[EM] RE: Equivalent defeat strength for Approval Sorted Margins / Approval Margins

[Simmons, Forest]

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:araucaria.araucana at gmail.com]
Sent: Tue 4/5/2005 10:50 AM
To: Simmons, Forest; Jobst Heitzig; Chris Benham; election-methods-electorama.com at electorama.com
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
--
araucaria dot araucana at gmail dot com


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