123363_4261">
<font id="yui_3_16_0_ym19_1_1558893123363_4289" size="2"
face="Arial">
<hr size="1"> <b><span style="font-weight:bold;">From:</span></b>
Chris Benham <a class="moz-txt-link-rfc2396E" href="mailto:cbenhamau@yahoo.com.au"><cbenhamau@yahoo.com.au></a><br>
<b><span style="font-weight: bold;">To:</span></b>
<a class="moz-txt-link-rfc2396E" href="mailto:tdp201b@yahoo.co.uk">"tdp201b@yahoo.co.uk"</a> <a class="moz-txt-link-rfc2396E" href="mailto:tdp201b@yahoo.co.uk"><tdp201b@yahoo.co.uk></a>;
<a class="moz-txt-link-rfc2396E" href="mailto:cbenham@adam.com.au">"cbenham@adam.com.au"</a> <a class="moz-txt-link-rfc2396E" href="mailto:cbenham@adam.com.au"><cbenham@adam.com.au></a>;
<a class="moz-txt-link-rfc2396E" href="mailto:election-methods@lists.electorama.com">"election-methods@lists.electorama.com"</a>
<a class="moz-txt-link-rfc2396E" 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, 18:08<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_1558893123363_4268"><br>
<div id="yiv0773282891">
<div id="yui_3_16_0_ym19_1_1558893123363_4267">
<div id="yui_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" target="_blank"
href="https://www.cse.wustl.edu/~legrand/rbvote/calc.html"
id="yui_3_16_0_ym19_1_1558893123363_4859"
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="yui_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="yiv0773282891moz-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="yiv0773282891ymail_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="yiv0773282891yMail_cursorElementTracker_1558884457619"><br
clear="none">
</div>
<div
id="yiv0773282891yMail_cursorElementTracker_1558884457758">46:
A</div>
<div
id="yiv0773282891yMail_cursorElementTracker_1558884462587">44:
B>C</div>
<div
id="yiv0773282891yMail_cursorElementTracker_1558884480116">10:
C</div>
<div
id="yiv0773282891yMail_cursorElementTracker_1558884503906"><br
clear="none">
</div>
<div
id="yiv0773282891yMail_cursorElementTracker_1558884504072">Is
the same as:</div>
<div
id="yiv0773282891yMail_cursorElementTracker_1558884512155"><br
clear="none">
</div>
<div
id="yiv0773282891yMail_cursorElementTracker_1558884512327">46:
A>B=C</div>
<div
id="yiv0773282891yMail_cursorElementTracker_1558884536910">44:
B>C>A</div>
<div
id="yiv0773282891yMail_cursorElementTracker_1558884560941">10:
C>A=B</div>
<div
id="yiv0773282891yMail_cursorElementTracker_1558884616720"><br
clear="none">
</div>
<div
id="yiv0773282891yMail_cursorElementTracker_1558884616935">Presented
with these ballots, does this change who you think
the winner should be?</div>
<div
id="yiv0773282891yMail_cursorElementTracker_1558884706281"><br
clear="none">
</div>
<div
id="yiv0773282891yMail_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="yiv0773282891yMail_cursorElementTracker_1558884772443"><br
clear="none">
</div>
<div
id="yiv0773282891yMail_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="yiv0773282891moz-txt-link-rfc2396E"
ymailto="mailto:cbenham@adam.com.au"
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>
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