[EM] Comments on Heitzig's utility essay

[Abd ul-Rahman Lomax]

At 05:57 PM 2/22/2007, Jobst Heitzig wrote:
>Not incorrect at all. I repeat: I would never enter a lottery which at
>worst kills my child and at best gives me one cent. That's a simple
>truth. I just wouldn't do it. And that's surely not irrational at all.

I wouldn't enter such a lottery where the entry was framed that way. 
However, what about a lottery that has a very small but nonzero 
possibility of causing such a terrible loss, for an individual, but 
which returns one cent for every person on earth? This is tantamount 
to all persons on earth entering the lottery in question. The return 
is on the order of sixty million dollars. Sixty million dollars, if 
amalgamated rather than distributed (and from a social utility point 
of view the two are the same), can save, probably, thousands of 
lives, maybe even millions in certain applications.

Put it another way. Entering the lottery is *not* contributing to 
that fund the one cent. You gain a penny by entering this lottery. 
And the result is an increased risk to your child.

So the answer to the question, really, depends on how it is framed. 
It's not about utility analysis, at least not directly. Rather it is 
about how we respond to imagination and risk *when we confront it.* I 
gave a very strong reason why we are this way, and it is not 
irrational, ultimately, because hidden in this whole discussion is 
the question of how we evaluate risk. When a risk comes to mind, we 
instinctively assume that it is reasonably possible, not possible on 
the order of 10^-20. (And, of course, missing from that probability 
figure is the time period involved. Perhaps if I give my child that 
candy bar it encourages a lifelong habit that leads to diabetes and 
premature death. When does this death occur? Within the next hundred 
years? If so, an increased risk of quite a lot larger than 10^-20 is 
still lost in the noise. As I mentioned, walking with your child, 
pick up the penny on the ground, there is a larger risk to the child 
from the moment of inattention. As I wrote, some of us no longer pick 
up pennies, but not because of this risk analysis, it is simply not 
worth the effort.

What if the lottery entry benefit was $20? $100? $1000? $1,000,000? 
Frankly, someone comes up to me and offers me $1,000,000 for an 
increased risk to my child that was exrremely small, I wouldn't take 
it, I expect. Not framed like that. But equivalent situations, yes, I 
make decisions all the time that are, from a utility point of view, similar.

So why wouldn't I take it? It's because of what I wrote: I would not 
trust the risk analysis presented to me. If I knew for a fact that 
the risk was that low, I'd take the money. Because that risk is lost 
in the noise. Quite simply, it is beneath consideration because there 
are constant risks that are so much greater, vastly greater. Not 
infinitely greater, to use the strange language that Forest 
introduced, but vastly greater.

>Then you interpreted me like this:
> > His whole point was that we neglect utilities under some
> > circumstances,
>
>That is a complete misunderstanding. I never said any such thing.

Well, either I understand you better than you understand yourself, or 
I'm wrong. Take your pick. I'm not attached....

>  The
>essay is about the question under what circumstances the term
>"utility" (as defined by preferences over lotteries) is meaningful, and
>what properties these "utilities" have when the term is meaningful.

Yes. And if I recall correctly, I thanked you for the effort. I'm 
certainly not presuming that I understand more than some of what you 
wrote, and my comments are about certain narrow details, and, in 
particular, about the discussion which ensued with Warren.