Reduction of Compound Lotteries with Objective Probabilities: Theory and Evidence

The reduction of compound lotteries axiom (ROCL) has assumed a central role in the evaluation of behavior toward risk and uncertainty. We present experimental evidence on its validity in the domain of objective probabilities. Our battery of lottery pairs includes simple one-stage lotteries, two-stages compound lotteries, and their actuarially equivalent one-stage lotteries. We find violations of ROCL and that behavior is better characterized by a source-dependent version of the Rank-Dependent Utility model rather than Expected Utility Theory. Since we use the popular “1-in-K” random lottery incentive mechanism payment procedure in our main test, our experiment explicitly recognizes the impact that this payment procedure may have on preferences. Thus we also collect data using the “1-in-1” payment procedure. We do not infer any violations of ROCL when subjects are only given one decision to make. These results are supported by both structural estimation of latent preferences as well as non-parametric analysis of choice patterns. The random lottery incentive mechanism, used as payment protocol, itself induces an additional layer of “compounding” by design that might create confounds in tests of ROCL. Therefore, we provide a word of caution for experimenters interested in studying ROCL for other purposes, such as the relationship between ambiguity attitudes and attitudes toward compound lotteries, to carefully think about the design to study ROCL, payment protocols and their interaction with the preferences being elicited.