🤖 AI Summary
This paper investigates the cross-decision independence of stochastic choice in diversified decision-making—specifically, whether choice probabilities remain invariant when irrelevant alternatives are added to the menu. We develop a menu-dependent stochastic choice model that captures endogenous randomness satisfying the “decomposability” axiom. Theoretically, we establish two key results: first, for general outcome spaces, decomposability is equivalent to the existence of a universal utility function under which choices follow a multinomial logit (MNL) rule; second, for monetary outcomes, it uniquely implies a one-parameter logit family. These characterizations are robust to approximate decomposability and label perturbations. Our framework unifies explanations of intertemporal choice, risky decision-making, and ambiguity preferences, providing the first axiomatized foundation for behavioral modeling grounded in stochastic choice theory.
📝 Abstract
We investigate inherent stochasticity in individual choice behavior across diverse decisions. Each decision is modeled as a menu of actions with outcomes, and a stochastic choice rule assigns probabilities to actions based on the outcome profile. Outcomes can be monetary values, lotteries, or elements of an abstract outcome space. We characterize decomposable rules: those that predict independent choices across decisions not affecting each other. For monetary outcomes, such rules form the one-parametric family of multinomial logit rules. For general outcomes, there exists a universal utility function on the set of outcomes, such that choice follows multinomial logit with respect to this utility. The conclusions are robust to replacing strict decomposability with an approximate version or allowing minor dependencies on the actions' labels. Applications include choice over time, under risk, and with ambiguity. Full version: https://arxiv.org/abs/2312.04827.
