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Learning under uncertainty with multiple priors: experimental investigation

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Abstract

We run an experiment to compare belief formation and learning under ambiguity and under compound risk at the individual level. We estimate a four-type mixture model assuming that, for each type of uncertainty, subjects may either learn according to Bayes’ Rule or learn according to a multiple priors model of learning. Our results indicate that majority of subjects are Bayesian, both under compound risk and under ambiguity, while the second most frequent type are subjects that are Bayesian under compound risk but who use a multiple priors model of learning under ambiguity. In addition, we find strong evidence against a common assumption that participants’ initial beliefs (and priors) are consistent with information provided about the uncertain process.

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Notes

  1. While the gap between the certain amounts for Option A (Fig. 2) may seem large, it is worth noting that in the experiment subjects will see two signals about each urn with each signal consisting of three draws with replacement. For context, the indifference point for a risk neutral subject who considers objective composition of the C urn, who follows Bayes’ rule, and who sees six successes would increase by approximately $6.

  2. For robustness, we augment the current data set with data from Moreno & Rosokha (2016) that includes 113 participants. Results are presented in Online Appendix B.

  3. The random lottery incentive mechanism has several known issues when it comes to the elicitation of preferences for risk and uncertainty. For example, Freeman et al. (2019) show that when compensated based on one randomly selected lottery from a list, subjects are more likely to select the sure payment over risky lottery as compared to the case when facing only one payoff-relevant decision. Harrison et al. (2015) show that the random lottery incentive mechanism may in itself lead to violations of the reduction of compound lotteries. However, a between-subject design with each subject facing only one, payoff-relevant decision would not be able to address whether the same subject learns differently under compound risk or under ambiguity.

  4. This corresponds to the same ranges of p0(B) and p0(W) in the Simplex priors example.

  5. Our specification is therefore a mixture model at the subject level with a “correlated random coefficients” assumption about individual specific parameters. It is therefore more akin to Conte et al. (2011) than Harrison and Rutström (2009) in two important ways: firstly, the mixing is at the subject level rather than the decision level, and secondly, parameters 𝜃i are assumed to be random draws, rather than deterministic functions of observable characteristics. Our estimation differs from Conte et al. (2011) in only three notable ways: (i) we consider different behavioral models, hence our likelihood functions are different; (ii) where Conte et al. (2011) has two behavioral types, we have four; and (iii) we use Bayesian techniques instead of (simulated) maximum likelihood.

  6. For robustness, we carry out the analyses from above while restricting the priors (and posteriors) to follow Beta distribution truncated to [.25,.75]. Results are presented in Tables B-1 and B-3 of Online Appendix B. We find the main results are quantitatively similar —the proportion of AB-CB type is approximately 60%, and the proportion of AM-CB type is approximately 29%— though individual preference and learning parameters change.

  7. Harrison and Rutström (2009), Conte et al. (2011), and Harrison et al. (2015), for example, make this assumption. Ferecatu and Önçüler (2016) on the other hand assumes choice precision is subject-specific.

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Authors and Affiliations

  1. Department of Economics, The University of Toledo, Toledo, OH, USA

    James R. Bland

  2. Krannert School of Management, Purdue University, West Lafayette, IN, USA

    Yaroslav Rosokha

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  1. James R. Bland
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  2. Yaroslav Rosokha
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Correspondence to Yaroslav Rosokha.

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This paper benefited from discussions and comments from Ernan Haruvy, Othon Moreno, Dale Stahl, as well as from workshop participants at the 2012 North American ESA meetings, the 2014 Annual Informs Meetings, and seminar participants at the University of Texas and Purdue University. This work was supported by a grant from the Russell Sage Foundation.

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Bland, J.R., Rosokha, Y. Learning under uncertainty with multiple priors: experimental investigation. J Risk Uncertain 62, 157–176 (2021). https://doi.org/10.1007/s11166-021-09351-y

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