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<div dir="Ltr" align="Left"><font face="Arial" color="#0000ff" size="2"><span class="684173822-13032005"><font color="#000000">
I</font><font color="#000000">f I understand this, Paul is saying that what
Condorcet does is not Round Robin BECAUSE Round Robin in sports only has
ONE match between each pair of teams,</font><br>
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In sport, there are no "cycles" in a round-robin. In a 3-team round-robin
there's only 2-0, 1-1, and 0-2 as possible outcomes for each team, and if
one team is 2-0 there's no "cycle". The only possible "cycle" is a 3-team
tie with all teams going 1-1 in the tournament.</span></font></div>
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<div dir="Ltr" align="Left"><font face="Arial" color="#0000ff" size="2"><span class="684173822-13032005">
The cases are:</span></font></div>
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2-0 is the winner, the other teams tie 1-1 for second</span></font></div>
<div dir="Ltr" align="Left"><font face="Arial" color="#0000ff" size="2"><span class="684173822-13032005">
2-0 is the winner, 1-1 is second, 0-2 is third.</span></font></div>
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All teams finish the round-robin 1-1.</span></font></div>
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<div dir="Ltr" align="Left"><font face="Arial" color="#0000ff" size="2"><span class="684173822-13032005">
So the equivalent of a "cycle" is the last case where A beat B but lost
to C, B lost to A but beat C, and (if you can't fill in this part you should
not read further) C beat A but lost to B.</span></font></div>
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<div dir="Ltr" align="Left"><font face="Arial" color="#0000ff" size="2"><span class="684173822-13032005">
The answer is that in sport the tournament winner in the case of a three-way
tie is pre-specified based upon an arbitrary tiebreaker (read: dictator
principle)) such as average margin of victory.</span></font></div>
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<div class="OutlookMessageHeader" lang="en-us" dir="Ltr" align="Left"><font face="Tahoma" size="2"><b>
</b>Alex Small<br>
<b>Sent:</b> Sunday, March 13, 2005 4:26 PM<br>
<b>To:</b> <a class="moz-txt-link-abbreviated" href="mailto:election-methods-electorama.com@electorama.com">election-methods-electorama.com@electorama.com</a><br>
<b>Subject:</b> [EM] Round Robins<br>
</font>Finally, what rule do people use in sports to break cycles in
round robin tournaments? I'd be inclined to use that rule in public
proposals for IRR, even if it should turn out that it isn't the optimal rule
from a theoretical perspective.<span class="684173822-13032005"><font face="Arial" color="#0000ff" size="2">
</font></span><span class="684173822-13032005"> <br>
</span><br>
<hr width="100%" size="2">-- <br>
davek@clarityconnect.com people.clarityconnect.com/webpages3/davek<br>
Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026<br>
Do to no one what you would not want done to you.<br>
If you want peace, work for justice.<br>
<br>
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