[EM] Approval-Completed Condorcet Redux

[Kevin Venzke]

I thought briefly about this method, and decided I wasn't clear on what it
would be good for.

If you take the ABC example (where B is the center candidate with little
support), B will have a majority pairwise vs. A or C.  I have a hard time
imagining that A or C could get enough approval to exceed this figure.

If the voters are polarized around three candidates, ABC, and all deem D to
be the least worst, D's pairwise victories will be even larger.  So I wonder
if this method is much good at eliminating turkey victories.

One instance I thought of, where the approval winner could beat the CW:
33: Left>all, approve Left
30: Center>Right>Left, approve Center
37: Right>Center>Left, approve Right and Center

Right is the CW but Center is the "AW."  The 67 approval votes would beat
the 37 Right>Center victory.  However, the Right voters shouldn't have
approved Center, and the Left voters could've ensured Center's victory as
both CW and AW.

Has anyone come up with a more interesting scenario?


I had the thought that perhaps if you used Condorcet with limited ranks,
in the event of a cycle it might be reasonable to use Borda points, assigning
points based on the rank.  This might be neater than having an approval
cutoff.  It would be clone-proof (entering clones is useless if you don't
get more ranks for them).  It would probably encourage some "approval strategy"
(try to minimize or maximize points), but I doubt it would be strong enough to 
convince many people to actually leave ranks empty.

Kevin Venzke
stepjak at yahoo.fr



> On Wed, 18 Jun 2003, Alex Small wrote:
> 
> > 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.


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