[EM] MinMax (pairwise opposition) and Approval

[Forest Simmons]

On Thu, 20 Mar 2003, [iso-8859-1] Kevin Venzke wrote:

>  --- 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).

I noticed that, too.  The approved candidates all get bunched together at
the top instead of the disapproved candidates getting bunched together at
the bottom.

Maybe there is a hybrid method that doesn't encourage bunching up at the
top or the bottom, but exerts a dispersing influence.


>
> (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.)

At first I thought that this was the solution to the insincere ranking
problem.  Then Bart pointed out the problem that Alex has reminded us of
more recently.

>
> 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.

Maybe something like this is what is needed to "disperse" the bunching
tendency.

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

Rob LeGrand has promised to do the simulations someday when he isn't so
busy.  He liked the idea of searching successively cruder pairwise
matrices for CW's.  The search comes to an end with the crudest (approval
level) pairwise matrix, if not before.

The question that Rob's simulation will answer is how likely is there to
be a CW at an intermediate stage of crudeness if not at the finest stage.

It would sure be nice if we could count on the intermediate stages coming
through a reasonable share of the time, but I don't have to much hope for
it.

Forest