[EM] Societal ranking from incomplete pairwise information. (Pinewood derby.)

Gervase Lam gervase.lam at group.force9.co.uk
Tue Mar 20 17:31:48 PDT 2012

> Andy Jennings elections at jenningsstory.com 
> Sat Mar 17 11:16:51 PDT 2012

> The question is what to do if you want to run more than n rounds, or if the
> number of cars is not exactly a power of two.  I think the idea of dividing
> them into tiers (or brackets) and racing them against other cars in the
> same tier is still good, but using just their win-loss record is not
> enough.  Lots of tiers will have an odd number of cars, so we need to know
> which are the best and worst cars in each tier and have a few inter-tier
> races.
> So we can think of it as needing to come up with a secondary sort criterion
> to use inside the win-loss tiers.
> Or we can generalize and say that after each round we just come up with a
> full societal ranking and then race the first against the second, the third
> against the fourth, the fifth against the sixth, etc.

The above is more or less what the Swiss tournament is, which is used
extensively in chess (and other) tournaments with a large number of

Win/Loss records (with 1/2 point been given for drawn games) are used to
determine the brackets in subsequent rounds.  Those with the same or
similar Win/Loss records are paired up in subsequent rounds.  The
complication comes in trying to avoid repeat pairings.

The "Swiss-system tournament" wikipedia page has examples of how the
pairings are done using the two main Swiss variants.

>From what I read about it in another mailing list, Swiss seems to be
good at ordering the best and worst participants.  However, determining
who are the best of those in the middle is a bit random.


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