[EM] Round Robins

[Paul Kislanko]

Actually, all Paul said is that the analogy is not perfect. 
 
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.
 
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." 
 
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. 
 
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.
 
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."
 
 


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From: election-methods-electorama.com-bounces at electorama.com
[mailto:election-methods-electorama.com-bounces at electorama.com] On Behalf Of
Dave Ketchum
Sent: Sunday, March 13, 2005 8:31 PM
To: 'Alex Small'; election-methods-electorama.com at electorama.com
Subject: RE: [EM] Round Robins


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.
 


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 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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-- 
 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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