Switching between utils and dollars is very confusing. You should be very clear when you do so, or you risk getting confused between cases of risk aversion with simple declining marginal utility.
If money has logarithmic value to you, then existing unresolved bets SHOULD have an effect on your preferences even if you’re risk-neutral.
Hmm. I think you’re right: I’ve never connected the terms in that way, using “risk-neutral” in tems of utility rather than money. Looking at it more closely, it appears it’s more commonly used for money, which would be risk-seeking in terms of utility, and probably non-optimal. (note: I also recognize that most people, including me, over-estimate the decline massively, and for small wagers it should be very close to linear).
The standard meaning of “risk-{adverse, neutral, seeking} in terms of X”, AFAICT, is that your utility is a {concave downward, linear, concave upward} function of X, and hence you cannot be risk-adverse or risk-seeking in terms of utility (assuming the von Neumann-Morgenstern axioms).
Switching between utils and dollars is very confusing. You should be very clear when you do so, or you risk getting confused between cases of risk aversion with simple declining marginal utility.
If money has logarithmic value to you, then existing unresolved bets SHOULD have an effect on your preferences even if you’re risk-neutral.
If money has logarithmic value to you, you are not risk neutral, the way I understand the term. How are you using the term?
Hmm. I think you’re right: I’ve never connected the terms in that way, using “risk-neutral” in tems of utility rather than money. Looking at it more closely, it appears it’s more commonly used for money, which would be risk-seeking in terms of utility, and probably non-optimal. (note: I also recognize that most people, including me, over-estimate the decline massively, and for small wagers it should be very close to linear).
The standard meaning of “risk-{adverse, neutral, seeking} in terms of X”, AFAICT, is that your utility is a {concave downward, linear, concave upward} function of X, and hence you cannot be risk-adverse or risk-seeking in terms of utility (assuming the von Neumann-Morgenstern axioms).