[EM] MinMax (pairwise opposition) and Approval

[Kevin Venzke]

 --- Forest Simmons <fsimmons at pcc.edu> a écrit : 
> >   20 ABCD
> >   20 BCAD
> >   20 CABD
> >   13 DABC
> >   13 DBCA
> >   13 DCAB
> >
> then we would have
> 
> 60 A=B=C>D
> 13 D>A>B>C
> 13 D>B>C>A
> 13 D>C>A>B
> 
> The max opposition would still be 60 for D, but A,B,
> and C's max
> opposition would be only 39, leaving plenty of room
> for expressing some
> preference among the clones.

True, but I don't much like the general strategy that
seems to come from this system.  ABC supporters can
get punished by ordering ABC, and D supporters have no
reason not to order ABC at least randomly.  Truncation
makes no sense for D supporters.  (I'm not positive,
but I suspect D supporters have incentive to "bury"
competitive candidates.  Ranking a single candidate
last guarantees that you contribute negatively to his
MMPO score.)

It's kind of the opposite of what we were recently
discussing, where unranked candidates would be
disapproved; here, approved candidates are likely to
be unranked (unordered).

(Incidentally, I was reading messages from two years
ago and I was amazed to see that you (Forest) first
came up with the "unranked candidates are disapproved"
idea.)

I'm not sure whether there is a big advantage to using
MMPO with ranked ballots as opposed to approval
ballots, especially if sincere ranking isn't safe.

One idea that occurs to me, to prevent the election of
rogues/turkeys, is to factor MMPO into the pairwise
matrix in the following simple fashion: Add to each
cell the largest value in that column.  That's a
decent way of considering "offensive strength" as well
as the MMPO "defensive" measurement.

Applying this to the original ballots, I get:
    A   B   C   D
A   . 132 132 120<
B 132   . 132 120<
C 132 132   . 120<
D 105^105^105^  .

So D still loses.


Have you done any kind of "utility experiments"
comparing Condorcet and "dyadic Condorcet" of various
resolutions?  The results would be interesting.

Kevin Venzke
stepjak at yahoo.fr


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