[EM] Re: DMC,AWP,AM

[Chris Benham]

Forest,
You wrote:

> "I wonder if the following Approval Margins Sort
(AMS) is equivalent to your Approval Margins method:

1. List the alternatives in order of approval with
highest approval at the top of the list. 

2. While any adjacent pair of alternatives is out of
order pairwise ... among all such pairs swap the
members of the pair that differ the least in approval.

This method is clone independent and monotonic, and
yields a social order that reverses exactly when the
ballots are reversed. If AMS and AM are the same, it
might be useful to have this alternative description. 

> AMS is monotonic in a strong sense: if ballots are
changed so as to increase alternative X's approval or
to give X a victory that it didn't have before, while
leaving all of the other approvals and pairwise
defeats the same, then X cannot move down in the
social order produced by this AMS method. In other
words, AMS is monotonic with respect to the entire
social order it produces. 

> After one example it is pretty obvious that AM and
AMS are equivalent when there are only three
alternatives, since they both yield the CW when there
is one, and they both preserve the approval order if
the only upward defeat arrow is from the bottom to the
top, and they both reverse the closest approval margin
pair, otherwise."

CB: AMS doesn't seem very "intuitive", especially to
the uninitiated, but I like it!   (My other worry is
that I even understand it.)
So how is this method worse than the best of the
methods you currently advocate?
A perhaps ridiculous question: does the AMS  process
always stabilize?

Chris  Benham


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