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<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=320054402-14032005>Actually, all Paul said is that the analogy is not
perfect. </SPAN></FONT></DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=320054402-14032005></SPAN></FONT> </DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=320054402-14032005>Condorcet methods are "like" as in "similar to" a
round-robin tournament in sport. The analogy is not identical because in sport
there is a well-determined outcome when team A plays team B, namely either A or
B wins.</SPAN></FONT></DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=320054402-14032005></SPAN></FONT> </DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=320054402-14032005>Where the analogy breaks down is that in an election
the "team" is an alternative and the "score" that determines whether it wins is
calculated differently depending upon which "condorcet" method is used to
determine which "team" won that "game." </SPAN></FONT></DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=320054402-14032005></SPAN></FONT> </DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=320054402-14032005>The analogy is an isomorphism if "win" is defined by "A
scores more points than B" in a head-to-head contest between A and B. But for it
to be a perfect analogy, "scores more" needs to be as precisely defined as it is
in sport. This is not the case when voter's prefences for A over B are obtained
from a ballot that includes C, since the voter is not being asked to choose
between A and B on such a ballot. </SPAN></FONT></DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=320054402-14032005></SPAN></FONT> </DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=320054402-14032005>To be perfectly analogous to the sport metaphor, the
ballot should allow the voter to record a score for one team vs other another
team. Any attempt to infer the voter's preference relative to a third team would
be like adjusting the score between A and B based upon the outcome of the game
played between B and C, and in sport that is not allowed.</SPAN></FONT></DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=320054402-14032005></SPAN></FONT> </DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=320054402-14032005>The reason that "cycles" can't happen in sport is that
every "game" has a definite outcome, and only involves one pair of contestants
at a time. If a ballot only contained choices between a pair of alternatives,
the mapping from ballot to pairwise-matrix would be just as well-defined, and
irrefutable. But to call any mapping of ranked ballots to the pairwise matrix
"the same as a round roubin sport tournament" is not accurate. It is "similar
to", or "like", but it is nowhere near the "same as."</SPAN></FONT></DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=320054402-14032005></SPAN></FONT> </DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=320054402-14032005></SPAN></FONT> </DIV><BR>
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<FONT face=Tahoma size=2><B>From:</B>
election-methods-electorama.com-bounces@electorama.com
[mailto:election-methods-electorama.com-bounces@electorama.com] <B>On Behalf
Of </B>Dave Ketchum<BR><B>Sent:</B> Sunday, March 13, 2005 8:31
PM<BR><B>To:</B> 'Alex Small';
election-methods-electorama.com@electorama.com<BR><B>Subject:</B> RE: [EM]
Round Robins<BR></FONT><BR></DIV>
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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><BR>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>
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</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> <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></DIV></BLOCKQUOTE></BLOCKQUOTE></BODY></HTML>