[EM] Sport ranking Condorcet method and Condorcet for sports leagues

[Kristofer Munsterhjelm]

Peter Zbornik wrote:
> Hi, just a quickie.
> 
> I wonder if you have discussed Condorcet tie-breaking using sport 
> scoring, like in football (soccer)?

In the Premier League, the scoring is essentially done by a modified 
version of Copeland's method. Instead of Copeland's method which either 
scores two for win and one for tie, or one for a win and nothing for a 
tie, it gives the winning team three points, and one point in the case 
of a tie. If a tiebreaker is needed, they use the goal difference.

Like Copeland's method, this method (call it Copeland/3-1-0) fails the 
independence of clones criterion. When there are no ties, both variants 
would elect from the Smith set, since members of the Smith set beat more 
candidates than those outside it.

I've been considering (on and off) an interesting variant which one 
could call "second order Copeland/2-1-0". First score according to 
Copeland/2-1-0. Then the final score of each candidate/team is equal to 
two times the (first order) scores of the candidates it beat, plus the 
first order scores of the candidates it tied. Unlike "ordinary" second 
order Copeland (/1-0-0), this method is monotone.

Also, consider elimination tournaments. In a Condorcet context, say that 
A wins against B if d[A,B] > d[B,A] (where d is defined according to WV, 
margins, whatever). As in an elimination tournament, pairs are compared 
and the winner of the matchup goes to the next level. Then it's clear 
that if a CW exists, that candidate can never be eliminated and so wins. 
Apart from that, the method outcome depends greatly on seeding and byes, 
so I don't think it's a very good election method. With random (but 
consistent) seeding, it's not monotone, either. What makes elimination 
tournaments useful in sports is that they require few queries - n log n 
instead of n^2 - to determine the winner.

Finally, I know that there's someone else on-list who have analyzed 
sports results using an advanced Condorcet method, but I don't recall 
who that was or which method he used (MAM or Schulze). I think it was 
Schulze, but again, I'm not certain.