[EM] Comments on Heitzig's utility essay

[Juho]

On Feb 22, 2007, at 1:12 , Jobst Heitzig wrote:

> Dear Warren,

>>> 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?

A businessman might make the decision Warren Smith proposes if a=your  
company goes bankrupt or a=you lose $10,000,000. I guess the social  
utilities of human beings that Jobst discusses take into account  
typically also other aspects than arithmetics on money and other  
goods. I see at least two directions that might make a difference.
1) Publicity. If the child and others would get to know that someone  
played games on her life that might change the utilities. If secret,  
then someone might toss the coin.
2) Time. After one week the utilities might look different and a  
clever person might anticipate that already when making the decision.  
One cent would be probably already spent but the fact that one played  
with the life would stay on one's memory quite long. Maybe this would  
make most people not toss the coin as proposed in 1 above.

Human life is a complex process that involves time and all kinds of  
cyclic relationships. Simplified economic theories may threat money  
as a utility with linear value and decisions that are based on  
calculator only. And the society may amplify this by letting people  
understand that such monetary values are indeed the meaning of life.  
But maybe we are luckily not forced to abstract our lives to  
equations to that extent. :-)

"Mathematically" speaking I think the difference between these two  
ways of thinking comes from the fact that life is a process to be  
lived, not a static equation to be solved. :-)

>> 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.

Also here I think the premises need some justification. Diving <20 km/ 
h would drive you insane. Maybe the child too. Your child would not  
like either of those scenarios. :-)

Juho


		
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