  Gambles are random variables that model possible changes in monetary wealth.
Classic decision theory transforms money into utility through a utility
function and defines the value of a gamble as the expectation value of utility
changes. Utility functions aim to capture individual psychological
characteristics, but their generality limits predictive power. Expectation
value maximizers are defined as rational in economics, but expectation values
are only meaningful in the presence of ensembles or in systems with ergodic
properties, whereas decision-makers have no access to ensembles and the
variables representing wealth in the usual growth models do not have the
relevant ergodic properties. Simultaneously addressing the shortcomings of
utility and those of expectations, we propose to evaluate gambles by averaging
wealth growth over time. No utility function is needed, but a dynamic must be
specified to compute time averages. Linear and logarithmic "utility functions"
appear as transformations that generate ergodic observables for purely additive
and purely multiplicative dynamics, respectively. We highlight inconsistencies
throughout the development of decision theory, whose correction clarifies that
our perspective is legitimate. These invalidate a commonly cited argument for
bounded utility functions.
