<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_1467146186436_10477"><span id="yui_3_16_0_ym19_1_1467146186436_10514">Hi Steve,</span></div><div id="yui_3_16_0_ym19_1_1467146186436_10477"><span><br></span></div><div id="yui_3_16_0_ym19_1_1467146186436_10477" dir="ltr"><span id="yui_3_16_0_ym19_1_1467146186436_11919">Majority Judgment is a variety of "median rating" methods which I see as pretty similar. Woodall made one himself called Quota-Limited Trickle-Down and in fact if you google "woodall qltd" you can find a .pdf with a chart of some of the properties. The most noteworthy here are the failures of Later-no-harm and Mono-add-top. (Both are failures that IRV does not share.) For Later-no-harm: Suppose that candidate A is elected. It's possible that there is a bloc of voters who rated B above A, but A above zero, and that if these voters had lowered their A rating to zero, then candidate B would win instead, which is an outcome this bloc of voters would have preferred. They could criticize that the method should be smart enough to not use their A ratings to elect A when it would have been possible for them to elect B. If not a fairness issue, it's at least an issue of the method requiring voters to keep certain strategy in mind.</span></div><div id="yui_3_16_0_ym19_1_1467146186436_10477" dir="ltr"><span><br></span></div><div id="yui_3_16_0_ym19_1_1467146186436_10477" dir="ltr"><span id="yui_3_16_0_ym19_1_1467146186436_12294">The Mono-add-top issue works like this: Suppose that C is elected. It's possible under median ratings methods that when some ballots rating a different candidate "D" first (i.e. D is the first preference) are removed from consideration, then a candidate D becomes the new winner. In other words, when C wins, the D-first voters can criticize that they were penalized for showing up to vote.</span></div><div id="yui_3_16_0_ym19_1_1467146186436_10477" dir="ltr"><span><br></span></div><div id="yui_3_16_0_ym19_1_1467146186436_10477" dir="ltr"><span id="yui_3_16_0_ym19_1_1467146186436_13220">I should note that while IRV does not have these issues, probably *most* of our proposed methods do, so they aren't necessarily deal-breakers.</span></div><div id="yui_3_16_0_ym19_1_1467146186436_10477" dir="ltr"><span><br></span></div><div id="yui_3_16_0_ym19_1_1467146186436_10477" dir="ltr"><span id="yui_3_16_0_ym19_1_1467146186436_13221">While median rating is more resistant to manipulation than Range, I still view the manipulation potential as bad. For example, if you "defensively" rate A as zero, in the Later-no-harm example above, out of a quite reasonable fear that you need to do this to help B win instead of A, this is the type of thing meant by manipulation. It is less likely to have an effect than in Range, but you will still have the incentive to do it.</span></div><div id="yui_3_16_0_ym19_1_1467146186436_10477" dir="ltr"><span><br></span></div><div id="yui_3_16_0_ym19_1_1467146186436_10477" dir="ltr"><span id="yui_3_16_0_ym19_1_1467146186436_13227">My main distaste for median rating comes from my feeling that in most scenarios (i.e. availability of information on others' rating intentions) strategic-minded voters would only use the top and bottom ratings. This is because (as we see from the Later-no-harm example) median rating doesn't really offer guarantees about how your ratings will be used in relation to each other. The rating/grade values have no independent, practical meaning. If voters have this perception and respond with this behavior, then the method is just an overly complicated form of approval voting. In that case I'd rather just use approval, because it's clearer what's going on. (There are arguments about whether median rating voters would actually try to be so strategic, and about whether it would be bad if they did, but I will skip over that.)</span></div><div id="yui_3_16_0_ym19_1_1467146186436_10477" dir="ltr"><span><br></span></div><div id="yui_3_16_0_ym19_1_1467146186436_10477" dir="ltr"><span id="yui_3_16_0_ym19_1_1467146186436_15243">Your definition for "one citizen one vote" is difficult for me because it seems focused on how the winner is found. For example you say preferences should be counted equally "</span>as long as possible, until" something happens, which seems to assume that an election method algorithm is something that unfolds over time. Normally I view an election method as defined by its results, and there need not be a single set of steps which finds the result. I wonder what would be an example of a method that violates "one citizen one vote," and if there might be another way of describing what is problematic about it.</div><div id="yui_3_16_0_ym19_1_1467146186436_10477" dir="ltr"><br></div><div id="yui_3_16_0_ym19_1_1467146186436_10477" dir="ltr">I find a lot of methods tolerable, and I've designed a lot of methods too (most of them tolerable). I care about certain properties more than others, but the ones I like aren't even all compatible with each other. In general I feel that election methods should produce an outcome that would be plausible if the voters had been able to gather and vote in person, just as a legislature.<br></div><div id="yui_3_16_0_ym19_1_1467146186436_10477" dir="ltr"><br></div><div id="yui_3_16_0_ym19_1_1467146186436_10477" dir="ltr">Kevin</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1467146186436_10363"><br><br></div><div class="yahoo_quoted" id="yui_3_16_0_ym19_1_1467146186436_10579" 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_1467146186436_10578"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 16px;" id="yui_3_16_0_ym19_1_1467146186436_10577"> <div dir="ltr" id="yui_3_16_0_ym19_1_1467146186436_10576"> <font size="2" face="Arial" id="yui_3_16_0_ym19_1_1467146186436_11923"> <hr size="1" id="yui_3_16_0_ym19_1_1467146186436_11922"> <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>; "stepjak@yahoo.fr" <stepjak@yahoo.fr> <br> <b id="yui_3_16_0_ym19_1_1467146186436_18345"><span style="font-weight: bold;" id="yui_3_16_0_ym19_1_1467146186436_18344">Envoyé le :</span></b> Lundi 27 juin 2016 18h00<br> <b><span style="font-weight: bold;">Objet :</span></b> [EM] The easiest method to 'tolerate'<br> </font> </div> <div class="y_msg_container" id="yui_3_16_0_ym19_1_1467146186436_10580"><br><div id="yiv7474249572">
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<span style="color:black;font-size:12pt;"><font face="Calibri">To everyone:</font></span></div>
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<font face="Calibri" id="yui_3_16_0_ym19_1_1467146186436_13424"><span style="color:black;font-size:12pt;" id="yui_3_16_0_ym19_1_1467146186436_13426">Thank you Kevin for responding to my questions about IRV being nonmonotonic.<span style="">
</span>I think our dialogue would be assisted by me also understanding your views about the Majority Judgment method.<span style="">
</span>You said:<span style=""> </span>‘</span><span style="color:black;font-size:12pt;" id="yui_3_16_0_ym19_1_1467146186436_13427">All proposed methods are unfair in some way, and people have different
views on what is or isn't tolerable’.<span style=""> </span>Currently I do not yet see how Majority Judgment is in any way ‘unfair’.<span style="">
</span>MJ seems to resist manipulation more than any one of the other proposed methods.<span style="">
</span>Also, it seems fully to satisfy what I mean by the ‘one-citizen-one-vote’ principle
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<font face="Calibri" id="yui_3_16_0_ym19_1_1467146186436_13429"><span style="color:black;font-size:12pt;" id="yui_3_16_0_ym19_1_1467146186436_17687">for electing a single-winner.<span style="" id="yui_3_16_0_ym19_1_1467146186436_17686">
</span></span><span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1467146186436_13428">In this context, this principle requires that each citizen’s vote (preferences or ‘grades’) be
counted equally as long as technically possible until the single-winner is discovered, i.e. the candidate who has received the highest average intensity available of majority support.</span></font></div>
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<font face="Calibri" id="yui_3_16_0_ym19_1_1467146186436_17709"><span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1467146186436_17708">Do you agree or do you see a different method as easiest to ‘tolerate’?</span><span lang="EN" style="color:black;font-size:12pt;">
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<b><span style="color:black;font-size:12pt;"><font face="Calibri">From:</font></span></b><span style="color:black;font-size:12pt;"><font face="Calibri">
Kevin Venzke <stepjak@yahoo.fr><br>
<b>Sent:</b> Wednesday, June 22, 2016 1:05 AM<br>
<b>To:</b> steve bosworth; election-methods@lists.electorama.com<br>
<b>Subject:</b> Re: [EM] Wiki says IRV is monotonic--not fully democratic? </font>
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<span style="color:black;font-size:12pt;"><font face="Calibri">Hi Steve,</font></span></div>
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<span style="color:black;font-size:12pt;"><font face="Calibri">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.</font></span></div>
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<span style="color:black;font-size:12pt;" id="yui_3_16_0_ym19_1_1467146186436_17803"><font face="Calibri" id="yui_3_16_0_ym19_1_1467146186436_17802">You used the terms "democratic" and "one citizen one vote" but I don't really know of definitions for these terms
at this level.</font></span></div>
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<span style="color:black;font-size:12pt;"><font face="Calibri">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.</font></span></div>
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<span style="color:black;font-size:12pt;"><font face="Calibri">Kevin</font></span></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">++++++++++++++++++++++++</font></span></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">To everyone:</font></span></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">Below, Steve is considering the following section of the following June 21, 2016 Wikipedia
article:<span style=""> </span>‘<span style="">Monotonicity criterion’.<span style="">
</span>He will refer to the author of that section as ‘Wiki’:</span></font></span></div>
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<font face="Calibri"><b><span lang="EN" style="font-size:12pt;">Instant-runoff voting and the two-round system are not monotonic[</span></b><span style="font-size:12pt;"><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;">edit</span></b></a></span></font></div>
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<font face="Calibri" id="yui_3_16_0_ym19_1_1467146186436_17574"><span lang="EN" style="font-size:12pt;">Using an example that applies to
</span><span style="font-size:12pt;"><a rel="nofollow" title="Instant-runoff voting" target="_blank" href="https://en.wikipedia.org/wiki/Instant-runoff_voting"><span lang="EN" style="color:blue;">instant-runoff
voting</span></a></span><span lang="EN" style="font-size:12pt;"> (IRV) and to the
</span><span style="font-size:12pt;"><a rel="nofollow" title="Two-round system" target="_blank" href="https://en.wikipedia.org/wiki/Two-round_system"><span lang="EN" style="color:blue;">two-round
system</span></a></span><span lang="EN" style="font-size:12pt;">, it is shown that these voting systems violate the mono-raise criterion. Suppose a
</span><span style="font-size:12pt;"><a rel="nofollow" title="President" target="_blank" href="https://en.wikipedia.org/wiki/President"><span lang="EN" style="color:blue;">president</span></a></span><span lang="EN" style="font-size:12pt;" id="yui_3_16_0_ym19_1_1467146186436_17573">
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></font></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">Suppose the votes are cast as follows:</font></span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><b><span style="font-size:12pt;"><font face="Calibri">Number of votes</font></span></b></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><b><span style="font-size:12pt;"><font face="Calibri">1st preference</font></span></b></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><b><span style="font-size:12pt;"><font face="Calibri">2nd preference</font></span></b></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"><font face="Calibri">28</font></span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"><font face="Calibri">5</font></span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"><font face="Calibri">30</font></span></div>
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<td 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;"><font face="Calibri">5</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Left</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Right</font></span></div>
<font face="Times New Roman"></font></td>
</tr>
<tr style="">
<td 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;"><font face="Calibri">16</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Center</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Left</font></span></div>
<font face="Times New Roman"></font></td>
</tr>
<tr style="">
<td 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;"><font face="Calibri">16</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Center</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Right</font></span></div>
<font face="Times New Roman"></font></td>
</tr>
</tbody>
</table>
<font face="Times New Roman"></font>
<div style="margin:0in 0in 8pt;line-height:normal;">
<span lang="EN" style="font-size:12pt;"><font face="Calibri">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.</font></span></div>
<font face="Times New Roman"></font>
<div style="margin:0in 0in 8pt;line-height:normal;">
<b><span lang="EN" style="font-size:12pt;"><font face="Calibri">[STEVE’S Additions:</font></span></b></div>
<font face="Times New Roman"></font>
<div style="margin:0in 0in 8pt;line-height:normal;">
<span lang="EN" style="font-size:12pt;"><font face="Calibri">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.</font></span></div>
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<table style="margin:auto auto auto 0.5in;" border="1" cellpadding="0">
<tbody>
<tr style="">
<td 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;"><font face="Calibri">Author’s
</font></span></div>
<font face="Times New Roman"></font>
<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"><font face="Calibri">1<sup>st</sup> IRV</font></span></div>
<font face="Times New Roman"></font>
<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"><font face="Calibri">COUNT</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Left</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Center</font></span></div>
<font face="Times New Roman"></font></td>
<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;"><font face="Calibri">Right</font></span></div>
<font face="Times New Roman"></font></td>
</tr>
<tr style="">
<td 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;"><font face="Calibri">1</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">35</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">32</font></span></div>
<font face="Times New Roman"></font></td>
<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;"><font face="Calibri">33</font></span></div>
<font face="Times New Roman"></font></td>
</tr>
<tr style="">
<td 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;"><font face="Calibri">2</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">51</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri"> </font></span></div>
<font face="Times New Roman"></font></td>
<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;"><font face="Calibri">49</font></span></div>
<font face="Times New Roman"></font></td>
</tr>
</tbody>
</table>
<font face="Times New Roman"></font>
<div style="margin:0in 0in 8pt;line-height:normal;">
<span lang="EN" style="font-size:12pt;"><font face="Calibri">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:</font></span></div>
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<table style="margin:auto auto auto 0.5in;" border="1" cellpadding="0">
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<td 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;"><b><span style="font-size:12pt;"><font face="Calibri">Number of votes</font></span></b></div>
<font face="Times New Roman"></font></td>
<td 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;"><b><span style="font-size:12pt;"><font face="Calibri">1st preference</font></span></b></div>
<font face="Times New Roman"></font></td>
<td 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;"><b><span style="font-size:12pt;"><font face="Calibri">2nd preference</font></span></b></div>
<font face="Times New Roman"></font></td>
</tr>
<tr style="">
<td 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;"><font face="Calibri">3</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Right</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Left</font></span></div>
<font face="Times New Roman"></font></td>
</tr>
<tr style="">
<td 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;"><font face="Calibri">7</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Left</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Right</font></span></div>
<font face="Times New Roman"></font></td>
</tr>
</tbody>
</table>
<font face="Times New Roman"></font>
<div style="margin:0in 0in 8pt;line-height:normal;">
<span lang="EN" style="font-size:12pt;"><font face="Calibri">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. </font></span></div>
<font face="Times New Roman"></font>
<div style="margin:0in 0in 8pt;line-height:normal;">
<b><span lang="EN" style="font-size:12pt;"><font face="Calibri">1-[STEVE’S IRV exploration:</font></span></b></div>
<font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font>
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<tbody>
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<td style="padding:1.5pt;border:rgb(0, 0, 0);background-color:transparent;" colspan="3">
<font face="Times New Roman"></font>
<div style="margin:0in 0in 0pt;line-height:normal;"><b><span style="font-size:12pt;"><font face="Calibri">Wiki’s changed preferences (2<sup>nd</sup> Set of Ballots)</font></span></b></div>
<font face="Times New Roman"></font></td>
</tr>
<tr style="">
<td 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;"><b><span style="font-size:12pt;"><font face="Calibri">Number of votes</font></span></b></div>
<font face="Times New Roman"></font></td>
<td 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;"><b><span style="font-size:12pt;"><font face="Calibri">1st preference</font></span></b></div>
<font face="Times New Roman"></font></td>
<td 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;"><b><span style="font-size:12pt;"><font face="Calibri">2nd preference</font></span></b></div>
<font face="Times New Roman"></font></td>
</tr>
<tr style="">
<td 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;"><font face="Calibri">28</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Right</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Center</font></span></div>
<font face="Times New Roman"></font></td>
</tr>
<tr style="">
<td 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;"><font face="Calibri">3</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Right</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Left</font></span></div>
<font face="Times New Roman"></font></td>
</tr>
<tr style="">
<td 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;"><font face="Calibri">2</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Left</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Right</font></span></div>
<font face="Times New Roman"></font></td>
</tr>
<tr style="">
<td 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;"><font face="Calibri">30</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Left</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Center</font></span></div>
<font face="Times New Roman"></font></td>
</tr>
<tr style="">
<td 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;"><font face="Calibri">5</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Left</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Right</font></span></div>
<font face="Times New Roman"></font></td>
</tr>
<tr style="">
<td 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;"><font face="Calibri">16</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Center</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Left</font></span></div>
<font face="Times New Roman"></font></td>
</tr>
<tr style="">
<td 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;"><font face="Calibri">16</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Center</font></span></div>
<font face="Times New Roman"></font></td>
<td 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;"><font face="Calibri">Right</font></span></div>
<font face="Times New Roman"></font></td>
</tr>
</tbody>
</table>
<font face="Times New Roman"></font>
<div style="margin:0in 0in 8pt;line-height:normal;">
<span lang="EN" style="font-size:12pt;"><font face="Calibri"> </font></span></div>
<font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font><font face="Times New Roman"></font>
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<tbody>
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<td 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;"><font face="Calibri">2<sup>nd</sup> IRV</font></span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"><font face="Calibri">COUNT</font></span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"><font face="Calibri">Left</font></span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"><font face="Calibri">Right</font></span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"><font face="Calibri">1</font></span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"><font face="Calibri">37</font></span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"><font face="Calibri">32</font></span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"><font face="Calibri">31</font></span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"><font face="Calibri">2</font></span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"><font face="Calibri">40</font></span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"><font face="Calibri">60</font></span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"><font face="Calibri">0</font></span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"><font face="Calibri">3</font></span></div>
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<div style="margin:0in 0in 0pt;line-height:normal;"><span style="font-size:12pt;"><font face="Calibri">60</font></span></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">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.</font></span></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">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></font></span></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">Intensity of support calculations:</font></span></div>
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<u><span lang="EN" style="font-size:12pt;"><font face="Calibri">1<sup>st</sup> Set of Ballots</font></span></u></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">35X10 +16X9=350+144=494</font></span></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">494 divided by 51=9.76</font></span></div>
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<u><span lang="EN" style="font-size:12pt;"><font face="Calibri">2<sup>nd</sup> Set of Ballots</font></span></u></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">32X10 +28X9=320+252=572</font></span></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">572 divided by 60=9.53</font></span></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">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:</font></span></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">32 X 1<sup>st</sup> preferences and 58 X 2<sup>nd</sup> preferences for the Center candidate:</font></span></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">32X10+58X9=320+522=842</font></span></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">842 divided by 90= 9.36</font></span></div>
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<font face="Calibri"><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;">mono-raise criterion’<span style="">:
‘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></font></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">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]?</font></span></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">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?</font></span></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">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].</font></span></div>
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<span lang="EN" style="font-size:12pt;font-variant:small-caps;">Later-no-help</span><span lang="EN" style="font-size:12pt;">:<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;">
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<span lang="EN" style="font-size:12pt;font-variant:small-caps;">Latter-no-harm</span><span lang="EN" style="font-size:12pt;">:<span style="">
</span>Adding a later preference to a ballot should not harm any candidate already listed.’</span></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">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.</font></span></div>
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<span lang="EN" style="font-size:12pt;font-variant:small-caps;"><font face="Calibri">Monotonicity:</font></span></div>
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<font face="Calibri"><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></font></div>
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<font face="Calibri"><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></font></div>
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<font face="Calibri"><span lang="EN" style="font-size:12pt;font-variant:small-caps;">3-(mono-raise random)
</span><span lang="EN" style="font-size:12pt;">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></font></div>
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<font face="Calibri"><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></font></div>
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<font face="Calibri"><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></font></div>
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<font face="Calibri"><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></font></div>
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<font face="Calibri"><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></font></div>
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<font face="Calibri"><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></font></div>
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<font face="Calibri"><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></font></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">I look forward to any of your replies.</font></span></div>
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<span lang="EN" style="font-size:12pt;"><font face="Calibri">Steve</font></span></div>
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<div style="margin:0in 0in 8pt;"><span style="line-height:107%;font-size:12pt;"><font face="Calibri"> </font></span></div>
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