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It's a little tough to spot without the coloring that CIVS does, but
#1 loses pairwise to #6. This makes #2 win according to Schulze. As
Markus points out, #2 is the candidate with the weakest pairwise
defeat (13-9 vs the 14-13 defeat of #1 by #6).<br>
<br>
-- Andrew<br>
<br>
On 1/30/11 2:33 PM, Paul Kislanko wrote:
<blockquote cite="mid:46B1D36D18304FF8BAE7503635CD6161@jkis01"
type="cite">
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<div dir="ltr" align="left"><span class="067343219-30012011"><font
color="#0000ff" face="Arial" size="2">How is #1 not a
Condorcet Winner, since #1 pairwise-beats every other
alternative?</font></span></div>
<br>
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lang="en-us">
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<font face="Tahoma" size="2"><b>From:</b>
<a class="moz-txt-link-abbreviated" href="mailto:election-methods-bounces@lists.electorama.com">election-methods-bounces@lists.electorama.com</a>
[<a class="moz-txt-link-freetext" href="mailto:election-methods-bounces@lists.electorama.com">mailto:election-methods-bounces@lists.electorama.com</a>] <b>On
Behalf Of </b>Andrew Myers<br>
<b>Sent:</b> Saturday, January 29, 2011 4:41 PM<br>
<b>To:</b> Election Methods Mailing List<br>
<b>Subject:</b> [EM] An interesting real election<br>
</font><br>
</div>
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="matrix">
<tbody>
<tr>
<td> </td>
<td> </td>
<th width="20">1.</th>
<th width="20">2.</th>
<th width="20">3.</th>
<th width="20">4.</th>
<th width="20">5.</th>
<th width="20">6.</th>
</tr>
<tr>
<th align="left">1. <br>
</th>
<td width="40"> </td>
<td class="count">-</td>
<td class="win" title="mead.hivemind.net beats
maya.hivemind.net 13–9">13</td>
<td class="win" title="mead.hivemind.net beats
buzz.hivemind.net 15–11">15</td>
<td class="win" title="mead.hivemind.net beats
sting.hivemind.net 17–9">17</td>
<td class="win" title="mead.hivemind.net beats
bumble.hivemind.net 16–11">16</td>
<td class="lose" title="mead.hivemind.net loses to
drone.hivemind.net 13–14">13</td>
</tr>
<tr>
<th align="left">2. <br>
</th>
<td width="40"> </td>
<td class="lose" title="maya.hivemind.net loses to
mead.hivemind.net 9–13">9</td>
<td class="count">-</td>
<td class="win" title="maya.hivemind.net beats
buzz.hivemind.net 13–11">13</td>
<td class="win" title="maya.hivemind.net beats
sting.hivemind.net 14–10">14</td>
<td class="win" title="maya.hivemind.net beats
bumble.hivemind.net 17–10">17</td>
<td class="win" title="maya.hivemind.net beats
drone.hivemind.net 15–11">15</td>
</tr>
<tr>
<th align="left">3.</th>
<td width="40"> </td>
<td class="lose" title="buzz.hivemind.net loses to
mead.hivemind.net 11–15">11</td>
<td class="lose" title="buzz.hivemind.net loses to
maya.hivemind.net 11–13">11</td>
<td class="count">-</td>
<td class="win" title="buzz.hivemind.net beats
sting.hivemind.net 13–10">13</td>
<td class="win" title="buzz.hivemind.net beats
bumble.hivemind.net 15–9">15</td>
<td class="win" title="buzz.hivemind.net beats
drone.hivemind.net 14–11">14</td>
</tr>
<tr>
<th align="left">4. <br>
</th>
<td width="40"> </td>
<td class="lose" title="sting.hivemind.net loses to
mead.hivemind.net 9–17">9</td>
<td class="lose" title="sting.hivemind.net loses to
maya.hivemind.net 10–14">10</td>
<td class="lose" title="sting.hivemind.net loses to
buzz.hivemind.net 10–13">10</td>
<td class="count">-</td>
<td class="win" title="sting.hivemind.net beats
bumble.hivemind.net 14–10">14</td>
<td class="tie" title="sting.hivemind.net ties
drone.hivemind.net 13–13">13</td>
</tr>
<tr>
<th align="left">5. <br>
</th>
<td width="40"> </td>
<td class="lose" title="bumble.hivemind.net loses to
mead.hivemind.net 11–16">11</td>
<td class="lose" title="bumble.hivemind.net loses to
maya.hivemind.net 10–17">10</td>
<td class="lose" title="bumble.hivemind.net loses to
buzz.hivemind.net 9–15">9</td>
<td class="lose" title="bumble.hivemind.net loses to
sting.hivemind.net 10–14">10</td>
<td class="count">-</td>
<td class="win" title="bumble.hivemind.net beats
drone.hivemind.net 13–10">13</td>
</tr>
<tr>
<th align="left">6. <br>
</th>
<td width="40"> </td>
<td class="win" title="drone.hivemind.net beats
mead.hivemind.net 14–13">14</td>
<td class="lose" title="drone.hivemind.net loses to
maya.hivemind.net 11–15">11</td>
<td class="lose" title="drone.hivemind.net loses to
buzz.hivemind.net 11–14">11</td>
<td class="tie" title="drone.hivemind.net ties
sting.hivemind.net 13–13">13</td>
<td class="lose" title="drone.hivemind.net loses to
bumble.hivemind.net 10–13">10</td>
<td class="count">-</td>
</tr>
</tbody>
</table>
</blockquote>
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