Forest Simmons wrote (16 Dec 2010):
Chris,
Thanks for reminding me of Approval-Sorted Margins. The covering
chain method applied to the list obtained
by approval sorted margins certainly has a maximal set of nice
properties, in that any additional nice
property would entail the loss of some highly desireable property.
Do you think it is better, in this context, to base approval on
ranked-above-last, or by use of an explicit
approval cutoff marker?
Forest,
I like both versions. I think the version that uses an approval
cut-off (aka threshold) marker is a bit more
philosophically justified. (It seems arbitrary to assume that
ranked-above-bottom signifies "approval", or
putting it the other way, unpleasantly restrictive to not allow voters
to rank among candidates they don't
approve.)
On the other hand the other version is simpler, and probably normally
elects higher SU winners and resists
burial strategy a bit better.
From your December 2 post:
I do suggest the following:
In any context where being as faithful as possible to the original
list order is
considered important, perhaps because the only reason for not
automatically
electing the top of the list is a desire to satisfy Condorcet
efficiency, then
in this case I suggest computing both the chain climbing winner and
the covering
chain winner for the list L, and then going with which ever of the two
comes out
higher on L.
Have you since retreated from this idea? Would using this on the list
obtained from Approval-Sorted Margins lose
(compared to just using the covering chain method) compliance with
Independence from Pareto-Dominated Alternatives?
Could the two ever give different winners?
Sorry to be a bit tardy in replying,
Chris Benham
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