I don’t think opportunities to make choices are usually considered to be in the domain of a utility function. (If I’m wrong, educate me. I’d appreciate it.)
Ok, I looked it up and it looks like you and thomblake (ETA: and Technologos. Thanks for correcting me!) are right: the usual way of doing it is to include risk aversion in the utility function. Sorry about that.
Wikipedia on risk-neutral measures does discuss the possibility of adjusting the probabilities, rather than the utility, when calculating the expected value of a choice, but it looks like that’s usually done for ease of financial calculation.
So, one explanation for why people don’t take the “half or double” gamble is that they do have the log(x) utility function, but don’t behave accordingly because of loss aversion (as opposed to risk aversion).
I don’t think opportunities to make choices are usually considered to be in the domain of a utility function. (If I’m wrong, educate me. I’d appreciate it.)
Ok, I looked it up and it looks like you and thomblake (ETA: and Technologos. Thanks for correcting me!) are right: the usual way of doing it is to include risk aversion in the utility function. Sorry about that.
Wikipedia on risk-neutral measures does discuss the possibility of adjusting the probabilities, rather than the utility, when calculating the expected value of a choice, but it looks like that’s usually done for ease of financial calculation.
So, one explanation for why people don’t take the “half or double” gamble is that they do have the log(x) utility function, but don’t behave accordingly because of loss aversion (as opposed to risk aversion).
The post is technical, but Stuart_Armstrong analyzed some special cases of not-quite-utility-function agents.