Abstract
“Decisions from experience” (DFE) refers to a body of work that emerged in research on behavioral decision making over the last decade. One of the major experimental paradigms employed to study experience-based choice is the “sampling paradigm,” which serves as a model of decision making under limited knowledge about the statistical structure of the world. In this paradigm respondents are presented with two payoff distributions, which, in contrast to standard approaches in behavioral economics, are specified not in terms of explicit outcome-probability information, but by the opportunity to sample outcomes from each distribution without economic consequences. Participants are encouraged to explore the distributions until they feel confident enough to decide from which they would prefer to draw from in a final trial involving real monetary payoffs. One commonly employed measure to characterize the behavior of participants in the sampling paradigm is the sample size, that is, the number of outcome draws which participants choose to obtain from each distribution prior to terminating sampling. A natural question that arises in this context concerns the “optimal” sample size, which could be used as a normative benchmark to evaluate human sampling behavior in DFE. In this theoretical study, we relate the DFE sampling paradigm to the classical statistical decision theoretic literature and, under a probabilistic inference assumption, evaluate optimal sample sizes for DFE. In our treatment we go beyond analytically established results by showing how the classical statistical decision theoretic framework can be used to derive optimal sample sizes under arbitrary, but numerically evaluable, constraints. Finally, we critically evaluate the value of deriving optimal sample sizes under this framework as testable predictions for the experimental study of sampling behavior in DFE.
Highlights
Optimal sample sizes in decisions from experience are presented with two payoff distributions on a computer screen
Assuming, that the decision maker in the simplified sampling problem” (SSP) (1) is adopting the “inference approach,” (2) is willing to commit to a classical, squared-loss parameter inference scheme, and (3) is willing to quantify its prior uncertainty about the binary payoff distribution parameter using a beta distribution, she may read-off the optimal sample size depending on her subjective sampling cost constant c > 0 and prior uncertainty captured by the beta distribution parameters α and β about the binary distributions from graphs such as Figure 5B
In this study we have shown how a normative benchmark for optimal sample sizes in the DFE sampling paradigm can be developed based on results from classical statistical decision theory
Summary
“Decisions from experience” (DFE) refers to a body of work that emerged in research on behavioral decision making over the last decade. As will be seen, the “inference assumption” renders the notion of optimal sample sizes in DFE a concept that can be addressed in the maximum expected utility (MEU) framework for statistical decisions, originally developed by Raïffa and Schlaifer (1961). It should be noted, that while the inference assumption in sampling DFE is widespread, it is by no means without alternatives, as we will address in more detail in the Discussion section.
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