People are adept at inferring novel causal relations, even from only a few observations. Prior knowledge about the probability of encountering causal relations of various types and the nature of the mechanisms relating causes and effects plays a crucial role in these inferences. We test a formal account of how this knowledge can be used and acquired, based on analyzing causal induction as Bayesian inference. Five studies explored the predictions of this account with adults and 4-year-olds, using tasks in which (...) participants learned about the causal properties of a set of objects. The studies varied the two factors that our Bayesian approach predicted should be relevant to causal induction: the prior probability with which causal relations exist, and the assumption of a deterministic or a probabilistic relation between cause and effect. Adults’ judgments (Experiments 1, 2, and 4) were in close correspondence with the quantitative predictions of the model, and children’s judgments (Experiments 3 and 5) agreed qualitatively with this account. (shrink)

This article outlines a theory of naive probability. According to the theory, individuals who are unfamiliar with the probability calculus can infer the probabilities of events in an extensional way: They construct mental models of what is true in the various possibilities. Each model represents an equiprobable alternative unless individuals have beliefs to the contrary, in which case some models will have higher probabilities than others. The probability of an event depends on the proportion of models in which it occurs. (...) The theory predicts several phenomena of reasoning about absolute probabilities, including typical biases. It correctly predicts certain cognitive illusions in inferences about relative probabilities. It accommodates reasoning based on numerical premises, and it explains how naive reasoners can infer posterior probabilities without relying on Bayes's theorem. Finally, it dispels some common misconceptions of probabilistic reasoning. (shrink)

We review the current status of fuzzy-trace theory. The presentation is organized around five topics. First, theoretical ideas that immediately preceded the development of fuzzy-trace theory are sketched. Second, experimental findings that challenged those ideas are summarized. Third, the core assumptions that comprised the initial version of fuzzy-trace theory are described. Fourth, some modifications to those assumptions are explored that were necessitated by subsequent experimental findings. Fifth, four areas of experimentation are considered in which research under the aegis of fuzzy-trace (...) theory is in progress: suggestibility and false memories; judgment and decision making; the development of forgetting; and the development of retrieval. (shrink)

Mind and environment evolve in tandem—almost a platitude. Much of judgment and decision making research, however, has compared cognition to standard statistical models, rather than to how well it is adapted to its environment. The author argues two points. First, cognitive algorithms are tuned to certain information formats, most likely to those that humans have encountered during their evolutionary history. In par ticular, Bayesian computations are simpler when the information is in a frequency format than when it is in a (...) probability format. The author investigates whether fre quency formats can make physicians reason more often the Bayesian way. Second, cognitive algorithms need to operate under constraints of limited time, knowledge, and computational power, and they need to exploit the structures of their environments. The author describes a fast and frugal algorithm, Take The Best, that violates standard principles of rational inference but can be as accurate as sophisticated "optimal" mod els for diagnostic inference. Key words: Bayes' theorem; bounded rationality; infor mation format; probabilistic reasoning; satisficing; training; medical education. (shrink)

Class inclusion, the conjunction fallacy, and other phenomena are presented to illustrate cognitive illusions, that reasoning can be misdirected so that errors of judgment violate known principles. Errors in class inclusion are traced to accessing and implementing logical knowledge, rather than logical deficits, memory overload, or misleading questions. It is argued that superordinate-set cuing does not afford subset comparisons, but, rather, facilitates implementation of logical knowledge. According to fuzzy-trace theory, successful performance involves applying the cardinality principle, but also suppressing solutions (...) based on judgments of relative numerosity, in which horizontal relationships between classes are apt to usurp the role of vertical ones. (shrink)

The phenomenon of base-rate neglect has elicited much debate. One arena of debate concerns how people make judgments under conditions of uncertainty. Another more controversial arena concerns human rationality. In this target article, we attempt to unpack the perspectives in the literature on both kinds of issues and evaluate their ability to explain existing data and their conceptual coherence. From this evaluation we conclude that the best account of the data should be framed in terms of a dual-process model of (...) judgment, which attributes base-rate neglect to associative judgment strategies that fail to adequately represent the set structure of the problem. Base-rate neglect is reduced when problems are presented in a format that affords accurate representation in terms of nested sets of individuals. (shrink)

In our view, a central issue in relating brain development to education is whether classroom interventions can alter neural networks related to cognition in ways that generalize beyond the specific domain of instruction. This issue depends upon understanding how neural networks develop under the influence of genes and experience. Imaging studies have revealed common networks underlying many important tasks undertaken at school, such as reading and number skills, and we are beginning to learn how genes and experience work together to (...) shape the development of these networks. The results obtained appear sufficient to propose research-based interventions that could prove useful in improving the ability of children to adjust to the school setting and to acquire skills like literacy and numeracy. (shrink)

Contemporary psychological research that studies how people apply mathematics has largely viewed mathematics as a computational tool for deriving an answer. The tacit assumption has been that people first understand a situation, and then choose which computations to apply. We examine an alternative assumption that mathematics can also serve as a tool that helps one to construct an understanding of a situation in the first place. Three studies were conducted with 6th‐grade children in the context of proportional situations because early (...) proportional reasoning is a premier example of where mathematics may provide new understanding of the world. The children predicted whether two differently‐sized glasses of orange juice would taste the same when they were filled from a single carton of juice made from concentrate and water. To examine the relative contributions and interactions of situational and mathematical knowledge, we manipulated the formal features of the problem display (e.g., diagram vs. photograph) and the numerical complexity (e.g., divisibility) of the containers and the ingredient ratios. When the problem was presented as a diagram with complex numbers, or “realistically” with easy numbers, the children predicted the glasses would taste different because one glass had more juice than the other. But, when the problem was presented realistically with complex numbers, the children predicted the glasses would taste the same on the basis of empirical knowledge (e.g., “Juice can't change by itself”). And finally, when the problem was presented as a diagram with easy numbers, the children predicted the glasses would taste the same on the basis of proportional relations. These complex interactions illuminate how mathematical and empirical knowledge can jointly constrain the construction of a new understanding of the world. We propose that mathematics helped in the case of successful proportional reasoning because it made a complex empirical situation cognitively tractable, and thereby helped the children construct mental models of that situation. We sketch one aspect of the mental models that are constructed in the domain of quantity—a preference for specificity—that helps explain the current findings. (shrink)

Can the general public learn to deal with risk and uncertainty, or do authorities need to steer people’s choices in the right direction? Libertarian paternalists argue that results from psychological research show that our reasoning is systematically flawed and that we are hardly educable because our cognitive biases resemble stable visual illusions. For that reason, they maintain, authorities who know what is best for us need to step in and steer our behavior with the help of “nudges.” Nudges are nothing (...) new, but justifying them on the basis of a latent irrationality is. In this article, I analyze the scientific evidence presented for such a justification. It suffers from narrow logical norms, that is, a misunderstanding of the nature of rational thinking, and from a confirmation bias, that is, selective reporting of research. These two flaws focus the blame on individuals’ minds rather than on external causes, such as industries that spend billions to nudge people into unhealthy behavior. I conclude that the claim that we are hardly educable lacks evidence and forecloses the true alternative to nudging: teaching people to become risk savvy. (shrink)

The terms nested sets, partitive frequencies, inside-outside view, and dual processes add little but confusion to our original analysis (Gigerenzer & Hoffrage 1995; 1999). The idea of nested set was introduced because of an oversight; it simply rephrases two of our equations. Representation in terms of chances, in contrast, is a novel contribution yet consistent with our computational analysis System 1.dual process theory” is: Unless the two processes are defined, this distinction can account post hoc for almost everything. In contrast, (...) an ecological view of cognition helps to explain how insight is elicited from the outside (the external representation of information) and, more generally, how cognitive strategies match with environmental structures. (shrink)

Previous research suggests that children can infer causal relations from patterns of events. However, what appear to be cases of causal inference may simply reduce to children recognizing relevant associations among events, and responding based on those associations. To examine this claim, in Experiments 1 and 2, children were introduced to a “blicket detector,” a machine that lit up and played music when certain objects were placed upon it. Children observed patterns of contingency between objects and the machine's activation that (...) required them to use indirect evidence to make causal inferences. Critically, associative models either made no predictions, or made incorrect predictions about these inferences. In general, children were able to make these inferences, but some developmental differences between 3- and 4-year-olds were found. We suggest that children's causal inferences are not based on recognizing associations, but rather that children develop a mechanism for Bayesian structure learning. Experiment 3 explicitly tests a prediction of this account. Children were asked to make an inference about ambiguous data based on the base rate of certain events occurring. Four-year-olds, but not 3-year-olds were able to make this inference. (shrink)

It is easy to construct pairs of sentences X, Y that lead many people to ascribe higher probability to the conjunction X-and-Y than to the conjuncts X, Y. Whether an error is thereby committed depends on reasoners’ interpretation of the expressions “probability” and “and.” We report two experiments designed to clarify the normative status of typical responses to conjunction problems. © 2004 Cognitive Science Society, Inc. All rights reserved.

Inductive reasoning requires exploiting links between evidence and hypotheses. This can be done focusing either on the posterior probability of the hypothesis when updated on the new evidence or on the impact of the new evidence on the credibility of the hypothesis. But are these two cognitive representations equally reliable? This study investigates this question by comparing probability and impact judgments on the same experimental materials. The results indicate that impact judgments are more consistent in time and more accurate than (...) probability judgments. Impact judgments also predict the direction of errors in probability judgments. These findings suggest that human inductive reasoning relies more on estimating evidential impact than on posterior probability. (shrink)