[EM] A Comparison of the Two Known Monotone, Clone Free Methods for Electing Uncovered Alternatives

[C.Benham]

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