[EM] Comments on Heitzig's utility essay

[Warren Smith]

> > 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).

>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.

>Lomax: This and the next example involve considerable expense. Suppose that 
increasing the safety of the child only involved spending a penny, or 
equivalent effort? That would be a more appropriate example, would it not?

>Second proof.  Have you, or have you not, erected a meteor shield 
>over your house?
>Q.E.D.

>Lomax: Once again, the expense of avoiding the risk is high. Far too high.
So N.E.D.

--WDS: OK, sure.  The car trip at 20 km/hr with flashing lights might cost you, not
1 cent, but in fact, $20 extra per trip, i.e. 2000 cents.   But nevertheless
you evidently consider your $20 worth more than p*(your child's life)
where p is the chance of a fatal car crash if you had driven with normal caution
levels.  In fact we know how frequent car crashes are, so we can estimate p,
and we find p = 1/5,000,000 roughly.
OK, now scaling by 2000, we find that you, by your behavior, have evidently considered
1 cent worth more than p*(your child's life)  where p=10^(-10).
I was only trying to prove it for p=10^(-20) so in fact, even if you do not
buy the validity of scaling by 2000, it still seems pretty clear I have a 
valid argument here since I have 10^10 worth of headroom.  Heitzig in fact
was arguing not only that I'm not right about p=10^(-20), but I'm also not right about 
p=10^(-100) or p=10^(-1000), or any p>0 whatever.

Concerning the meteor shield, ok, fine.  Do you, or do you not, toss 1 cent pieces
out of your pocket all day over the head of your child, in an effort to possibly deflect 
(or diminish the force of) incoming meteor fragements and stray bullets?

The point is, people risk their lives and their children's lives in tiny ways
all the time in order to gain money or convenience or other stuff exchangeable for money,
and if you had the gall to try to prevent them, they would be furious.  
What we have here - in an effort to deny that obvious fact and to disparage all of
utility theory - is a massive departure from a rational assessment of reality
(which appears to occur in certain people's heads whenever the word "child" is mentioned).
Social choice theorists cannot afford to be irrational to anywhere near that extent if they
wish to *be* social choice theorists.  Also, I point out that if you are that irrational, 
then you also are an extremely poor parent!

>Heitzig: As to fairness: I think it should be obvious that a lottery in which 
participants have equal chances to win is more fair than one in which 
the winner is predetermined.

--WDS: well, you have not either here or in your original post, defined "fairness"
or "social good" but you have asked me if I consider fairness to be a social good.
So I cannot answer you.   But if you are asking "is a lottery in which
participants have equal chances to win, more socially good than a lottery in
which the winner is predetermined?" I guess my reply would be "sometimes yes, sometimes no."
It depends on the circumstances of the "lottery" (which by the way, you also have
not defined).  For example, suppose you go to the store and pay money to buy an apple.  
Is it more socially good for them then to give you the apple (determined) or for the apple
to be given to a random person within 1 mile?   For example,
suppose we hold an election and Chirac wins.  Is it better for Chirac to win, or
for a random candidate to win?   Anyway, I have trouble and see
little point to arguing about things that are not clearly defined (at least not to me).
I have a pretty decent idea what utility is, although getting to that point is not trivial as
we see. If you want to debate the meaning of or importance of "fairness" (which I gather
you believe to be a disticnt notion from "utility"?), then
by all means write another essay about whatever you think it might be.

Warren D Smith
http://rangevoting.org