[EM] Round Robins

[Paul Kislanko]

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: election-methods-electorama.com at electorama.com
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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