[EM] Problems with finding the probable best governor

[Markus Schulze]

Dear participants,

Blake wrote (24 July 2000):
> In simpler terms, maximizing satisfaction with the election result
> is not the same as maximizing the percieved social utility of the
> outcome, because more selfish people will be less satisfied with
> benefits going to others than will less selfish people.  So, to
> maximize satisfaction, it is necessary to give more benefits to the
> selfish, where they cause more satisfaction, even though this may
> decrease the overall benefit to society.

R. Smullyan ("This Book needs no Title," 1980) suggests that if
the median candidate isn't the candidate with the highest SU then
this usually means that some fringe voters have exaggerated their
sentiments about the candidates. He uses the following example:

   Once upon a time two boys found a cake. One of them said,
   'Splendid! I will eat the cake.' The other said, 'No that is
   not fair! We found the cake together, and we should share and
   share alike, half for you and half for me.' The first boy said,
   'No, I should have the whole cake!' Along came an adult who
   said, 'Gentlemen, you shouldn't fight about this: you should
   _compromise_. Give him three quarters of the cake.'

******

Bart wrote (25 July 2000):
> I'm not sure we have the same exact definition of vN-M utilities.

Suppose that there are M candidates. Suppose that in situation X
candidate j is elected with the probability p(j). Suppose that in
situation Y candidate j is elected with the probability q(j).
Suppose that N(i,j) is the von Neumann-Morgenstern utility of
voter i about candidate j. Suppose that
P := N(i,1)*p(1)+...+N(i,M)*p(M) and
Q := N(i,1)*q(1)+...+N(i,M)*q(M).

Suppose that P > Q. Then this means:

(1) Voter i strictly prefers situation X to situation Y,
(2) voter i would spend up to (P-Q)$ to change the election
    result from situation Y to situation X and
(3) if voter i gets a compensation of more than (P-Q)$ when
    the election result is changed from situation X to
    situation Y then voter i will strictly prefer situation Y
    to situation X.

[I believe that for our discussion only statement (1) is
interesting.]

Markus Schulze
schulze at sol.physik.tu-berlin.de
schulze at math.tu-berlin.de
markusschulze at planet-interkom.de