[EM] Uncovered set methods (Re: How close can we get to the IIAC)

[fsimmons at pcc.edu]

Markus wrote ...

>'..how do you define "clones"? In the approval
>voting paradigm, the term "clones" implies that
>all candidates have the same approval score.

>So when you apply UncAAO to a clone set, then
>all candidates of its uncovered set are tied.'

Your suggested interpretation of clones (always being tied in approval) would
satisfy my claim, breaking ties with random ballot, for example.  But that's not
what I had in mind.

Here's what I had in mind:

Since Approval and Cardinal Ratings are strategically equivalent, if the
standard high resolution Cardinal Ratings methods satisfy clone independence,
then at a strategic level, so must Approval. 

Beyond that consideration, in the context of many voters we can assume that each
candidate's average approval will be approximately equal to each candidate's
average cardinal rating even with non-strategic voting. For similar reasons
(except in rare borderline cases) it doesn't matter (to their grade) if I give
my students partial credit or not when grading hundreds of problems over a term.
 (It does matter psychologically to the students.)

It may be that X, Y, and Z are always ranked solid on the cardinal ratings
ballots of some election, but unless they are usually rated near each other, and
frequently approved or disapproved together in strategic voting, we would have
to judge the clone relationship to be quite loose.  In other words, we could
call them pseudo-clones.  It takes Cardinal Ratings or Approval to distinguish
pseudo-clones from true clones.  Visually compare in one dimension

original:

****A*********************C*************************************************B**********

Tight clone set {X, Y, Z} replaces  C:

****A********************X**Y**Z********************************************B***********

Loose clone set:

*****A*********X*************Y****************************Z*******************B**********

Since rankings do not distinguish between pseudo and true clones, MinMax
Condorcet based on rankings fails clone dependence.  But if we base MinMax on
ratings ballots (or ranked ballots with approval information) and use James
Green-Armytage's weighted pairwise (whether CWP or AWP) measure of strength of
defeat, the method acquires clone independence.  And because of its simplicity,
together with the other advantages of using weighted pairwise measures of
strength (see James' discussion at
http://fc.antioch.edu/~james_green-armytage/vm/antistratsum.htm), MinMax(CWP or
AWP) is an obvious public proposal.

In summary the stronger the clone relationship, the stronger the tendency to
approve or disapprove all of the members of the clone family together.  The
looser the relationship, the greater the number of ballots that split them up in
approval/disapproval.  So they are more or less split up in the approval totals
depending on how strong or weak the clone relationship.

Forest