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<DIV dir=ltr align=left><SPAN class=479412503-14032005><FONT face=Arial
color=#0000ff size=2>Actually, I addressed this in my original post. In a
sporting tournament involving a 3-team round-robin, the only possible tie for
first is if every team goes 1-1 in the match.</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=479412503-14032005><FONT face=Arial
color=#0000ff size=2></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=479412503-14032005><FONT face=Arial
color=#0000ff size=2>Which team is the winner is based upon an arbirtrary
criterion declared ahead of time by the tournament sponsor. </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=479412503-14032005><FONT face=Arial
color=#0000ff size=2></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=479412503-14032005><FONT face=Arial
color=#0000ff size=2>There is no "next level of competition" for a team to
advance to. It is a round-robin tournament that ends when the teams get back on
their buses. As to which gets the champoionship trophy, it depends upon the
tiebreakers defined by the tournament sponsor. (My preference would be total
wins vs the home team, to make sure that a visiting team got it, but they didn't
ask me...)</FONT></SPAN></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>Alex Small<BR><B>Sent:</B> Sunday, March 13, 2005 9:17 PM<BR><B>To:</B>
Election Methods List<BR><B>Subject:</B> RE: [EM] Round
Robins<BR></FONT><BR></DIV>
<DIV></DIV>
<DIV>OK, maybe Condorcet elections aren't exactly analogous to round robin
sports tournaments, but I still want somebody, anybody, to tell me how
the winner is determined in a round robin if each of the 3 teams wins one game
and loses one game. I've been told that the method of resolution has
something to do with margins of victory, but I'm wondering if anybody can
offer a more precise explanation.</DIV>
<DIV> </DIV>
<DIV>I'll make my question concrete. Say we have a round robin
tournament between soccer teams from USC, UCLA, and UCSB. (And if
it turns out that these 3 schools don't compete in the same league, I'm hoping
somebody will be kind enough to answer the hypothetical question
anyway.) Say that USC beats UCLA 2-1, UCLA beats UCSB 4-1, and UCSB
beats USC 2-0.</DIV>
<DIV> </DIV>
<DIV>Who would be declared the winner of that round robin and advance to the
next level of competition? If a version of that "cycle resolution"
method can be formulated for public elections and it doesn't have any
egregiously awful flaws (no method is perfect, after all), I'd be just as
happy to offer that as a public proposal. It would have the virtue of
bein gsomething that people already know.<BR><BR><B><I>Paul Kislanko
<kislanko@airmail.net></I></B> wrote:</DIV>
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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 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>
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-- <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></BLOCKQUOTE>
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