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<DIV dir=ltr align=left><SPAN class=067343219-30012011><FONT color=#0000ff
size=2 face=Arial>How is #1 not a Condorcet Winner, since #1 pairwise-beats
every other alternative?</FONT></SPAN></DIV><BR>
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<HR tabIndex=-1>
<FONT size=2 face=Tahoma><B>From:</B>
election-methods-bounces@lists.electorama.com
[mailto:election-methods-bounces@lists.electorama.com] <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>
<DIV></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></BODY></HTML>