[EM] Problems with finding the probable best governor

[Bart Ingles]

Markus Schulze wrote:
> 
> 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.'


Two boys find a $100 bill lying on the pavement.  "I saw it first, it's
mine!" said the first.  "No you didn't, I saw it first!" said the
second.  Just then a kindly stranger notices the commotion, and decides
to resolve the dispute: "Now boys, there's no need to fight!  Here, I'll
take care of that $100 bill.  And here's a dollar for each of you.  Now
we're all better off than before!"

Bart



> ******
> 
> 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