[EM] Recursive Elimination Supervisor

[Forest Simmons]

Tony, I am a little worried that this simplification gives room for a
"Independence of Irrelevant Alternatives" problem to creep in.

Many methods suffer from this IIA problem (which says that the Winner
shouldn't change when some other candidate sits out) and it may be too
much to expect that we can make IIA hold in our recursion, yet in a way
a weak variant of IIA is the whole basis of my idea:

Weak version of IIA: The winner shouldn't change if the worst candidate is
thrown out.  This seems like a reasonable requirement for a decent method.

The unsimplified version implicitly uses a slightly stronger version (but
still close to the weak version): The winner shouldn't change if the worst
candidate or next to the worst candidate is thrown out.

In this simplified version we're using a much stronger version of IIA: The
winner shouldn't change if the Seed Loser is thrown out (unless the winner
is the seed loser).

Forest

  

On Tue, 27 Feb 2001, Forest Simmons wrote:

> Tony,
> 
> here's a simpler version of the Recursive Elimination Supervisor,
> based on a suggestion of yours.
> 
> Step 1.  Use the seed method in reverse to find the "Seed Loser" SL, from
> among the N candidates.
> 
> Step 2.  While the SL sits out, recursively supervise the seed method to
> find an N-1 stage recursive winner RW from among the N-1 remaining
> candidates.
> 
> Step 3.  Compare SL and RW directly.  Whichever is better is the N stage
> recursive winner. In case of a tie between these two, choose RW.
> 
> 
> Forest
> 
>