<table cellspacing="0" cellpadding="0" border="0" ><tr><td valign="top" style="font: inherit;">1 has a path to 6 at least as strong as 6's path to 1, namely 1>3>6, at 15-11 and 14-11. It<br>seems a little odd, to me at least, that 6's path to 1 should benefit 2 but not 6 itself.<br>Starting from the top seems the only way of ensuring that the path that orders the two<br>candidates relative to each other is the one which actually contributes to the final outcome.<br><br>--- On <b>Sat, 1/29/11, Andrew Myers <i><andru@cs.cornell.edu></i></b> wrote:<br><blockquote style="border-left: 2px solid rgb(16, 16, 255); margin-left: 5px; padding-left: 5px;"><br>From: Andrew Myers <andru@cs.cornell.edu><br>Subject: [EM] An interesting real election<br>To: "Election Methods Mailing List" <election-methods@electorama.com><br>Date: Saturday, January 29, 2011, 4:40 PM<br><br><div id="yiv565028494">

  

    
  Here is an unusual case from a real poll run recently by a group
    using CIVS. Usually there is a Condorcet winner, but not this time.
    Who should win?<br>
    <br>
    Ranked pairs says #1, and ranks the six choices as shown. It only
    has to reverse one preference. Schulze says #2, because it beats #6
    by 15-11, and #6 beats #1 by 14-13. So #2 has a 14-13 beatpath vs.
    #1. Hill's method ("Condorcet-IRV") picks #6 as the winner.<br>
    <br>
    -- Andrew<br>
    <br>
    <table class="yiv565028494matrix">
      <tbody>
        <tr>
          <td> </td>
          <td> </td>
          <th width="20px">1.</th>
          <th width="20px">2.</th>
          <th width="20px">3.</th>
          <th width="20px">4.</th>
          <th width="20px">5.</th>
          <th width="20px">6.</th>
        </tr>
        <tr>
          <th align="left">1. <br>
          </th>
          <td width="40px"> </td>
          <td class="yiv565028494count">-</td>
          <td class="yiv565028494win">13</td>
          <td class="yiv565028494win">15</td>
          <td class="yiv565028494win">17</td>
          <td class="yiv565028494win">16</td>
          <td class="yiv565028494lose">13</td>
        </tr>
        <tr>
          <th align="left">2. <br>
          </th>
          <td width="40px"> </td>
          <td class="yiv565028494lose">9</td>
          <td class="yiv565028494count">-</td>
          <td class="yiv565028494win">13</td>
          <td class="yiv565028494win">14</td>
          <td class="yiv565028494win">17</td>
          <td class="yiv565028494win">15</td>
        </tr>
        <tr>
          <th align="left">3.</th>
          <td width="40px"> </td>
          <td class="yiv565028494lose">11</td>
          <td class="yiv565028494lose">11</td>
          <td class="yiv565028494count">-</td>
          <td class="yiv565028494win">13</td>
          <td class="yiv565028494win">15</td>
          <td class="yiv565028494win">14</td>
        </tr>
        <tr>
          <th align="left">4. <br>
          </th>
          <td width="40px"> </td>
          <td class="yiv565028494lose">9</td>
          <td class="yiv565028494lose">10</td>
          <td class="yiv565028494lose">10</td>
          <td class="yiv565028494count">-</td>
          <td class="yiv565028494win">14</td>
          <td class="yiv565028494tie">13</td>
        </tr>
        <tr>
          <th align="left">5. <br>
          </th>
          <td width="40px"> </td>
          <td class="yiv565028494lose">11</td>
          <td class="yiv565028494lose">10</td>
          <td class="yiv565028494lose">9</td>
          <td class="yiv565028494lose">10</td>
          <td class="yiv565028494count">-</td>
          <td class="yiv565028494win">13</td>
        </tr>
        <tr>
          <th align="left">6. <br>
          </th>
          <td width="40px"> </td>
          <td class="yiv565028494win">14</td>
          <td class="yiv565028494lose">11</td>
          <td class="yiv565028494lose">11</td>
          <td class="yiv565028494tie">13</td>
          <td class="yiv565028494lose">10</td>
          <td class="yiv565028494count">-</td>
        </tr>
      </tbody>
    </table>
  
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