Modeling the Dynamics of Risky Choice

Abstract

Individuals make decisions under uncertainty every day. Decisions are based on incomplete information concerning the potential outcome or the predicted likelihood with which events occur. In addition, individuals' choices often deviate from the rational or mathematically objective solution. Accordingly, the dynamics of human decision making are difficult to capture using conventional, linear mathematical models. Here, we present data from a 2-choice task with variable risk between sure loss and risky loss to illustrate how a simple nonlinear dynamical system can be employed to capture the dynamics of human decision making under uncertainty (i.e., multistability, bifurcations). We test the feasibility of this model quantitatively and demonstrate how the model can account for up to 86% of the observed choice behavior. The implications of using dynamical models for explaining the nonlinear complexities of human decision making are discussed as well as the degree to which the theory of nonlinear dynamical systems might offer an alternative framework for understanding human decision making processes.

Notes

¹Note that objectively, in each risky choice, S is the better choice as soon as the sure loss of S is lower than the expected value of R, whereas R is the better choice as soon as the expected value of R becomes lower than the sure loss of S.

²A fluctuation is defined as each choice that is different from the previous choice.

³A switch-point is defined as the closest fluctuation to the middle choice for which, in case of an ID sequence, the number of R choices in between this fluctuation and the first S choice in a continuous stretch of S choices spanning the middle is less than the number of S in between. In case of a DI sequence, it is the other way around.