[EM] Problems with finding the probable best governor

[Bart Ingles]

MIKE OSSIPOFF wrote:

> Average social utility is a measure of something similar to
> Blake's goal.

I had a couple of lengthy debates with Blake on the subject on EM, most
recently between 1/24/2000 and 3/2/2000.  As I recall, it started and
ended with Blake not seeing any validity in SUE, at least when up
against the CW.  We didn't get into what the standard should be when
there was no CW.

My position was that while I didn't consider it necessary to always
maximize SUE, I did think it important to avoid electing candidates with
a very low SUE.  If I were to try to put it into the form of a criterion
today, I would say that the winner's SUE should never be lower than
about 1/2 or 3/4 of the maximum SUE for a given election.  Satisfying
that, Condorcet or Smith Set would be next in importance (at least in
terms of outcome-based criteria).  Lower priority still might be to
maximize SUE among multiple Smith Set members.


> Under sincere voting,
> all the pairwise-count methods that Norm & Steve
> tested seem to do about equal in that regard, and better than
> other methods, except maybe for Borda. It seems to me that Merrill
> got a similar result, though he may have only tested Copeland.

Merrill called the pairwise method Black -- I don't know if it goes by
any other name.  It was pairwise w/ Borda completion method (which
wouldn't have made much difference in the spatial models, since cycles
were rare at only 1-2% of elections.

With a random society, the SUEs favored Borda > Black > Approval, all
separated by a few of percentage points, except that Approval barely had
the edge at 3 candidates.

With 2-D issue space (actually more like 1.5-D, since the correlation
between the two dimensions was 0.5) there was not much difference
between the three, no more than one or two percentage points between
highest and lowest.

All three methods were well above FPP and IRV/Runoff.  And of course the
models assumed sincere voting with 0-info.


> That's with sincere ranking. Since the pairwise-count methods seem
> to do about equally in terms of social utility under sincere voting,
> then it makes sense to use some other standard to choose between
> them. Most of us who participate here feel that the methods'
> strategic demands on voters is the standard by which to compare the
> methods, and that's why we use the criteria that we use.
> 
> It seems to me that Norm said that Borda does noticibly better than
> the pairwise-count methods, for social utililty, when everyone
> ranks sincerely. It would be interesting to test Points-Assignment
> with sincere rating. For instance, say each voter gives a candidate
> a negative point assignment equal to the distance between
> that candidate & that voter in issue-space. The winner is the
> candidate whose combined negative score has the lowest magnitude.
> Though Points-Assignment, like Borda, and Tideman(m), isn't
> practical for public elections, it would be interesting to find
> out how Points-Assignment does, in average social utility, in
> comparison to the other methods that were tested.
> 
> How much better did Borda do, in comparison to the pairwise-count
> methods that were tested?

Borda and Black were never more than 2.4 percentage points apart ( < 1%
when using the spatial models).

Bart