Decisions with Compound Lotteries

Violations of the Reduction of Compound Lottery axiom (ROCL) were documented, but they are not fully understood, and only few descriptive models were offered to model decision makers' (DMs) decisions in such cases. This article comprehensively tests the effects of 6 factors that could influence DMs’ evaluations of compound lotteries, and models how DMs make decisions in their presence. In an experiment with 6 groups of subjects (n = 125), the authors elicited certainty equivalents of simple and compound lotteries via a 2-stage choice procedure. The authors confirmed the existence of the systematic violations of ROCL. The authors tested the effect of each factor and their interactions, and found that the number of stages and the global probability had prominent effects. The authors developed three classes of models to describe the weighting process for compound lotteries. The best fitting model was the one that assumes that DMs anchor on the lowest stage probability and then apply the weighting function. The “aggregate first and weigh second” overall outperformed the “weight first and aggregate second” models, presumably because this process is cognitively easier and more natural.