The Disjunction Effect in two-stage simulated gambles. An experimental study and comparison of a heuristic logistic, Markov and quantum-like model

Savage’s rational axiom of decision making under uncertainty, called the ‘Sure Thing’ principle, was purportedly falsified in a two-stage gamble paradigm by Tversky and Shafir (1992). This work revealed that participants would take a second-stage gamble for both possible outcomes of the initial-stage gamble, but would significantly depress this choice when no information was available on the outcome of the initial-stage gamble. Subsequent research has reported difficulty to replicate this Disjunction Effect in the two-stage gamble paradigm. We repeated this simulated two-stage gamble paradigm in an online study (N = 1119) but adapted the range of payoff amounts, and controlled the order of the blocks of two-stage gambles with, respectively without, information on the outcome of the first-stage gamble. The main empirical contributions of this study are that more risk averse participants produced (i) a reliable order effect in relation to the Disjunction Effect and the violation of the Law of Total Probability, and (ii) a novel inflation effect on gambling in the Unknown outcome condition analogous but opposite to the Disjunction Effect when Unknown outcome conditioned two-stage gambles precede the Known outcome conditioned ones. By contrast, we found that less risk averse participants produced neither of these effects. We discuss the underlying choice processes and compare the effectiveness of a logistic model, a Markov model and a quantum-like model. Our main theoretical findings are (i) a standard utility model and a Markov model using heuristic linear utility, contextual influence and carry-over effect cannot accommodate the present empirical results, and (ii) a model based on quantum dynamics, matched in form to the Markov model, can successfully describe all major aspects of our data.