Kathy:<div><br></div><div>Below is the explanation of Majority Judgment from Wikipedia. I agree that it is not the simplest tiebreaker; actually, in the thread "majority judgement question", there's a discussion of some simpler tiebreakers. All of the proposed tiebreakers would tend to give the same results almost always; the underlying idea is to take a median, which is usually one of the options given, and see "how close it is" to being higher or lower.</div>
<div><br></div><div>Anyway, here's Wikipedia:</div><div><span class="Apple-style-span" style="font-family: sans-serif; font-size: 13px; line-height: 19px; background-color: rgb(255, 255, 255); "><h2 style="color: black; background-image: none; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: initial; margin-top: 0px; margin-right: 0px; margin-bottom: 0.6em; margin-left: 0px; overflow-x: hidden; overflow-y: hidden; padding-top: 0.5em; padding-bottom: 0.17em; border-bottom-width: 1px; border-bottom-style: solid; border-bottom-color: rgb(170, 170, 170); width: auto; font-size: 19px; ">
<span class="mw-headline" id="Example_application">Example application</span></h2><p style="margin-top: 0.4em; margin-right: 0px; margin-bottom: 0.5em; margin-left: 0px; line-height: 1.5em; "><a href="http://en.wikipedia.org/wiki/File:Tennessee_map_for_voting_example.svg" class="image" style="text-decoration: none; color: rgb(6, 69, 173); background-image: none; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: initial; background-position: initial initial; background-repeat: initial initial; "><img alt="Tennessee and its four major cities: Memphis in the south-west; Nashville in the centre, Chattanooga in the south, and Knoxville in the east" src="http://upload.wikimedia.org/wikipedia/commons/thumb/8/88/Tennessee_map_for_voting_example.svg/500px-Tennessee_map_for_voting_example.svg.png" width="500" height="122" style="border-top-style: none; border-right-style: none; border-bottom-style: none; border-left-style: none; border-width: initial; border-color: initial; vertical-align: middle; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "></a></p>
<p style="margin-top: 0.4em; margin-right: 0px; margin-bottom: 0.5em; margin-left: 0px; line-height: 1.5em; ">Imagine that <a href="http://en.wikipedia.org/wiki/Tennessee" title="Tennessee" style="text-decoration: none; color: rgb(6, 69, 173); background-image: none; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: initial; background-position: initial initial; background-repeat: initial initial; ">Tennessee</a> is having an election on the location of its <a href="http://en.wikipedia.org/wiki/Capital_(political)" title="Capital (political)" class="mw-redirect" style="text-decoration: none; color: rgb(6, 69, 173); background-image: none; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: initial; background-position: initial initial; background-repeat: initial initial; ">capital</a>. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire <a href="http://en.wikipedia.org/wiki/Constituency" title="Constituency" class="mw-redirect" style="text-decoration: none; color: rgb(6, 69, 173); background-image: none; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: initial; background-position: initial initial; background-repeat: initial initial; ">electorate</a> lives in these four cities, and that everyone wants to live as near to the capital as possible.</p>
<p style="margin-top: 0.4em; margin-right: 0px; margin-bottom: 0.5em; margin-left: 0px; line-height: 1.5em; ">The candidates for the capital are:</p><ul style="line-height: 1.5em; list-style-type: square; margin-top: 0.3em; margin-right: 0px; margin-bottom: 0.5em; margin-left: 1.5em; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; list-style-image: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAUAAAANCAMAAABW4lS6AAAAGXRFWHRTb2Z0d2FyZQBBZG9iZSBJbWFnZVJlYWR5ccllPAAAAAZQTFRFAFKM////QIUK9QAAAAJ0Uk5T/wDltzBKAAAAGklEQVR42mJgBAEGokgGBjBGBxBxsBqAAAMACHwALd5r8ygAAAAASUVORK5CYII=); ">
<li style="margin-bottom: 0.1em; "><a href="http://en.wikipedia.org/wiki/Memphis,_Tennessee" title="Memphis, Tennessee" style="text-decoration: none; color: rgb(6, 69, 173); background-image: none; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: initial; background-position: initial initial; background-repeat: initial initial; ">Memphis</a>, the state's largest city, with 42% of the voters, but located far from the other cities</li>
<li style="margin-bottom: 0.1em; "><a href="http://en.wikipedia.org/wiki/Nashville,_Tennessee" title="Nashville, Tennessee" style="text-decoration: none; color: rgb(6, 69, 173); background-image: none; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: initial; background-position: initial initial; background-repeat: initial initial; ">Nashville</a>, with 26% of the voters, near the center of Tennessee</li>
<li style="margin-bottom: 0.1em; "><a href="http://en.wikipedia.org/wiki/Knoxville,_Tennessee" title="Knoxville, Tennessee" style="text-decoration: none; color: rgb(6, 69, 173); background-image: none; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: initial; background-position: initial initial; background-repeat: initial initial; ">Knoxville</a>, with 17% of the voters</li>
<li style="margin-bottom: 0.1em; "><a href="http://en.wikipedia.org/wiki/Chattanooga,_Tennessee" title="Chattanooga, Tennessee" style="text-decoration: none; color: rgb(6, 69, 173); background-image: none; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: initial; background-position: initial initial; background-repeat: initial initial; ">Chattanooga</a>, with 15% of the voters</li>
</ul><p style="margin-top: 0.4em; margin-right: 0px; margin-bottom: 0.5em; margin-left: 0px; line-height: 1.5em; ">The preferences of the voters would be divided like this:</p><table class="wikitable" style="font-size: 13px; margin-top: 1em; margin-right: 1em; margin-bottom: 1em; margin-left: 0px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: rgb(249, 249, 249); border-top-width: 1px; border-right-width: 1px; border-bottom-width: 1px; border-left-width: 1px; border-top-color: rgb(170, 170, 170); border-right-color: rgb(170, 170, 170); border-bottom-color: rgb(170, 170, 170); border-left-color: rgb(170, 170, 170); border-top-style: solid; border-right-style: solid; border-bottom-style: solid; border-left-style: solid; border-collapse: collapse; color: black; background-position: initial initial; background-repeat: initial initial; ">
<tbody><tr><th width="25%" style="border-top-width: 1px; border-right-width: 1px; border-bottom-width: 1px; border-left-width: 1px; border-top-color: rgb(170, 170, 170); border-right-color: rgb(170, 170, 170); border-bottom-color: rgb(170, 170, 170); border-left-color: rgb(170, 170, 170); border-top-style: solid; border-right-style: solid; border-bottom-style: solid; border-left-style: solid; padding-top: 0.2em; padding-right: 0.2em; padding-bottom: 0.2em; padding-left: 0.2em; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: rgb(255, 221, 221); text-align: center; background-position: initial initial; background-repeat: initial initial; ">
42% of voters<br><small>(close to Memphis)</small></th><th width="25%" style="border-top-width: 1px; border-right-width: 1px; border-bottom-width: 1px; border-left-width: 1px; border-top-color: rgb(170, 170, 170); border-right-color: rgb(170, 170, 170); border-bottom-color: rgb(170, 170, 170); border-left-color: rgb(170, 170, 170); border-top-style: solid; border-right-style: solid; border-bottom-style: solid; border-left-style: solid; padding-top: 0.2em; padding-right: 0.2em; padding-bottom: 0.2em; padding-left: 0.2em; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: rgb(204, 255, 204); text-align: center; background-position: initial initial; background-repeat: initial initial; ">
26% of voters<br><small>(close to Nashville)</small></th><th width="25%" style="border-top-width: 1px; border-right-width: 1px; border-bottom-width: 1px; border-left-width: 1px; border-top-color: rgb(170, 170, 170); border-right-color: rgb(170, 170, 170); border-bottom-color: rgb(170, 170, 170); border-left-color: rgb(170, 170, 170); border-top-style: solid; border-right-style: solid; border-bottom-style: solid; border-left-style: solid; padding-top: 0.2em; padding-right: 0.2em; padding-bottom: 0.2em; padding-left: 0.2em; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: rgb(221, 221, 255); text-align: center; background-position: initial initial; background-repeat: initial initial; ">
15% of voters<br><small>(close to Chattanooga)</small></th><th width="25%" style="border-top-width: 1px; border-right-width: 1px; border-bottom-width: 1px; border-left-width: 1px; border-top-color: rgb(170, 170, 170); border-right-color: rgb(170, 170, 170); border-bottom-color: rgb(170, 170, 170); border-left-color: rgb(170, 170, 170); border-top-style: solid; border-right-style: solid; border-bottom-style: solid; border-left-style: solid; padding-top: 0.2em; padding-right: 0.2em; padding-bottom: 0.2em; padding-left: 0.2em; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: rgb(255, 238, 221); text-align: center; background-position: initial initial; background-repeat: initial initial; ">
17% of voters<br><small>(close to Knoxville)</small></th></tr><tr><td style="border-top-width: 1px; border-right-width: 1px; border-bottom-width: 1px; border-left-width: 1px; border-top-color: rgb(170, 170, 170); border-right-color: rgb(170, 170, 170); border-bottom-color: rgb(170, 170, 170); border-left-color: rgb(170, 170, 170); border-top-style: solid; border-right-style: solid; border-bottom-style: solid; border-left-style: solid; padding-top: 0.2em; padding-right: 0.2em; padding-bottom: 0.2em; padding-left: 0.2em; ">
<ol style="line-height: 1.5em; margin-top: 0.3em; margin-right: 0px; margin-bottom: 0.5em; margin-left: 3.2em; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; list-style-image: none; text-align: left; ">
<li style="margin-bottom: 0.1em; "><b>Memphis</b></li><li style="margin-bottom: 0.1em; ">Nashville</li><li style="margin-bottom: 0.1em; ">Chattanooga</li><li style="margin-bottom: 0.1em; ">Knoxville</li></ol></td><td style="border-top-width: 1px; border-right-width: 1px; border-bottom-width: 1px; border-left-width: 1px; border-top-color: rgb(170, 170, 170); border-right-color: rgb(170, 170, 170); border-bottom-color: rgb(170, 170, 170); border-left-color: rgb(170, 170, 170); border-top-style: solid; border-right-style: solid; border-bottom-style: solid; border-left-style: solid; padding-top: 0.2em; padding-right: 0.2em; padding-bottom: 0.2em; padding-left: 0.2em; ">
<ol style="line-height: 1.5em; margin-top: 0.3em; margin-right: 0px; margin-bottom: 0.5em; margin-left: 3.2em; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; list-style-image: none; text-align: left; ">
<li style="margin-bottom: 0.1em; "><b>Nashville</b></li><li style="margin-bottom: 0.1em; ">Chattanooga</li><li style="margin-bottom: 0.1em; ">Knoxville</li><li style="margin-bottom: 0.1em; ">Memphis</li></ol></td><td style="border-top-width: 1px; border-right-width: 1px; border-bottom-width: 1px; border-left-width: 1px; border-top-color: rgb(170, 170, 170); border-right-color: rgb(170, 170, 170); border-bottom-color: rgb(170, 170, 170); border-left-color: rgb(170, 170, 170); border-top-style: solid; border-right-style: solid; border-bottom-style: solid; border-left-style: solid; padding-top: 0.2em; padding-right: 0.2em; padding-bottom: 0.2em; padding-left: 0.2em; ">
<ol style="line-height: 1.5em; margin-top: 0.3em; margin-right: 0px; margin-bottom: 0.5em; margin-left: 3.2em; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; list-style-image: none; text-align: left; ">
<li style="margin-bottom: 0.1em; "><b>Chattanooga</b></li><li style="margin-bottom: 0.1em; ">Knoxville</li><li style="margin-bottom: 0.1em; ">Nashville</li><li style="margin-bottom: 0.1em; ">Memphis</li></ol></td><td style="border-top-width: 1px; border-right-width: 1px; border-bottom-width: 1px; border-left-width: 1px; border-top-color: rgb(170, 170, 170); border-right-color: rgb(170, 170, 170); border-bottom-color: rgb(170, 170, 170); border-left-color: rgb(170, 170, 170); border-top-style: solid; border-right-style: solid; border-bottom-style: solid; border-left-style: solid; padding-top: 0.2em; padding-right: 0.2em; padding-bottom: 0.2em; padding-left: 0.2em; ">
<ol style="line-height: 1.5em; margin-top: 0.3em; margin-right: 0px; margin-bottom: 0.5em; margin-left: 3.2em; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; list-style-image: none; text-align: left; ">
<li style="margin-bottom: 0.1em; "><b>Knoxville</b></li><li style="margin-bottom: 0.1em; ">Chattanooga</li><li style="margin-bottom: 0.1em; ">Nashville</li><li style="margin-bottom: 0.1em; ">Memphis</li></ol></td></tr></tbody></table>
<p style="margin-top: 0.4em; margin-right: 0px; margin-bottom: 0.5em; margin-left: 0px; line-height: 1.5em; ">If there were four ratings named "Excellent", "Good", "Fair", and "Poor", and each voter assigned four different ratings to the four cities, then the sorted scores would be as follows:</p>
<table style="font-size: 13px; "><tbody><tr><td align="right">City </td><td><table cellpadding="0" width="500" border="0" cellspacing="0" style="font-size: 13px; "><tbody><tr><td width="49%"> </td><td width="2%">↓</td>
<td width="49%">
Median point</td></tr></tbody></table></td></tr><tr><td align="right">Nashville</td><td><table cellpadding="0" width="500" border="0" cellspacing="0" style="font-size: 13px; "><tbody><tr><td bgcolor="green" width="26%"> </td>
<td bgcolor="YellowGreen" width="42%"></td><td bgcolor="Gold" width="32%"></td></tr></tbody></table></td></tr><tr><td align="right">Chattanooga</td><td><table cellpadding="0" width="500" border="0" cellspacing="0" style="font-size: 13px; ">
<tbody><tr><td bgcolor="green" width="15%"> </td><td bgcolor="YellowGreen" width="43%"></td><td bgcolor="Gold" width="42%"></td></tr></tbody></table></td></tr><tr><td align="right">Knoxville</td><td><table cellpadding="0" width="500" border="0" cellspacing="0" style="font-size: 13px; ">
<tbody><tr><td bgcolor="green" width="17%"> </td><td bgcolor="YellowGreen" width="15%"></td><td bgcolor="Gold" width="26%"></td><td bgcolor="DarkOrange" width="42%"></td></tr></tbody></table></td></tr><tr><td align="right">
Memphis</td><td><table cellpadding="0" width="500" border="0" cellspacing="0" style="font-size: 13px; "><tbody><tr><td bgcolor="green" width="42%"> </td><td bgcolor="DarkOrange" width="58%"></td></tr></tbody></table></td>
</tr><tr><td> </td><td> </td></tr><tr><td> </td><td><table cellpadding="1" border="0" cellspacing="1" style="font-size: 13px; "><tbody><tr><td> </td><td bgcolor="green"> </td><td> Excellent </td><td bgcolor="YellowGreen">
</td><td> Good </td><td bgcolor="Gold"> </td><td> Fair </td><td bgcolor="DarkOrange"> </td><td> Poor </td></tr></tbody></table></td></tr></tbody></table><p style="margin-top: 0.4em; margin-right: 0px; margin-bottom: 0.5em; margin-left: 0px; line-height: 1.5em; ">
The median rating for Nashville and Chatanooga is "Good"; for Knoxville, "Fair"; and for Memphis, "Poor". Nashville and Chatanooga are tied, so "Good" ratings have to be removed from both, until their medians become different. After removing 16% "Good" ratings from the votes of each, the sorted ratings are now:</p>
<table style="font-size: 13px; "><tbody><tr><td align="right">City </td><td><table cellpadding="0" width="500" border="0" cellspacing="0" style="font-size: 13px; "><tbody><tr><td width="49%"> </td><td width="2%">↓</td>
<td width="49%">
Median point</td></tr></tbody></table></td></tr><tr><td align="right">Nashville</td><td><table cellpadding="0" width="500" border="0" cellspacing="0" style="font-size: 13px; "><tbody><tr><td bgcolor="gray" width="8%"> </td>
<td bgcolor="green" width="26%"> </td><td bgcolor="YellowGreen" width="26%"></td><td bgcolor="Gold" width="32%"></td><td bgcolor="gray" width="8%"></td></tr></tbody></table></td></tr><tr><td align="right">Chattanooga</td>
<td><table cellpadding="0" width="500" border="0" cellspacing="0" style="font-size: 13px; "><tbody><tr><td bgcolor="gray" width="8%"></td><td bgcolor="green" width="15%"> </td><td bgcolor="YellowGreen" width="27%"></td><td bgcolor="Gold" width="42%">
</td><td bgcolor="gray" width="8%"></td></tr></tbody></table></td></tr><tr><td> </td><td> </td></tr><tr><td> </td><td><table cellpadding="1" border="0" cellspacing="1" style="font-size: 13px; "><tbody><tr><td> </td>
<td bgcolor="gray">
</td><td> Removed ratings (sorted to both ends evenly for easy comparison of medians with above).</td></tr></tbody></table></td></tr></tbody></table><p style="margin-top: 0.4em; margin-right: 0px; margin-bottom: 0.5em; margin-left: 0px; line-height: 1.5em; ">
Chatanooga now has the same number of "Fair" ratings as "Good" and "Excellent" combined, so its median is rounded down to "Fair", while Nashville's median remains at "Good"<sup id="cite_ref-6" class="reference" style="line-height: 1em; font-style: normal; "><a href="http://en.wikipedia.org/wiki/Majority_Judgment#cite_note-6" style="text-decoration: none; color: rgb(6, 69, 173); background-image: none; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: initial; white-space: nowrap; background-position: initial initial; background-repeat: initial initial; "><span>[</span>7<span>]</span></a></sup> and so <b>Nashville</b>, the capital in real life, wins.</p>
<p style="margin-top: 0.4em; margin-right: 0px; margin-bottom: 0.5em; margin-left: 0px; line-height: 1.5em; ">If voters from Knoxville and Chattanooga were to rate Nashville as "Poor" and/or both sets of voters were to rate Chattanooga as "Excellent", in an attempt to make their preferred candidate Chatanooga win, the winner would still be Nashville.</p>
</span><br><div class="gmail_quote">2011/10/19 Kathy Dopp <span dir="ltr"><<a href="mailto:kathy.dopp@gmail.com">kathy.dopp@gmail.com</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
> 3. Re: Declaration Status<br>
<br>
I still don't fully understand this statement:<br>
<br>
Majority Judgment ... If there is a tie for first place, the method<br>
repeatedly removes one median score from each tied candidate until the<br>
tie is broken.<br>
<br>
My question is: How is the one median score selected to be removed<br>
from each tied candidate? And why is this a good tie-breaking method?<br>
<br>
Thanks.<br>
<br>
Kathy Dopp<br>
<a href="http://electionmathematics.org" target="_blank">http://electionmathematics.org</a><br>
Town of Colonie, NY 12304<br>
"One of the best ways to keep any conversation civil is to support the<br>
discussion with true facts."<br>
"Renewable energy is homeland security."<br>
<br>
Fundamentals of Verifiable Elections<br>
<a href="http://kathydopp.com/wordpress/?p=174" target="_blank">http://kathydopp.com/wordpress/?p=174</a><br>
<br>
View some of my research on my SSRN Author page:<br>
<a href="http://ssrn.com/author=1451051" target="_blank">http://ssrn.com/author=1451051</a><br>
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</blockquote></div><br></div>