Correlation neglect and case-based decisions

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In most theories of choice under uncertainty, decision-makers are assumed to evaluate acts in terms of subjective values attributed to consequences and probabilities assigned to events. Case-based decision theory (CBDT), proposed by Gilboa and Schmeidler, is fundamentally different, and in the tradition of reinforcement learning models. It has no state space and no concept of probability. An agent evaluates each available act in terms of the consequences he has experienced through choosing that act in previous decision problems that he perceives to be similar to his current problem. Gilboa and Schmeidler present CBDT as a complement to expected utility theory (EUT), applicable only when the state space is unknown. Accordingly, most experimental tests of CBDT have used problems for which EUT makes no predictions. In contrast, we test the conjecture that case-based reasoning may also be used when relevant probabilities can be derived by Bayesian inference from observations of random processes, and that such reasoning may induce violations of EUT. Our experiment elicits participants’ valuations of a lottery after observing realisations of the lottery being valued and realisations of another lottery. Depending on the treatment, participants know that the payoffs from the two lotteries are independent, positively correlated, or negatively correlated. We find no evidence of correlation neglect indicative of case-based reasoning. However, in the negative correlation treatment, valuations cannot be explained by Bayesian reasoning, while stated qualitative judgements about chances of winning can.