[EM] MinMax (pairwise opposition) and Approval

[Kevin Venzke]

Looking at Schulze's example of:
  20 ABCD 
  20 BCAD 
  20 CABD 
  13 DABC 
  13 DBCA 
  13 DCAB 

The scores are 66 for ABC and 60 for D, so D winning
is of course not best.  But I think the problem is
that an ordering low in the list is weighed as heavily
as a first- and second-place ranking.  It's not
intuitive, for instance, that the DABC voters should
be able to create B opposition against C.

My adaptation for Approval ballots is somewhat saved
from this because all orderings require actually
"approving" one candidate and not the other.  You
can't order "strategically" or randomly.

For instance, if we suppose that only the first two
candidates ranked are "approved," we get ballots:
20 AB, 20 BC, 20 CA, 13 DA, 13 DB, 13 DC

The table looks like: (row's votes over column)
     A     B     C     D
A    0    33    33    40
B   33     0    33    40
C   33    33     0    40
D   26    26    26     0

And D is the loser.

Is this system not interesting?

Has anyone ever suggested an approval/ranked hybrid of
some kind whereby all candidates are deemed approved,
who are not ranked last?  I'm not positive what the
best method would be, but this comes to mind:

Approval for a candidate is calculated as the number
of ballots on which he is not ranked last.  (Ties are
permitted, of course, and truncation means non-ranked
candidates are last.)  If someone has majority
approval, the highest approval wins.  Otherwise, find
the Condorcet winner.  (Break ties with Approval, or
any other acceptable method.)

I'm not certain if there's a flaw in the above system,
but at least it would take away incentive to
distinguish the order of candidates you dislike.

Thoughts?

Kevin Venzke
stepjak at yahoo.fr

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