Before revision: The classic decision-theory problem of evaluating a gamble is treated from a modern perspective using dynamics . Linear and logarithmic utility functions appear not as expressions for the value of money but as mappings that result in ergodic observables for purely additive and purely multiplicative dynamics, the most natural stochastic processes to model wealth. This perspective is at odds with the boundedness requirement for utility functions in the dominant formalism of decision theory. We highlight conceptual and mathematical inconsistencies throughout the development of decision theory, whose correction clarifies that the modern perspective is legitimate and that boundedness of utility functionsis not required .
After revision: The classic decision-theory problem of evaluating a gamble is treated from a modern perspective using dynamics . Linear and logarithmic utility functions appear not as expressions for the value of money but as mappings that result in ergodic observables for purely additive and purely multiplicative dynamics, respectively. We highlight inconsistencies throughout the development of decision theory, whose correction clarifies that the modern perspective is legitimate and that boundedness of utility functionsis not required .