[EM] Round Robins

[Dave Ketchum]

If 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,

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.  

    ------------------------------------------------------------------------
    -- 
     davek at clarityconnect.com    people.clarityconnect.com/webpages3/davek
     Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
               Do to no one what you would not want done to you.
                     If you want peace, work for justice.

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