[EM] Comments on Heitzig's utility essay

[Jobst Heitzig]

Dear Warren,

you wrote:
> I have no probem with (Archi).

Congratulations. But many people do have, and still can compute utility 
functions. What is bad about that?

> > Heitzig: Archi violation can easily happen when, e.g.,
> >   a = your only child is shot dead,
> >   b = you receive 1 cent,
> >   c = nothing happens.
> >If (Archi) would be true, there would have to be a lottery in which
> > your child is shot dead with some positive probability  p,  in
> > which you receive 1 cent otherwise, and which lottery you prefer to
> > nothing happening.  (Heitzig opines Archi is not true for him &
> > tational people.)
>
> --WDS: Au contraire:
> Archi in the child/cent example is valid for any rational human being
> with p = 10^(-20).

Interesting. Is there any evidence for this claim?

> In particular, it is also valid for Heitzig being the human.

At least you consider me "rational" :-)

> Disagree?  Ok, I'll prove you are lying!

Lying about preferring not to risk my child's life for the chance to get 
a cent? I wonder how you will succeed in that.

> First proof.
> Do you, or do you not, take your child on a car trip, and do you, or
> do you not, drive at <20 Km/hour the entire trip while festooning
> your car with flashing lights and constantly sounding your horn?
> Q.E.D.

As we know you're a mathematician, I think we can expect more rigorous 
"proofs" from you.

> > Heitzig 3.5:  Deriving "social utility = mean individual utility"
>
> --WDS: I don't understand Heitzig's "derivation" here.  I.e. I do not
> see why "MonT" is the same thing as  "social utility = mean
> individual utility".

It's not, of course. The theorem only shows that under certain 
conditions, social preference is in accordance with mean individual 
utility. This is the most important part. The second part about 
expected utility can be proved as well, as I claim in the note after 
the proof of the theorem, but that proof is not included in the 
posting.
 
> What if Social Utility = (sum of individual utilities)^3 ?

Right, that would be a monotonic transformation which does not change 
preferences and is thus of minor importance.

> --WDS: I have considered these issues too.
> I direct your attention to puzzles #36, 37, 38, 39, 44 here
>   http://rangevoting.org/PuzzlePage.html
> for some of my thoughts.

In puzzle 36, by "combining", do you mean a lottery resulting in either 
option with some known probability? What exactly do you mean by 
"smooth" and for what reasons does that claim seem "reasonable"? I 
guess the most questionable demand, no. 5, is the real clue to your 
proof, right? So why is it "reasonable" to demand 5? 

You see, of course one can demand all kinds of nice and seemingly 
harmless properties, but as soon as it turns out that they are in 
conflict with observed reality, it turns out that they may not be so 
harmless at all.

I find Axiom 2 of puzzle 37 more interesting. Why should the addition of 
some constant be irrelevant then at the same time multiplication with 
some constant is not at all irrelevant?
 
By the way, it would be nice if you posted your "answers" wheny you cite 
your "puzzles" since I don't plan to play RV supporter to get a 
password to see them...

However, the really interesting question is: do you consider fairness a 
social good?

Good night, Jobst