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 ---- election-methods mailing list - see http://electorama.com/em for list info
