Ted,
I've been working on that, but the answer
is not yet clear.
Part of the problem is that only pairs that
are currently adjacent in the list are considered for swapping (the equivalent
of firming up the defeat ).
So if at some time the current list order is
A>B>C>D>E>F, and (A,B) is the out-of-order adjacent pair with the
smallest approval difference (a-b), while the approval difference (b-d) is even
smaller, the B>A defeat would be set in stone before (or ultimately
instead of?) the D>B defeat.
Whether this ultimately causes a problem, I do not know.
Forest
From: Monkey Puzzle
[mailto:[EMAIL PROTECTED]
Sent: Tue 4/5/2005 10:50 AM
To: Simmons, Forest; Jobst Heitzig; Chris Benham; [email protected]
Subject: Equivalent defeat strength for Approval Sorted Margins / Approval Margins
Sent: Tue 4/5/2005 10:50 AM
To: Simmons, Forest; Jobst Heitzig; Chris Benham; [email protected]
Subject: Equivalent defeat strength for Approval Sorted Margins / Approval Margins
Forest, Jobst, Chris:
As earlier shown by Jobst, Pairwise
(bubble) Sorted Approval finds the
same social ordering as Ranked Pairs,
Beatpath or River, when defeat
strength is determined by the total approval
of the winning pairwise
candidate.
Is it possible to find a similar
equivalence for Approval Sorted
Margins? In other words, is ASM
equivalent to Ranked Pairs (and/or
Beatpath and/or River) when defeat
strength is measured by the margin
of approval?
Ted
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