[EM] Problems with finding the probable best governor
Markus Schulze
schulze at sol.physik.tu-berlin.de
Sat Jul 22 11:30:08 PDT 2000
Dear Bart,
dear Mike,
Bart wrote (20 July 2000):
> 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.
Mike wrote (20 July 2000):
> I don't think there's need for concern about SU vs CW. It
> seems to me that our partisan political elections are close
> to being 1-dimensional, though not entirely. Under those
> conditions there's always a sincere CW, who will also be the
> SU maximizer, if the voters' distribution density increases with
> decreasing distance from the voter-median position. Maybe that
> relation between sincere CW & SU maximizer extends to more
> dimensions, to some degree. Besides, my interest in electing
> the sincere CW is based on my concerns about defensive strategy
> need, and the methods that do well by criteria that measure
> that standard tend to do well by SU anyway.
There seems to me to be a discrepancy about what the SUE is.
As far as I remember correctly, the social utility expectation
of a given candidate is the sum of the von Neumann-Morgenstern
utilities of the voters about this candidate.
But the von Neumann-Morgenstern utilities are defined only on a
relative scale and not on an absolute scale. Example: If voter
V has a von Neumann-Morgenstern utility of candidate A of
N(V,A)=8000$ and a von Neumann-Morgenstern utility of candidate
B of N(V,B)=10000$ then this means (1) that this voter would
spend N(V,B)-N(V,A)=2000$ if he could change the winner from
candidate A to candidate B and (2) that if this voter got a
compensation of N(V,B)-N(V,A)=2000$ when candidate A was elected
instead of candidate B then he wouldn't care about the winner
any more. Therefore it is the same whether voter V has a von
Neumann-Morgenstern utility of candidate A of 8000$ and a von
Neumann-Morgenstern utility of candidate B of 10000$ or whether
voter V has a von Neumann-Morgenstern utility of candidate A of
3000$ and a von Neumann-Morgenstern utility of candidate B of
5000$.
But in so far as the von Neumann-Morgenstern utilities are
defined only on a relative scale and not on an absolute scale,
it isn't feasible to say that a given candidate has a SUE of
1/2 or 3/4 of the maximum SUE.
Also Mike's statement that the Condorcet winner usually has a
high SUE seems to me to be not justified. Especially in a divided
society, the SUE of the Condorcet winner and even of the majority
winner can be very small. The reason why I support the majority
criterion (resp. the Condorcet criterion) is not that the
majority winner (resp. the Condorcet winner) usually has a high
SUE but that a method that meets the majority criterion (resp.
the Condorcet criterion) is less manipulable.
Markus Schulze
schulze at sol.physik.tu-berlin.de
schulze at math.tu-berlin.de
markusschulze at planet-interkom.de
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