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)

Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian reasoning relative to normalized formats (e.g. probabilities, percentages), both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on “transparent” Bayesian problems varies widely, and generally remains rather unimpressive. (...) We suggest there has been an over-focus on this representational facilitator (i.e. transparent problem structures) at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct versus incorrect reasoners depart, and how individual difference might influence this time point. (shrink)

For more than 20 years, research has proven the beneficial effect of natural frequencies when it comes to solving Bayesian reasoning tasks (Gigerenzer & Hoffrage, 1995). In a recent meta-analysis, McDowell & Jacobs (2017) showed that presenting a task in natural frequency format increases performance rates to 24% compared to only 4% when the same task is presented in probability format. Nevertheless, on average three quarters of participants in their meta-analysis failed to obtain the correct solution for such a task (...) in frequency format. In this paper, we present an empirical study on what participants typically do wrong when confronted with natural frequencies. We found that many of them did not actually use natural frequencies for their calculations, but translated them back into complicated probabilities instead. This switch from the intuitive presentation format to a less intuitive calculation format will be discussed within the framework of psychological theories (e.g., the Einstellung effect). (shrink)

(2013). Evolutionary modules and Bayesian facilitation: The role of general cognitive resources. Thinking & Reasoning: Vol. 19, No. 1, pp. 27-53. doi: 10.1080/13546783.2012.713177.

Our target article identified normativism as the view that rationality should be evaluated against unconditional normative standards. We believe this to be entrenched in the psychological study of reasoning and decision making and argued that it is damaging to this empirical area of study, calling instead for a descriptivist psychology of reasoning and decision making. The views of 29 commentators (from philosophy and cognitive science as well as psychology) were mixed, including some staunch defences of normativism, but also a number (...) that were broadly supportive of our position, although critical of various details. In particular, many defended a position that we call which sees a role for normative evaluation within boundaries alongside more descriptive research goals. In this response, we clarify our use of the term and add discussion of defining both as descriptive and non-normative concepts. We consider the debate with reference to dual-process theory, the psychology of reasoning, and empirical research strategy in these fields. We also discuss cognitive variation by age, intelligence, and culture, and the issue of relative versus absolute definitions of norms. In conclusion, we hope at least to have raised consciousness about the important boundaries between norm and description in the psychology of thinking. (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)

Normative theories can be useful in developing descriptive theories, as when normative subjective expected utility theory is used to develop descriptive rational choice theory and behavioral game theory. “Ought” questions are also the essence of theories of moral reasoning, a domain of higher mental processing that could not survive without normative considerations.

The framework of elementary probabilistic operations (EPO) explains the structure of elementary probabilistic reasoning tasks as well as people’s performance on these tasks. The framework comprises three components: (a) Three types of probabilities: joint, marginal, and conditional probabilities; (b) three elementary probabilistic operations: combination, marginalization, and conditioning, and (c) quantitative inference schemas implementing the EPO. The formal part of the EPO framework is a computational level theory that provides a problem space representation and a classification of elementary probabilistic problems based (...) on computational requirements for solving a problem. According to the EPO framework, current methods for improving probabilistic reasoning are of two kinds: First, reduction of Bayesian problems to a type of probabilistic problems requiring less conceptual and procedural competencies. Second, enhancing people’s utilization competence by fostering the application of quantitative inference schemas. The approach suggests new applications, including the teaching of probabilistic reasoning, using analogical problem solving in probabilistic reasoning, and new methods for analyzing errors in probabilistic problem solving. (shrink)

We agree that current evolutionary accounts of base-rate neglect are unparsimonious, but we dispute the authors' account of the effect in terms of parallel associative and rule-based processes. We also question their assumption that cueing of nested set relations facilitates performance due to recruitment of explicit reasoning processes. In our account, such reasoning is always involved, but usually unsuccessful.

Nisbett et al. claim that East Asians are likely to use holistic thought to solve problems, whereas Westerners use analytic thought more, and discuss the differences in the frame of the individualism/collectivism distinction. The holistic versus analytic distinction has been the greatest point of interest of dual process theories, which imply that human thinking has two sub processes. We apply a revised dual process model that proposes meme-acquired goals in both systems to explain cultural differences in thought. According to this, (...) gene-installed goals are universal across cultures, whereas meme-acquired goals depend upon culture. To introduce a dual process model means that we discuss adaptation both in terms of culture and natural selection. Hence, we propose an interactive view that supports an adaptive relation between mind and culture. (shrink)

Over the last decades, understanding the sources of the difficulty of Bayesian problem solving has been an important research goal, with the effects of numerical format and individual numeracy being widely studied. However, the focus on the comprehension of probability numbers has overshadowed the relational reasoning demand of the Bayesian task. This is particularly the case when the statistical data are verbally described since the requested quantitative relation (posterior ratio) is misaligned with the presented ones (prior and likelihood ratios). In (...) this regard, here I develop the proposal that research on Bayesian reasoning might improve by considering the notational alignment framework of mathematical problem-solving. Specifically, this framework can help to understand the sources of the main difficulties underlying Bayesian inferences based on verbal descriptions. In essence, the present proposal supports the general claim in math education regarding the need to foster relational comprehension to avoid misleading alignments and improve problem solving. (shrink)

In this paper we contrast bounded and ecological rationality with a proposed alternative, generative rationality. Ecological approaches to rationality build on the idea of humans as “intuitive statisticians” while we argue for a more generative conception of humans as “probing organisms.” We first highlight how ecological rationality’s focus on cues and statistics is problematic for two reasons: the problem of cue salience, and the problem of cue uncertainty. We highlight these problems by revisiting the statistical and cue-based logic that underlies (...) ecological rationality, which originate from the misapplication of concepts in psychophysics. We then work through the most popular experimental task in the ecological rationality literature—the city size task—to illustrate how psychophysical assumptions have informally been linked to ecological rationality. After highlighting these problems, we contrast ecological rationality with a proposed alternative, generative rationality. Generative rationality builds on biology—in contrast to ecological rationality’s focus on statistics. We argue that in uncertain environments cues are rarely given or available for statistical processing. Therefore we focus on the psychogenesis of awareness rather than psychophysics of cues. For any agent or organism, environments “teem” with indefinite cues, meanings and potential objects, the salience or relevance of which is scarcely obvious based on their statistical or physical properties. We focus on organism-specificity and the organism-directed probing that shapes awareness and perception. Cues in teeming environments are noticed when they serve as cues-for-something, requiring what might be called a “cue-to-clue” transformation. In this sense, awareness toward a cue or cues is actively “grown.” We thus argue that perception might more productively be seen as the presentation of cues and objects rather than their representation. This generative approach not only applies to relatively mundane organism interactions with their environments—as well as organism-object relationships and their embodied nature—but also has significant implications for understanding the emergence of novelty in economic settings. We conclude with a discussion of how our arguments link with—but modify—Herbert Simon’s popular “scissors” metaphor, as it applies to bounded rationality and its implications for decision making in uncertain, teeming environments. (shrink)

We are neither as pessimistic nor as optimistic as Elqayam & Evans (E&E). The consequences of normativism have not been uniformly disastrous, even among the examples they consider. However, normativism won't be going away any time soon and in the literature on causal Bayes nets new debates about normativism are emerging. Finally, we suggest that to concentrate on expert reasoners as an antidote to normativism may limit the contribution of research on thinking to basic psychological science.

This work examines the influence of reference dependence, including value selection bias and congruence effects, on diagnostic reasoning. Across two studies, we explored how dependence on the initial problem structure influences the ability to solve simplified precursors to the more traditional Bayesian reasoning problems. Analyses evaluated accuracy and types of response errors as a function of congruence between the problem presentation and question of interest, amount of information, need for computation, and individual differences in numerical abilities. Across all problem variations, (...) there was consistent and strong evidence of a value selection bias in that incorrect responses almost always conformed to values that were provided in the problem rather than other errors including those related to computation. The most consistent and unexpected error across all conditions in the first experiment was that people were often more likely to utilize the superordinate value as part of their solution rather than the anticipated reference class values. This resulted in a weakened effect of congruence, with relatively low accuracy even in congruent conditions, and a dominant response error of the superordinate value. Experiment 2 confirmed that the introduction of a new sample drew attention away from the provided reference class, increasing reliance on the overall sample size. This superordinate preference error, along with the benefit of repeating the PPV reference class within the question, demonstrated the importance of reference dependence based on the salience of information within the response prompt. Throughout, higher numerical skills were generally associated with higher accuracy, whether calculations were required or not. (shrink)

Bayesian reasoning, defined here as the updating of a posterior probability following new information, has historically been problematic for humans. Classic psychology experiments have tested human Bayesian reasoning through the use of word problems and have evaluated each participant’s performance against the normatively correct answer provided by Bayes’ theorem. The standard finding is of generally poor performance. Over the past two decades, though, progress has been made on how to improve Bayesian reasoning. Most notably, research has demonstrated that the use (...) of frequencies in a natural sampling framework —as opposed to single-event probabilities—can improve participants’ Bayesian estimates. Furthermore, pictorial aids and certain individual difference factors also can play significant roles in Bayesian reasoning success. The mechanics of how to build tasks which show these improvements is not under much debate. The explanations for why naturally-sampled frequencies and pictures help Bayesian reasoning remain hotly contested, however, with many researchers falling into ingrained “camps” organized around two dominant theoretical perspectives. The present paper evaluates the merits of these theoretical perspectives, including the weight of empirical evidence, theoretical coherence, and predictive power. By these criteria, the ecological rationality approach is clearly better than the heuristics and biases view. Progress in the study of Bayesian reasoning will depend on continued research that honestly, vigorously, and consistently engages across these different theoretical accounts rather than staying “siloed” within one particular perspective. The process of science requires an understanding of competing points of view, with the ultimate goal being integration. (shrink)