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.
The cases are:
2-0 is the winner, the other teams tie 1-1 for
second
2-0 is the winner, 1-1 is second, 0-2 is
third.
All teams finish the round-robin
1-1.
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.
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.
Alex Small
Sent: Sunday, March 13, 2005 4:26 PM
To: [email protected]
Subject: [EM] Round Robins
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.
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