We conduct two experiments where subjects make a sequence of binary choices between risky and ambiguous binary lotteries. Risky lotteries are deﬁned as lotteries where the relative frequencies of outcomes are known. Ambiguous lotteries are lotteries where the relative frequencies of outcomes are not known or may not exist. The trials in each experiment are divided into three phases: pre-treatment, treatment and post-treatment. The trials in the pre-treatment and post-treatment phases are the same. As such, the trials before and after the treatment phase are dependent, clustered matched-pairs, that we analyze with the alternating logistic regression (ALR) package in SAS. In both experiments, we reveal to each subject the outcomes of her actual and counterfactual choices in the treatment phase. The treatments diﬀer in the complexity of the random process used to generate the relative frequencies of the payoﬀs of the ambiguous lotteries. In the ﬁrst experiment, the probabilities can be inferred from the converging sample averages of the observed actual and counterfactual outcomes of the ambiguous lotteries. In the second experiment the sample averages do not converge. If we deﬁne ﬁctive learning in an experiment as statistically signiﬁcant changes in the responses of subjects before and after the treatment phase of an experiment, then we expect ﬁctive learning in the ﬁrst experiment, but no ﬁctive learning in the second experiment. The surprising ﬁnding in this paper is the presence of ﬁctive learning in the second experiment. We attribute this counterintuitive result to apophenia: “seeing meaningful patterns in meaningless or random data.” A reﬁnement of this result is the inference from a subsequent Chi-squared test, that the eﬀects of ﬁctive learning in the ﬁrst experiment are signiﬁcantly diﬀerent from the eﬀects of ﬁctive learning in the second experiment.
Bunn, Oliver D.; Calsamiglia, Caterina; and Brown, Donald J., "Testing for Fictive Learning in Decision-Making under Uncertainty" (2013). Cowles Foundation Discussion Papers. 2262.