It occurred to me today that the VNM utility functions model preferences concerning income rather than wealth in general.
Consider the continuity axiom, for example. This axiom seems to imply that a rational agent would be willing to gamble their entire life savings for an extra dollar provided that the probability of losing is small enough. Barring the possibility of charity, going broke is tantamount to death, since it costs money to make money. It seems reasonable to me that a rational agent would treat their own death as infinitely bad. Under this assumption no probability of losing is small enough.
This criticism doesn’t apply if lotteries are only allowed positive payouts, of course, but no such assumption is ever made. This is what I mean when I say that the axioms describe preferred income streams rather than wealth levels. The obvious fix is to add a parameter for current wealth, but I’m unsure if a result will follow that is analogous to the VNM Utility Theorem.
It occurred to me today that the VNM utility functions model preferences concerning income rather than wealth in general.
Consider the continuity axiom, for example. This axiom seems to imply that a rational agent would be willing to gamble their entire life savings for an extra dollar provided that the probability of losing is small enough. Barring the possibility of charity, going broke is tantamount to death, since it costs money to make money. It seems reasonable to me that a rational agent would treat their own death as infinitely bad. Under this assumption no probability of losing is small enough.
This criticism doesn’t apply if lotteries are only allowed positive payouts, of course, but no such assumption is ever made. This is what I mean when I say that the axioms describe preferred income streams rather than wealth levels. The obvious fix is to add a parameter for current wealth, but I’m unsure if a result will follow that is analogous to the VNM Utility Theorem.