Good point! St. Petersburg requires utility being monotonic (ideally linear) in something other than probability (and optionally something like unbounded or at least increasing for a while).
This doesn’t have to be the case for all utility functions. (Especially since unbounded utilities are bad). Probabilities are strictly bounded, so having utility being linear in them is not a huge problem. Thanks for changing my mind!
Good point! St. Petersburg requires utility being monotonic (ideally linear) in something other than probability (and optionally something like unbounded or at least increasing for a while).
This doesn’t have to be the case for all utility functions. (Especially since unbounded utilities are bad). Probabilities are strictly bounded, so having utility being linear in them is not a huge problem. Thanks for changing my mind!
My general reasoning about unbounded utilities see here