Testing for independence while allowing for probabilistic choice

We propose a broad framework for individual choice under risk which can accommodate many stochastic formulations of various deterministic theories. Using this framework to guide an experimental design, we show that most individuals’ departures from the independence axiom cannot be explained by adding a ‘random noise’ term to a deterministic ‘core’ theory which incorporates this axiom. We also find behaviour that cannot be explained in terms of the standard assumptions of Cumulative Prospect Theory, often invoked to account for violations of independence. Our results suggest that ‘similarity’ effects may explain the data better.