[EM] Comments on Heitzig's utility essay

[Jobst Heitzig]

Dear Abd ul-Rahman!

You answered to Warren wrote:
> > 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.
>
> And he is obviously incorrect. 

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.

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. 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. 

Contrary to what you say, I showed that even for voters for whose 
preferences the Archimedean property is wrong it is still meaningful to 
speak of utilities. Only these utilities are not standard real numbers 
but may contain infinitesimal components. (This is, by the way, not a 
new result but well known to utility theorists).

Warren seems to insist that for some reason the Archimedean property is 
essential, but he doesn't tell why. Without it, you can still sum up 
utilities and do all kinds of arithmetics with them, so why should we 
care about that property?

Yours, Jobst