<html><head></head><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:12px"><div id="yui_3_16_0_ym19_1_1466556275910_3914"><span>Hi Steve,</span></div><div id="yui_3_16_0_ym19_1_1466556275910_3913"><span><br></span></div><div dir="ltr" id="yui_3_16_0_ym19_1_1466556275910_3862"><span id="yui_3_16_0_ym19_1_1466556275910_3861">The first one on the list (mono-raise) is what people are referring to when they say IRV (or two-round) violates monotonicity. But certainly there are other ones from the list that it doesn't satisfy either.</span></div><div dir="ltr" id="yui_3_16_0_ym19_1_1466556275910_3673"><span><br></span></div><div dir="ltr" id="yui_3_16_0_ym19_1_1466556275910_3672"><span id="yui_3_16_0_ym19_1_1466556275910_3671">You used the terms "democratic" and "one citizen one vote" but I don't really know of definitions for these terms at this level.</span></div><div dir="ltr" id="yui_3_16_0_ym19_1_1466556275910_3676"><span><br></span></div><div dir="ltr" id="yui_3_16_0_ym19_1_1466556275910_3679"><span id="yui_3_16_0_ym19_1_1466556275910_3678">The reason mono-raise failures are criticized is that they involve situations where a candidate (or his supporters) could complain that they are penalized for getting better rankings. A perception of unfairness could undermine perceived legitimacy of the winner. All proposed methods are unfair in some way, and people have different views on what is or isn't tolerable.</span></div><div dir="ltr" id="yui_3_16_0_ym19_1_1466556275910_3680"><span><br></span></div><div dir="ltr" id="yui_3_16_0_ym19_1_1466556275910_3687"><span>Kevin</span></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1466556275910_3688"><br><br></div><div class="yahoo_quoted" id="yui_3_16_0_ym19_1_1466556275910_3089" style="display: block;"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 12px;" id="yui_3_16_0_ym19_1_1466556275910_3088"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 16px;" id="yui_3_16_0_ym19_1_1466556275910_3087"> <div dir="ltr" id="yui_3_16_0_ym19_1_1466556275910_3172"> <font size="2" face="Arial" id="yui_3_16_0_ym19_1_1466556275910_3690"> <hr size="1" id="yui_3_16_0_ym19_1_1466556275910_3689"> <b><span style="font-weight:bold;">De :</span></b> steve bosworth <stevebosworth@hotmail.com><br> <b><span style="font-weight: bold;">À :</span></b> "election-methods@lists.electorama.com" <election-methods@lists.electorama.com> <br> <b><span style="font-weight: bold;">Envoyé le :</span></b> Mardi 21 juin 2016 17h07<br> <b><span style="font-weight: bold;">Objet :</span></b> [EM] Wiki says IRV is monotonic--not fully democratic?<br> </font> </div> <div class="y_msg_container" id="yui_3_16_0_ym19_1_1466556275910_3086"><br><div id="yiv9653240219">
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<span lang="EN" style="font-size:12pt;"> </span></div>
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<span lang="EN" style="font-size:12pt;">To everyone:</span></div>
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<span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1466556275910_3929">Below, Steve is considering the following section of the following June 21, 2016
</span><span lang="EN" style="" id="yui_3_16_0_ym19_1_1466556275910_3234">Wikipedia article:<span style="">
</span>‘</span><span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1466556275910_3638">Monotonicity criterion’.<span style="">
</span>He will refer to the author of that section as ‘Wiki’:</span></div>
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<b id="yui_3_16_0_ym19_1_1466556275910_3931"><span lang="EN" style="font-size:18pt;" id="yui_3_16_0_ym19_1_1466556275910_3930">Instant-runoff voting and the two-round system are not monotonic[</span></b><a rel="nofollow" title="Edit section: Instant-runoff voting and the two-round system are not monotonic" target="_blank" href="https://en.wikipedia.org/w/index.php?title=Monotonicity_criterion&action=edit§ion=1"><b><span lang="EN" style="color:blue;font-size:18pt;">edit</span></b></a></div>
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<span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1466556275910_3932">Using an example that applies to
</span><a rel="nofollow" title="Instant-runoff voting" target="_blank" href="https://en.wikipedia.org/wiki/Instant-runoff_voting"><span lang="EN" style="color:blue;font-size:12pt;">instant-runoff
voting</span></a><span lang="EN" style="font-size:12pt;"> (IRV) and to the
</span><a rel="nofollow" title="Two-round system" target="_blank" href="https://en.wikipedia.org/wiki/Two-round_system"><span lang="EN" style="color:blue;font-size:12pt;">two-round
system</span></a><span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1466556275910_3640">, it is shown that these voting systems violate the mono-raise criterion. Suppose a
</span><a rel="nofollow" title="President" target="_blank" href="https://en.wikipedia.org/wiki/President"><span lang="EN" style="color:blue;font-size:12pt;">president</span></a><span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1466556275910_3250">
were being elected among three candidates, a left, a right, and a center candidate, and 100 votes cast. The number of votes for an absolute majority is therefore 51.</span></div>
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<span lang="EN" style="font-size:12pt;">Suppose the votes are cast as follows:</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><b><span style="font-size:12pt;">Number of votes</span></b></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><b><span style="font-size:12pt;">1st preference</span></b></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><b><span style="font-size:12pt;">2nd preference</span></b></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">28</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Right</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Center</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">5</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Right</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Left</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">30</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Left</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Center</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">5</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Left</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Right</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">16</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Center</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Left</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">16</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Center</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Right</span></div>
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<span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1466556275910_3273">According to the 1st preferences, Left finishes first with 35 votes, Right gets 33 votes, and Center 32 votes,
thus all candidates lack an absolute majority of first preferences. In an actual runoff between the top two candidates, Left would win against Right with 30+5+16=51 votes. The same happens (in this example) under IRV, Center gets eliminated, and Left wins
against Right with 51 to 49 votes.</span></div>
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<b><span lang="EN" style="font-size:13.5pt;">[STEVE’S Additions:</span></b></div>
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<span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1466556275910_3238">S: Given these preferences, the Center candidate rather than the Right candidate should get eliminated because
he receives fewer 1<sup>st</sup> preference votes.<span style="">
</span>Still, the principle of one-citizen-one-vote requires that the preference of each of these supporter be counted until a majority winner is discovered.<span style="">
</span>Since 16 of them preferred the Left candidate next and 16 preferred the Right candidate next, the Left candidate receive a total of 51 votes and the Right candidate 49.<span style="">
</span>Given both that only one candidate can win in this election and the principle of one-citizen-one-vote, no citizen would be able to sustain an objection to this result.</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Author’s
</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">1<sup>st</sup> IRV</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">COUNT</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Left</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Center</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">1</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">35</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">32</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">33</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">2</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">51</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"> </span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">49</span></div>
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<span lang="EN" style="font-size:12pt;">Wiki: But if at least two of the five voters who ranked Right first, and Left second, would raise Left, and vote
1st Left, 2nd Right; then Left would be defeated by these votes in favor of Center. Let's assume that two voters change their preferences in that way, which changes two rows of the table:</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><b><span style="font-size:12pt;">Number of votes</span></b></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><b><span style="font-size:12pt;">1st preference</span></b></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><b><span style="font-size:12pt;">2nd preference</span></b></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">3</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Right</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Left</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">7</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Left</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Right</span></div>
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</tr>
</tbody>
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<div style="margin:0in 0in 8pt;line-height:normal;" id="yui_3_16_0_ym19_1_1466556275910_3400">
<span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1466556275910_3399">Now Left gets 37 first preferences, Right only 31 first preferences, and Center still 32 first preferences, and
there is again no candidate with an absolute majority of first preferences. But now Right gets eliminated, and Center remains in round 2 of IRV (or the actual runoff in the Two-round system). And Center beats its opponent Left with a remarkable majority of
60 to 40 votes. </span></div>
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<b><span lang="EN" style="font-size:13.5pt;">1-[STEVE’S IRV exploration:</span></b></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;" colspan="3">
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<div style="margin:0in 0in 0pt;line-height:normal;"><b><span style="font-size:12pt;">Wiki’s changed preferences (2<sup>nd</sup> Set of Ballots)</span></b></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><b><span style="font-size:12pt;">Number of votes</span></b></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><b><span style="font-size:12pt;">1st preference</span></b></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><b><span style="font-size:12pt;">2nd preference</span></b></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">28</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Right</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Center</span></div>
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<tr style="">
<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">3</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Right</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Left</span></div>
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<tr style="">
<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">2</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Left</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Right</span></div>
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</tr>
<tr style="">
<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">30</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Left</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Center</span></div>
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</tr>
<tr style="">
<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">5</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Left</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Right</span></div>
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</tr>
<tr style="">
<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">16</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Center</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Left</span></div>
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</tr>
<tr style="">
<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">16</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Center</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Right</span></div>
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<div style="margin:0in 0in 8pt;line-height:normal;">
<span lang="EN" style="font-size:12pt;"> </span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">2<sup>nd</sup> IRV</span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">COUNT</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Left</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Center</span></div>
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<td valign="top" style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">Right</span></div>
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</tr>
<tr style="">
<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">1</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">37</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">32</span></div>
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<td valign="top" style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">31</span></div>
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</tr>
<tr style="">
<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">2</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">40</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">60</span></div>
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<td valign="top" style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">0</span></div>
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</tr>
<tr style="">
<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">3</span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"> </span></div>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;">60</span></div>
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<td valign="top" style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;">
<font face="Times New Roman"></font>
<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"> </span></div>
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</tr>
</tbody>
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<div style="margin:0in 0in 8pt;line-height:normal;" id="yui_3_16_0_ym19_1_1466556275910_3810">
<span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1466556275910_3811">S: These 28 make the Center candidate’s total of 60 (and the winner) while the 2 make
the total of the Left candidate 40.<span style=""> </span>While it is true that this change in preferences changes the win for the Left candidate to a defeat, they still helped the Left candidate both by increasing the number of first preferences
he received and the average intensity of preference given to him.<span style="">
</span>At the same time, he could not expect to win because he had received only a total of 40 to the total of 60 votes received by the Center candidate.</span></div>
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<div style="margin:0in 0in 8pt;line-height:normal;" id="yui_3_16_0_ym19_1_1466556275910_3244">
<span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1466556275910_3243">Consequently, currently I do not yet see this example as containing any anti-democratic element. As I see it, the
principle of ‘one-citizen-one vote’ only requires that each citizen’s vote (preferences) be counted equally as long as technically possible until the single-winner is discovered, i.e. the candidate who has received the highest intensity possible of majority
support.<span style=""> </span>Accordingly, before the 2 preferences were changed by Wiki, the Left candidate won with 51 votes with an average intensity of 9.76 on a scale of 10.<span style="">
</span>After the change, the Center candidate won with 60 votes with an average intensity of 9.53<span style="color:red;">.<span style="">
</span></span></span></div>
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<div style="margin:0in 0in 8pt;line-height:normal;" id="yui_3_16_0_ym19_1_1466556275910_3637">
<span lang="EN" style="font-size:12pt;">Intensity of support calculations:</span></div>
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<div style="margin:0in 0in 8pt;line-height:normal;" id="yui_3_16_0_ym19_1_1466556275910_3636">
<u><span lang="EN" style="font-size:12pt;">1<sup>st</sup> Set of Ballots</span></u></div>
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<div style="margin:0in 0in 8pt;line-height:normal;">
<span lang="EN" style="font-size:12pt;">35X10 +16X9=350+144=494</span></div>
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<div style="margin:0in 0in 8pt;line-height:normal;">
<span lang="EN" style="font-size:12pt;">494 divided by 51=9.76</span></div>
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<div style="margin:0in 0in 8pt;line-height:normal;">
<u><span lang="EN" style="font-size:12pt;">2<sup>nd</sup> Set of Ballots</span></u></div>
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<div style="margin:0in 0in 8pt;line-height:normal;">
<span lang="EN" style="font-size:12pt;">32X10 +28X9=320+252=572</span></div>
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<div style="margin:0in 0in 8pt;line-height:normal;">
<span lang="EN" style="font-size:12pt;">572 divided by 60=9.53</span></div>
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<div style="margin:0in 0in 8pt;line-height:normal;" id="yui_3_16_0_ym19_1_1466556275910_3809">
<span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1466556275910_3808">In contrast, the intensity of support for a forced win by the Center candidate from the 1<sup>st</sup> Set of Ballots
would only be 9.36:</span></div>
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<div style="margin:0in 0in 8pt;line-height:normal;" id="yui_3_16_0_ym19_1_1466556275910_3635">
<span lang="EN" style="font-size:12pt;">32 X 1<sup>st</sup> preferences and 58 X 2<sup>nd</sup> preferences for the Center candidate:</span></div>
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<div style="margin:0in 0in 8pt;line-height:normal;" id="yui_3_16_0_ym19_1_1466556275910_3633">
<span lang="EN" style="font-size:12pt;">32X10+58X9=320+522=842</span></div>
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<div style="margin:0in 0in 8pt;line-height:normal;" id="yui_3_16_0_ym19_1_1466556275910_3247">
<span lang="EN" style="font-size:12pt;">842 divided by 90= 9.36</span></div>
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<div style="margin:0in 0in 8pt;line-height:normal;" id="yui_3_16_0_ym19_1_1466556275910_3426">
<span lang="EN" style="font-size:12pt;">S: Again, using IRV, the originally winning Left candidate was defeated after the author
changed the two voters’ preferences.<span style=""> </span>This happened even though the Left candidate was now given two 1<sup>st</sup>, rather than two 2<sup>nd</sup>, preferences.<span style="">
</span>Wiki sees this as a violation of the ‘</span><span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1466556275910_3788">mono-raise criterion’<span style="" id="yui_3_16_0_ym19_1_1466556275910_3787">:
‘giving higher preferences to a candidate should never harm him’.<span style="">
</span>However, at least in some senses, these two higher preferences did help the Left candidate, i.e. they gave him two more 1st preferences. They also helped him by reducing the intensity of 2 preferences given to one of his competitors, i.e. by giving the
Right candidate two 2<sup>nd</sup> rather than two 1<sup>st </sup>preferences.<span style="">
</span>By themselves, these changes would make it more likely that the Left candidate would win.<span style="">
</span>It is only because more other citizens gave their 1<sup>st</sup> preference to the Center candidate over the Right candidate that the Right candidate correctly had to be eliminated in the second count.<span style="">
</span>In turn, this appropriately required candidate Right’s 2<sup>nd</sup> preferences to be transferred:
<span style=""> </span>28 to the Center candidate and 3 to the Center candidate.<span style="">
</span>Given these two change made by these two citizens, the particular preferences given by the other voters required that the Left candidate not be elected.<span style="">
</span>Consequently, it was not the isolated giving of two higher preferences to the Left candidate that ‘harmed’ him.<span style="">
</span>It was how these preferences had to be combined with the preferences of all the other citizens that required the Left candidate to be defeated.<span style="">
</span>This follows from the principle of one-citizen-one-vote.<span style="">
</span>Again, g</span>iven both this principle and the fact that only one candidate can win in this election, no one would seem to be able to sustain an objection to this result.</span></div>
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<div style="margin:0in 0in 8pt;line-height:normal;">
<span lang="EN" style="font-size:12pt;">S: Nevertheless, Wiki claims that IRV is not monotonic (i.e. violates the mono-raise
criterion).<span style=""> </span>Does Wiki have Woodall’s definition of a
<span style="font-variant:small-caps;">mono-raise random</span> criterion (see below) in mind [Douglas R. Woodall Discrete Applied Mathematics 77 (1997) 81-98]?</span></div>
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<div style="margin:0in 0in 8pt;line-height:normal;" id="yui_3_16_0_ym19_1_1466556275910_3786">
<span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1466556275910_3785">In the light of the above discussion and the following definitions, I would very much
appreciate it if anyone could explain why they might still want to criticize IRV for being nonmonotonic.<span style="">
</span>Is IRV fully democratic in the sense defined above?</span></div>
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<div style="margin:0in 0in 8pt;line-height:normal;" id="yui_3_16_0_ym19_1_1466556275910_3422">
<span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1466556275910_3421">Section 1.3 in Woodall’s article defines how a nonmotonic set of rules might ‘harm’
or ‘help’ candidate x:<span style=""> </span>‘We shall say a candidate x is either
<i style="">helped</i> or <i style="">
harmed</i> by a change in the <i style="">profile</i> if the result, respectively, is to increase or decrease [the probability of electing x, i.e] P<sub>E</sub>(x). The following two properties are well known to hold for STV [which
reduces to IRV in a single-winner raced].</span></div>
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<ul style="list-style-type:disc;direction:ltr;" id="yui_3_16_0_ym19_1_1466556275910_3420">
<li style="color:rgb(0, 0, 0);font-size:12pt;font-style:normal;font-weight:normal;" id="yui_3_16_0_ym19_1_1466556275910_3419">
<div style="color:rgb(0, 0, 0);line-height:normal;font-size:11pt;font-style:normal;font-weight:normal;margin-top:0in;margin-bottom:0pt;" id="yui_3_16_0_ym19_1_1466556275910_3418">
<span lang="EN" style="font-size:12pt;font-variant:small-caps;">Later-no-help</span><span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1466556275910_3417">:<span style="">
</span>Adding a later preference to a ballot should not help any candidate already listed.</span></div>
</li><li style="color:rgb(0, 0, 0);font-size:12pt;font-style:normal;font-weight:normal;" id="yui_3_16_0_ym19_1_1466556275910_3425">
<div style="color:rgb(0, 0, 0);line-height:normal;font-size:11pt;font-style:normal;font-weight:normal;margin-top:0in;margin-bottom:8pt;" id="yui_3_16_0_ym19_1_1466556275910_3424">
<span lang="EN" style="font-size:12pt;font-variant:small-caps;">Latter-no-harm</span><span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1466556275910_3423">:<span style="">
</span>Adding a later preference to a ballot should not harm any candidate already listed.’</span></div>
</li></ul>
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<span lang="EN" style="font-size:12pt;">Next, Woodall goes on to define nine different ‘versions of monotonicity.<span style="">
</span>The basic theme is that a candidate x should not be harmed by a change in the profile that appears to give more support to candidate x.</span></div>
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<span lang="EN" style="font-size:12pt;font-variant:small-caps;">Monotonicity:</span></div>
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<span lang="EN" style="font-size:12pt;font-variant:small-caps;">1-(mono-raise)</span><span lang="EN" style="font-size:12pt;">
x is raised on some ballots without changing the orders of other candidates<span style="font-variant:small-caps;">;</span></span></div>
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<span lang="EN" style="font-size:12pt;font-variant:small-caps;">2-(mono-raise delete)
</span><span lang="EN" style="font-size:12pt;">x is raised on some ballots and all the candidates now below x on those ballots
are deleted from them;</span></div>
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<span lang="EN" style="font-size:12pt;font-variant:small-caps;">3-(mono-raise random)
</span><span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1466556275910_3401">x is raised on some ballots and the positions now below x are filled (or left
empty) in any way that results in a valid ballot;<span style="font-variant:small-caps;">
</span></span></div>
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<span lang="EN" style="font-size:12pt;font-variant:small-caps;">4-(mono-append)</span><span lang="EN" style="font-size:12pt;">
x is added to the end of some ballots that did not previously contain x<span style="font-variant:small-caps;">;</span></span></div>
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<span lang="EN" style="font-size:12pt;font-variant:small-caps;">5-(mono-sub-plump)</span><span lang="EN" style="font-size:12pt;">
some ballots without x are replace by ballots with x placed top and with no second choice<span style="font-variant:small-caps;">;</span></span></div>
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<span lang="EN" style="font-size:12pt;font-variant:small-caps;">6-(mono-sub-top)</span><span lang="EN" style="font-size:12pt;">
some ballots that do not have x placed top are replaced with ballots that do place x top (and are otherwise arbitrary)<span style="font-variant:small-caps;">;</span></span></div>
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<span lang="EN" style="font-size:12pt;font-variant:small-caps;">7-(mono-add-plump)
</span><span lang="EN" style="font-size:12pt;">further ballots are added that place x top and with no second choices<span style="font-variant:small-caps;">;</span></span></div>
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<span lang="EN" style="font-size:12pt;font-variant:small-caps;">8-(mono-sub-top)</span><span lang="EN" style="font-size:12pt;">
further ballots are added that place x top (and are otherwise arbitrary)<span style="font-variant:small-caps;">;</span></span></div>
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<span lang="EN" style="font-size:12pt;font-variant:small-caps;">9-(mono-remove-bottom)</span><span lang="EN" style="font-size:12pt;">
some ballots are removed, all of which have x at bottom, below all other candidate<span style="font-variant:small-caps;">.’</span></span></div>
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<span lang="EN" style="font-size:12pt;">I look forward to any of your replies.</span></div>
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<span lang="EN" style="font-size:12pt;">Steve</span></div>
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<div style="margin:0in 0in 8pt;"><font face="Calibri"> </font></div>
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