Nonlinear Decision Weights or Skewness Preference? A Model Competition

Abstract

An extensive literature exists comparing the predictive power of Cumulative Prospect Theory (CPT) and Expected Utility Theory (EUT) in decisions from description. CPT accommodates the empirically observed deviations from EUT primarily by assuming a nonlinear probability weighting function and loss aversion. An alternative explanation is that decision makers have preferences for higher-order moments, beyond the mean and variance of lotteries — we extensively test the Mean-Variance-Skewness (MVS) preference model. We estimate the proportion of EUT, CPT and the MVS populations using a latent-class hierarchical Bayesian model for six different datasets, including both decisions from description and experience. In decisions from description, subjects are explicitly presented with the probabilities and outcome values of the lotteries. In decisions from experience subjects must sample (without cost) from the lottery distributions to learn both the probabilities and outcome values. In the latter, CPT and EUT require the explicit calculation of probabilities from experience; however, the MVS model only requires that decision-makers hold estimates of the three moments of the outcome distributions. In decisions from experience and description with simple lotteries (one safe option and one risky lottery with only two outcomes), we find significant subject heterogeneity — some subjects are classified as CPT and others as MVS. In the remaining four datasets with multiple (two to three) outcomes per lottery, a single class is sufficient to characterize subjects. Specifically, in two datasets of decisions from experience all subjects are classified as MVS, thus implying that preferences for skewness are more predictive than nonlinear probability weighting. In two datasets with decisions from description all subjects are classified as CPT. We find no evidence of an EUT population in any of the datasets. We conclude that the scope of CPT is primarily limited to decisions from description, while the scope of MVS to decisions from experience. Furthermore, out of the four datasets with a CPT population, only in one dataset did we observe the standard inverse-S shaped probability weighting function; this was the only dataset with simple lotteries (as defined above) and no multi-outcome lotteries.