[EM] Re: Approval/Condorcet Compromise

[Chris Benham]

Russ,
You recently asked for opinions of this Condorcet completed by Approval 
Elimination method:

"The voters rank the candidates and also specify an Approval cutoff. The
CW wins if one exists, otherwise the least approved candidate is
repeatedly eliminated until a CW is obtained."

I agree that for something with such a short and succinct description, 
this method is pretty good.
But I'm surprised that you think that the "sound byte" advantage 
overcomes the extra complication of having
an approval cutoff.
That issue aside, I prefer another method that uses that type of 
ballot,  "Approval Margins":

(1) Voters rank the candidates and also give an Approval cutoff
(2) Eliminate non-members of  the Schwartz set, and  then "move" the 
approval cutoffs on those ballots that
either approve all or none of the remaining candidates the minimum 
distance so that they now approve or not approve
at least one of the remaining candidates.
(3)Determine the winners and losers in the pairwise comparisons among 
the remaining candidates (the directions of the defeats)
purely by the rankings, but determine their "weights" by the the margins 
between the candidates' pairs of  Approval scores.
(4) On that basis use Ranked Pairs or  Beat Path or   River to pick the 
winner.

Some people might be in favour of  simplifying it by omitting step 2.

An old example given by Adam Tarr.
Sincere rankings:
49 R>C>L
12 C>R>L
12 C>L>R
27 L>C>R
C is the CW.

Suppose there is pre-polling and so the L supporters decide to approve 
C, while the C supporters sincerely divide their approvals.
Further suppose that the R supporters all decide to completely Bury C.  
Then we might get:

49 R>L>>C
06 C>R>>L
06 C>>R>L
06 C>>L>R
06 C>L>>R
27 L>C>>R

Now all the candidates are in the top cycle: L>C>R>L.  The approval 
scores are  L82,  R55, C51.

The Approval Elimination method you propose eliminates C and elects the 
Buriers candidate R.

Approval Margins:
L>C  82-51 = +31
C>R  51-55 =   -4
R>L  55-82 = -27

The "weakest defeat" is L's (by an margin of  negative 27), so the 
Burying backfires and L wins!


Chris Benham