Stochastic Choice and Preference Reversals

Abstract

The preference reversal phenomenon is one of the most important, long-standing, and widespread anomalies contradicting economic models of decisions under risk. It describes the robust observation of frequent "standard reversals" where long-shot gambles are valued above moderate ones but then the latter are chosen, while the opposite "nonstandard reversals" happen rarely. This inconsistency casts severe doubts on commonly-used preference elicitation methods. Strikingly, alternative designs which should eliminate the phenomenon produce frequent nonstandard reversals instead, in a puzzling reversal of the phenomenon. We develop and test a model predicting when the phenomenon should occur, when its reversal should occur instead, and what determines the magnitude of the effects. The reversal of the phenomenon is predicted as a consequence of stochastic choice and risk aversion, without invoking any behavioral bias. The original phenomenon arises from stochastic choice and a systematic bias in monetary valuations, which is restricted to long-shot gambles. To validate the model, we conduct two experiments leading to the preference reversal phenomenon and its reversal, respectively. We employ a novel empirical approach allowing us to disentangle choice and valuation errors by relying on utilities estimated out of sample, and confirm that reversals are associated with errors in monetary valuations of long-shots, with the upward bias quantified at 293% in monetary terms. The data also confirms the model's novel predictions, showing that a larger bias strengthens the phenomenon and higher risk aversion strengthens its reversal. Surprisingly, our analysis implies that the magnitude of the original phenomenon has been underestimated so far.

Attentional shifts and preference reversals: An eye-tracking study

“…To accomplish this, a measure of overpricing is needed. For this reason, our design included an initial phase with 32 lottery pairs, independent of the preference reversal design, which served the purpose of providing an out-of-sample estimation of the subjects' individual preferences (following Alós-Ferrer et al, 2020). The main goal of this estimation was to obtain individual utility functions and certainty equivalents which can be used to quantify the overpricing of lotteries in the evaluation phase of the Price treatment, and relate it to attention as measured by fixation data.…”

“…Finally, we complement the demonstration of an attentional shift across different evaluation modes at the aggregate level with evidence for the role of attention at the level of individual decisions. Following Alós-Ferrer et al (2020), we included an additional, independent block of decisions under risk in the experiment, allowing for an out-of-sample estimation of individual utilities and certainty equivalents. For the treatment with monetary evaluations, we then obtain a quantitative measure of overpricing, in the form of the difference between the certainty equivalent and the elicited valuation.…”

Strength of preference and decisions under risk

“…Following a standard approach, we the main analysis estimates an additive random utility model (RUM) which considers a given utility function plus an additive noise component (e.g., Thurstone, 1927;Luce, 1959;McFadden, 2001). The estimation procedure employs well-established techniques as used in many recent contributions (Van Gaudecker et al, 2011;Conte et al, 2011;Moffatt, 2015;Alós-Ferrer & Garagnani, 2020;Garagnani, 2020;Alós-Ferrer et al, 2019, 2021. We provide a short description in Appendix A.…”

Evidence Accumulates for Individual Attributes during Value-Based Decisions

“…In the domain of risky choice, it has long been established that individuals’ preferences over options that combine monetary gains and losses with probabilities or time delays may reverse when different methods are used to elicit those preferences. For example, preferences revealed through choices have been shown to reverse compared to those elicited by matching, pricing, or rating procedures (Alós-Ferrer et al, 2016; Alos-Ferrer et al, 2020; Alós-Ferrer et al, 2021; Fischer et al, 1999; Grether & Plott, 1979; Lichtenstein & Slovic, 1971; Seidl, 2002; Tversky et al, 1988, 1990; Weber & Johnson, 2009). A leading explanation for these preference reversals is that the importance weights on the probability, time, and/or money dimensions differ across the preference elicitation procedures (Seidl, 2002; Tversky et al, 1988).…”