Ergodicity transformations predict human decision-making under risk

Decision theories commonly model human behavior as maximizing the expected value of a utility function. This function may vary from one person to another but is assumed to be stable over time. Recent theoretical developments demonstrate that these assumptions are generally incompatible with growing wealth at the fastest rate. Growth optimality requires utility functions to mirror ergodicity transformations and adapt to the dynamic environment. We exposed human participants to different wealth dynamics in a consequential risky decision-making experiment. Via Bayesian modelling, we estimated utility functions separately for each dynamic. Pre-registered analyses revealed strong evidence supporting the quantitative predictions of the ergodicity model. Our study provides evidence that human risk-taking can adapt quickly to the dynamical context, in ways that align closely to the theoretical optimum for maximizing wealth over time.Author summary: Why do people sometimes take risks and other times play it safe? Classic decision theories often assume each person has a stable “utility function”—a fixed way of valuing gains and losses—and that people choose options that maximize expected utility. Recent theory suggests this picture can fail when the real goal is to grow resources over time. In particular, the strategy that maximizes long-run growth can depend on how wealth changes: sometimes gains and losses add up (additive dynamics), while in other settings outcomes compound (multiplicative dynamics). Growth-optimization theory predicts that the utility function that best describes behavior should therefore shift with the underlying wealth dynamics. We tested this idea in a fully consequential risky decision-making experiment in which participants experienced different wealth dynamics and their wealth was updated on every trial. Using Bayesian models, we estimated participants’ utility functions separately under each dynamic. We found strong evidence that people change their risk taking under these different conditions. These results suggest that human risk-taking is not governed by a single fixed preference curve, but can adapt rapidly to the dynamical context in a way consistent with long-run growth optimization.