<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_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="">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 size="2" face="Arial" id="yui_3_16_0_ym19_1_1558893123363_4289"> <hr size="1"> <b><span style="font-weight:bold;">From:</span></b> Chris Benham <cbenhamau@yahoo.com.au><br> <b><span style="font-weight: bold;">To:</span></b> "tdp201b@yahoo.co.uk" <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> 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">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"><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>
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