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