<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=Content-Type content="text/html; charset=us-ascii">
<META content="MSHTML 6.00.2900.2604" name=GENERATOR></HEAD>
<BODY>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=684173822-13032005>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>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=684173822-13032005></SPAN></FONT> </DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=684173822-13032005>The cases are:</SPAN></FONT></DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=684173822-13032005> 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>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=684173822-13032005> All teams finish the round-robin
1-1.</SPAN></FONT></DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=684173822-13032005></SPAN></FONT> </DIV>
<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>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=684173822-13032005></SPAN></FONT> </DIV>
<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>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=684173822-13032005></SPAN></FONT> </DIV><BR>
<BLOCKQUOTE
style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #0000ff 2px solid; MARGIN-RIGHT: 0px">
<DIV class=OutlookMessageHeader lang=en-us dir=ltr align=left>
<HR tabIndex=-1>
</DIV>
<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>
election-methods-electorama.com@electorama.com<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> </SPAN></DIV></BLOCKQUOTE></BODY></HTML>