The gambler’s fallacy is the tendency to expect random processes to switch more often than they actually do—for example, to think that after a string of tails, a heads is more likely. It’s often taken to be evidence for irrationality. It isn’t. Rather, it’s to be expected from a group of Bayesians who begin with causal uncertainty, and then observe unbiased data from an (in fact) statistically independent process. Although they converge toward the truth, they do so in an asymmetric (...) way—ruling out “streaky” hypotheses more quickly than “switchy” ones. As a result, the majority (and the average) exhibit the gambler’s fallacy. If they have limited memory, this tendency persists even with arbitrarily-large amounts of data. Indeed, such Bayesians exhibit a variety of the empirical trends found in studies of the gambler’s fallacy: they expect switches after short streaks but continuations after long ones; these nonlinear expectations vary with their familiarity with the causal system; their predictions depend on the sequence they’ve just seen; they produce sequences that are too switchy; and they exhibit greater rates of gambler’s reasoning when forming binary predictions than when forming probability estimates. In short: what’s been thought to be evidence for irrationality may instead be rational responses to limited data and memory. (shrink)

Experts often communicate probabilities verbally (e.g., unlikely) rather than numerically (e.g., 25% chance). Although criticism has focused on the vagueness of verbal probabilities, less attention has been given to the potential unintended, biasing effects of verbal probabilities in communicating probabilities to decision-makers. In four experiments (Ns = 201, 439, 435, 696), we showed that probability format (i.e., verbal vs. numeric) influenced participants’ inferences and decisions following a hypothetical financial expert’s forecast. We observed a format effect for low probability forecasts: verbal (...) probabilities were interpreted more pessimistically than numeric equivalents. We attributed the difference to directionality, a linguistic property that biases attention toward an outcome. In the high-probability conditions, the directionality of verbal and numeric probabilities aligned (both were positive), whereas they differed in the low-probability conditions (verbal probabilities were more negative). Participants inferred recommendations congruent with the communicated direction and these inferences mediated the effect of probability format on decisions. (shrink)

This article refines a foundational tenet of rational choice theory known as the principle of description invariance. Attempts to apply this principle to human agents with imperfect knowledge have paid insufficient attention to two aspects: first, agents’ epistemic situations, i.e. whether and when they recognize alternative descriptions of an object to be equivalent; and second, the individuation of objects of description, i.e. whether and when objects count as the same or different. An important consequence is that many apparent ‘framing effects’ (...) may not violate the principle of description invariance, and the subjects of these effects may not be irrational. (shrink)

Common-sense (or folk) psychology holds that (generally) we do what we do for the reasons we have. This common-sense approach is embodied in claims like ‘I went to the kitchen because I wanted a drink’ and ‘She took a coat because she thought it might rain and hoped to stay dry’. However, the veracity of these common-sense psychological explanations has been challenged by experimental evidence (primarily from behavioural economics and social psychology) which appears to show that individuals are systematically irrational—that (...) often we do not do what we do because of the reasons we have. Recently, some of the same experimental evidence has also been used to level a somewhat different challenge at the common-sense view, arguing that the overarching aim of reasoning is not to deliver better or more reason-governed decisions for individual reasoners, but to improve group decision making or to protect an individual’s sense of self. This paper explores the range of challenges that experimental work has been taken to raise for the common-sense approach and suggests some potential responses. Overall, I argue that the experimental evidence surveyed should not lead us to a rejection of individual rationality. (shrink)