Question: how to reconcile the fact that expected value is linear with preferences being possibly nonlinear?
Example: people are tipically willing to pay more than expected value for a small chance of a big benefit (lottery), or to remove a small chance of a big loss (insurance).
This example could be rejected as a “mental bias” or “irrational”. However, it is not obvious to me that linearity is a virtue, and even if it is, we are human and our subjective experience is not linear.
Thank you for pointing out log utility, I am aware of this model (and also other utility functions). Any reasonable utility function is concave (diminishing returns), which can explain insurance to some extent but not lotteries.
I could imagine that, for an altruistic actor, altruistic utility becomes “more linear” if it’s a linear combination of the utility functions of the recipients of help. This might be defensible, but it is not obvious for me unless that actor is utilitarian, at least in their altruistic actions.
Question: how to reconcile the fact that expected value is linear with preferences being possibly nonlinear?
Example: people are tipically willing to pay more than expected value for a small chance of a big benefit (lottery), or to remove a small chance of a big loss (insurance).
This example could be rejected as a “mental bias” or “irrational”. However, it is not obvious to me that linearity is a virtue, and even if it is, we are human and our subjective experience is not linear.
Look into logarithmic utility of money; there is some rich literature here
For an altruistic actor, money becomes more linear again, but I don’t have a quick reference here.
Thank you for pointing out log utility, I am aware of this model (and also other utility functions). Any reasonable utility function is concave (diminishing returns), which can explain insurance to some extent but not lotteries.
I could imagine that, for an altruistic actor, altruistic utility becomes “more linear” if it’s a linear combination of the utility functions of the recipients of help. This might be defensible, but it is not obvious for me unless that actor is utilitarian, at least in their altruistic actions.