[EM] Approval-Completed Condorcet Redux

[Alex Small]

Somebody on another mailing list has put forth an interesting
Approval-Condorcet hybrid.  I throw it out for consideration.  I know some
people here have done careful analyses of strategy in standard
Approval-Completed Condorcet, I'm curious what people think of this:

1)  Everybody submits a ranked ballot, equal rankings allowed, and also
indicates yes/no for each candidate.
2)  If there is no Condorcet Winner then elect the Approval winner.
3)  If there is a CW, and he also has the highest approval, elect him.
4)  If the Approval and Condorcet winners differ, compare the Approval
winner's approval rating with the number of people who prefer the CW to
the Approval winner.

ex.  Say that A beats B 51-49, but B has an approval rating of 55% while A
has a 45% approval rating.  B's 55 approval votes are greater than A's 51
votes over B, so B wins.

Or, if A beats B 55-45, and the approval ratings are 52% (B) and 46% (A),
A's 55 votes over B are greater than B's 52% approval rating.


Possible variations:

1)  If there is no CW, and the approval winner is not in the inner-most
unbeaten set, do some sort of comparison between the Approval winner's
approval rating and the magnitude of victory of each candidate who defeats
the Approval winner.

I don't recommend this one, but I toss it out for any interested parties
to chew on.


2)  For the margins fans:  When the CW and Approval winners are different,
compare the margin in the pairwise contest with the margin between them in
the approval contest.  Whoever has the larger margin of victory wins.

I toss this one out there to avoid the lengthy "Margins vs. Winning Votes"
debate, so that neither side feels slighted.



Alex