Re: Atlantic Coast Regionals



It's simple and easy to replicate, which I like.   The part of the
algorithm that troubles me is that the seedings it provides are not
locally stable which is a property I think any good seedings should
have.  I call a set of seedings locally stable if there is no pair of
teams A and B such that A is seeded immediately below B and A would be
seeded ahead of B if the two teams were considered in isolation.  For
example, if the algorithm seeded Georgia 3 and Virginia 4 then the
seeds would be unstable because the algorithm would reverse the order
if they were the only two teams under consideration.

Question:  are the notions of locally stable seeds (no pair of
adjacent seeds should be swapped) and a globally stable seeding
algorithm (top down or bottom up yields the same results) mutually
exclusive?

well, yes.

Take this very hypothetical example with 13 teams (any odd number
greater than 1 will do, for even numbers just add one team that lost
everything and is consensus last seed):
Every team has played every other team exactly once, and the score was
15-10 in every game. No games outside this group of teams, no
historical strength record...
12 teams have consistent scores, i.e. you can order these teams
(linearly and uniquely) according to their results, and the 66 head-to-
heads are all according to this order.
Now odd team number 13 comes along, and it has wins against the 6 top
teams and losses against the 6 bottom teams.
Any locally stable algorithm will put team 13 either as the first seed
or as the last. And if you use this algorithm backwards (switching top
and bottom), you will get the opposite result. This example also
magnifies the problem in demanding local stability. Most people would
seed team 13 somewhere in the middle as good wins and bad losses
somewhat cancel.

This example is the 3-way-tie blown up to a ridiculous size. In
reality, a variant of it often happens with 3 teams and sometimes with
5, but probably never with 7 or more teams.

But it demonstrates that in a 3-way-tie where A>B is forced due to
sectional finish, and B>C and C>A in head-to-heads, maybe ACB is the
best choice as average of the possible three orders ABC, CAB, ACB,
even though ACB has two local instabilities.
At least in ACB, misseeding is limited to one seed per team, and the
other two seeding sets have the potential of getting C's seed wrong by
2 (if we agree that one of the three sets is correct, but you don't
know which one).

Btw, the algorithm I proposed above would also get a different result
here...

.

Relevant Pages

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  • Re: Atlantic Coast Regionals
    ... algorithm that troubles me is that the seedings it provides are not ... seeds would be unstable because the algorithm would reverse the order ... teams and losses against the 6 bottom teams. ... other two seeding sets have the potential of getting C's seed wrong by ...
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  • Re: Online poker RNG...
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