Beliefs like the Gambler's Fallacy and the Hot Hand have interested cognitive scientists, economists, and philosophers for centuries. We propose that these judgment patterns arise from the observer's mental models of the sequence-generating mechanism, moderated by the strength of belief in an a priori base rate. In six behavioral experiments, participants observed one of three mechanisms generating sequences of eight binary events: a random mechanical device, an intentional goal-directed actor, and a financial market. We systematically manipulated participants’ beliefs about the (...) base rate probabilities at which different outcomes were generated by each mechanism. Participants judged 18 sequences of outcomes produced by a mechanism with either an unknown base rate, a specified distribution of three equiprobable base rates, or a precise, fixed base rate. Six target sequences ended in streaks of between two and seven identical outcomes. The most common predictions for subsequent events were best described as pragmatic belief updating, expressed as an increasingly strong expectation that a streak of identical signals would repeat as the length of that streak increased. The exception to this pattern was for sequences generated by a random mechanical device with a fixed base rate of.50. Under this specific condition, participants exhibited a bias toward reversal of streaks, and this bias was larger when participants were asked to make a dichotomous choice versus a numerical probability rating. We review alternate accounts for the anomalous judgments of sequences and conclude with our favored interpretation that is based on Rabin's version of Tversky & Kahneman's Law of Small Numbers. (shrink)

It is argued that current attempts to model human learning behavior commonly fail on one of two counts: either the model assumptions are artificially restricted so as to permit the application of mathematical techniques in deriving their consequences, or else the required complex assumptions are imbedded in computer programs whose technical details obscure the theoretical content of the model. The first failing is characteristic of so-called mathematical models of learning, while the second is characteristic of computer simulation models. An approach (...) to model building which avoids both these failings is presented under the title of a black-box theory of learning. This method permits the statement of assumptions of any desired complexity in a language which clearly exhibits their theoretical content.Section II of the paper is devoted to the problem of testing and comparing alternative learning theories. The policy advocated is to abandon attempts at hypothesis testing. It is argued that, in general, we not only lack sufficient data and sufficiently powerful techniques to test hypotheses, but that the truth of a model is not really the issue of basic interest. A given model may be true in the sense that on the basis of available evidence we cannot statistically reject it, but not interesting in the sense that it provides little information about the processes underlying behavior. Rather, we should accept or reject models on the basis of how much information they provide about the way in which subjects respond to environmental structure. This attitude toward model testing is made precise by introducing a formal measure of the information content of a model. Finally, it is argued that the statistical concept of degrees-of-freedom is misleading when used in the context of model testing and should be replaced by a measure of the information absorbed from the data in estimating parameters. (shrink)

The statistics of small samples are often quite different from those of large samples, and this needs to be taken into account in assessing the rationality of human behavior. Specifically, in evaluating human responses to environmental statistics, it is the effective environment that matters; that is, the environment actually experienced by the agent needs to be considered, not simply long‐run frequencies. Significant deviations from long‐run statistics may arise through experiential limitations of the agent that stem from resource constraints and/or information‐processing (...) bounds. The article draws together recent work from a number of areas in judgment and decision making ranging from randomness perception (Hahn & Warren, ), information sampling (Hertwig & Pleskac, ; Kareev et al., ), and consequences of choice for exploration or exploitation (e.g., Denrell, ) to demonstrate how proper consideration of these deviations leads to reevaluation of behaviors that are otherwise deemed irrational. (shrink)