  Ergodicity describes an equivalence between the expectation value and the
time average of observables. Applied to human behaviour, ergodic theories of
decision-making reveal how individuals should tolerate risk in different
environments. To optimise wealth over time, agents should adapt their utility
function according to the dynamical setting they face. Linear utility is
optimal for additive dynamics, whereas logarithmic utility is optimal for
multiplicative dynamics. Whether humans approximate time optimal behavior
across different dynamics is unknown. Here we compare the effects of additive
versus multiplicative gamble dynamics on risky choice. We show that utility
functions are modulated by gamble dynamics in ways not explained by prevailing
decision theory. Instead, as predicted by time optimality, risk aversion
increases under multiplicative dynamics, distributing close to the values that
maximise the time average growth of wealth. We suggest that our findings
motivate a need for explicitly grounding theories of decision-making on ergodic
considerations.
