The pigeonhole principle is a well-known mathematical principle and is quite simple to understand. It goes as follows: If n items are placed into m containers, and if m (...) an identifier (nominal). They suggest quantities first need to be turned into categories. We believe this difference can instead be explained by pragmatic factors not taken into account in their study. We disambiguate the problems given to participants and study the effects of their disambiguation and the influence of different kinds of quantities: countable and mass. We show that using a problem with countable quantities instead of hair, usually understood as non-countable, increase the performance of participants, no longer distinguishable from that of the nominal problem. (shrink)

The Monty Hall Dilemma (MHD) is a two-step decision problem involving counterintuitive conditional probabilities. The first choice is made among three equally probable options, whereas the second choice takes place after the elimination of one of the non-selected options which does not hide the prize. Differing from most Bayesian problems, statistical information in the MHD has to be inferred, either by learning outcome probabilities or by reasoning from the presented sequence of events. This often leads to suboptimal decisions and erroneous (...) probability judgments. Specifically, decision makers commonly develop a wrong intuition that final probabilities are equally distributed, together with a preference for their first choice. Several studies have shown that repeated practice enhances sensitivity to the different reward probabilities, but does not facilitate correct Bayesian reasoning. However, modest improvements in probability judgments have been observed after guided explanations. To explain these dissociations, the present review focuses on two types of causes producing the observed biases: Emotional-based choice biases and cognitive limitations in understanding probabilistic information. Among the latter, we identify a crucial cause for the universal difficulty in overcoming the equiprobability illusion: Incomplete representation of prior and conditional probabilities. We conclude that repeated practice and/or high incentives can be effective for overcoming choice biases, but promoting an adequate partitioning of possibilities seems to be necessary for overcoming cognitive illusions and improving Bayesian reasoning. (shrink)

We explore which types of probabilistic updating commute with convex IP pooling. Positive results are stated for Bayesian conditionalization, imaging, and a certain parameterization of Jeffrey conditioning. This last observation is obtained with the help of a slight generalization of a characterization of externally Bayesian pooling operators due to Wagner :336–345, 2009). These results strengthen the case that pooling should go by imprecise probabilities since no precise pooling method is as versatile.

The Monty Hall dilemma is a notorious probability problem with a counterintuitive solution. There is a strong tendency to stay with the initial choice, despite the fact that switching doubles the probability of winning. The current randomised experiment investigates whether feedback in a series of trials improves behavioural performance on the MHD and increases the level of understanding of the problem. Feedback was either conditional or non-conditional, and was given either in frequency format or in percentage format. Results show that (...) people learn to switch most when receiving conditional feedback in frequency format. However, problem understanding does not improve as a consequence of receiving feedback. Our study confirms the dissociation between behavioural performance on the MHD, on one hand, and actual understanding of the MHD, on the other. We discuss how this dissociation can be understood. (shrink)

The rational status of the Bayesian calculus for revising likelihoods is compromised by the common but still unfamiliar phenomenon of information distortion. This bias is the distortion in the evaluation of a new datum toward favoring the currently preferred option in a decision or judgment. While the Bayesian calculus requires the independent combination of the prior probability and a new datum, information distortion invalidates such independence (because the prior influences the datum). Although widespread, information distortion has not generally been recognized. (...) First, individuals are not aware when they themselves commit this bias. In addition, it is often hidden in more obvious suboptimal phenomena. Finally, the Bayesian calculus is usually explained only with undistortable data like colored balls drawn randomly. Partly because information distortion is unrecognized by the individuals exhibiting it, no way has been devised for eliminating it. Partial reduction is possible in some situation such as presenting all data simultaneously rather than sequentially with revision after each datum. The potential dangers of information distortion are illustrated for three professional revision tasks: forecasting, predicting consumer choices from internet data, and statistical inference from experimental results. The optimality of the Bayesian calculus competes with people’s natural desire that their belief systems remain coherent in the face of new data. Information distortion provides this coherence by biasing those data toward greater agreement with the currently preferred position – but at the cost of Bayesian optimality. (shrink)

An experiment was conducted to test the effectiveness of brief instruction in information structuring (i.e., representing and integrating information) for improving the coherence of probability judgments and binary choices among intelligence analysts. Forty-three analysts were presented with comparable sets of Bayesian judgment problems before and immediately after instruction. After instruction, analysts’ probability judgments were more coherent (i.e., more additive and compliant with Bayes theorem). Instruction also improved the coherence of binary choices regarding category membership: after instruction, subjects were more likely (...) to invariably choose the category to which they assigned the higher probability of a target’s membership. The research provides a rare example of evidence-based validation of effectiveness in instruction to improve the statistical assessment skills of intelligence analysts. Such instruction could also be used to improve the assessment quality of other types of experts who are required to integrate statistical information or make probabilistic assessments. (shrink)

A diagnostic judgment of a teacher can be seen as an inference from manifest observable evidence on a student’s behavior to his or her latent traits. This can be described by a Bayesian model of in-ference: The teacher starts from a set of assumptions on the student (hypotheses), with subjective probabilities for each hypothesis (priors). Subsequently, he or she uses observed evidence (stu-dents’ responses to tasks) and knowledge on conditional probabilities of this evidence (likelihoods) to revise these assumptions. Many systematic (...) deviations from this model (biases, e.g. base-rate neglect, inverse fallacy) are reported in literature on Bayesian reasoning. In a teacher’s situation the information (hypotheses, priors, likelihoods) is usually not explicitly represented numerically (as in most research on Bayesian reasoning), but only by qualitative esti-mations in the mind of the teacher. In our study, we ask to which extent individuals (approximately) apply a rational Bayesian strategy or resort on other biased strategies of processing information for their diagnostic judgments. We explicitly pose this question with respect to non-numerical settings. To investigate this question, we developed a scenario that visually displays all relevant information (hypotheses, priors, likelihoods) in a graphically displayed hypothesis space (called “hypothegon”) – without recurring to numerical representations or mathematical procedures. 42 pre-service teach-ers were asked to judge the plausibility of different misconceptions of six students based on their responses to decimal comparison tasks (e.g. 3.39 > 3.4). Applying a Bayesian classification proce-dure, we identified three updating strategies: A Bayesian update strategy (BUS, processing all probabilities), a combined evidence strategy (CES, ignoring the prior probabilities but including all likelihoods), and a single evidence strategy (SES, only using the likelihood of the most probable hypothesis). In study 1, an instruction on the relevance of using all probabilities (priors and likelihoods) only weakly increased the processing of more information. In study 2, we found strong evidence that a visual explication of the prior-likelihood interaction led to an increase of processing the interaction of all relevant information. These results show that the phenomena found in general research on Bayesian reasoning in numerical settings extend to diagnostic judgments in non-numerical settings. (shrink)

It is well known that aggregating the degree-of-belief functions of different subjects by linear pooling or averaging is subject to a commutativity dilemma: other than in trivial cases, conditionalizing the individual degree-of-belief functions on a piece of evidence E followed by linearly aggregating them does not yield the same result as rst aggregating them linearly and then conditionalizing the resulting social degree- of-belief function on E. In the present paper we suggest a novel way out of this dilemma: adapting the (...) method of update or learning such that linear pooling com- mutes with it. As it turns out, the resulting update scheme – imaging on the evidence – is well-known from areas such as the study of conditionals and cau- sal decision theory, and a formal result from which the required commutativity property is derivable was supplied already by Gärdenfors in a different con- text. We end up determining under which conditions imaging would seem to be right method of update, and under which conditions, therefore, group update would not be affected by the commutativity dilemma. (shrink)

It is well known that aggregating the degree-of-belief functions of different subjects by linear pooling or averaging is subject to a commutativity dilemma: other than in trivial cases, conditionalizing the individual degree-of-belief functions on a piece of evidence E followed by linearly aggregating them does not yield the same result as rst aggregating them linearly and then conditionalizing the resulting social degree- of-belief function on E. In the present paper we suggest a novel way out of this dilemma: adapting the (...) method of update or learning such that linear pooling com- mutes with it. As it turns out, the resulting update scheme – imaging on the evidence – is well-known from areas such as the study of conditionals and cau- sal decision theory, and a formal result from which the required commutativity property is derivable was supplied already by Gärdenfors in a different con- text. We end up determining under which conditions imaging would seem to be right method of update, and under which conditions, therefore, group update would not be affected by the commutativity dilemma. (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)

Studies of categorical induction typically examine how belief in a premise (e.g., Falcons have an ulnar artery) projects on to a conclusion (e.g., Robins have an ulnar artery). We study induction in cases in which the premise is uncertain (e.g., There is an 80% chance that falcons have an ulnar artery). Jeffrey's rule is a normative model for updating beliefs in the face of uncertain evidence. In three studies we tested the descriptive validity of Jeffrey's rule and a related probability (...) theorem, the rule of total probability. Although these rules provided good approximations to mean judgments in some cases, the results from regression and correlation analyses suggest that participants focus on the parts of these rules that are associated with the highest overall probability. We relate our findings to rational models of judgment. (shrink)

There has been a probabilistic turn in contemporary cognitive science. Far and away, most of the work in this vein is Bayesian, at least in name. Coinciding with this development, philosophers have increasingly promoted Bayesianism as the best normative account of how humans ought to reason. In this paper, we make a push for exploring the probabilistic terrain outside of Bayesianism. Non-Bayesian, but still probabilistic, theories provide plausible competitors both to descriptive and normative Bayesian accounts. We argue for this general (...) idea via recent work on explanationist models of updating, which are fundamentally probabilistic but assign a substantial, non-Bayesian role to explanatory considerations. (shrink)

Knauff and Gazzo Castañeda (2022) criticise the use of the term “new paradigm” in the psychology of reasoning and raise important issues about how to advance research in the field. In this commentary I argue that for the latter it would be helpful to clarify further the concepts that reasoning theories rely on, and to strengthen the links between the theories and the empirical observations that would and would not be compatible with them.

Causal reasoning is one of our most central cognitive competencies, enabling us to adapt to our world. Causal knowledge allows us to predict future events, or diagnose the causes of observed facts. We plan actions and solve problems using knowledge about cause-effect relations. Without our ability to discover and empirically test causal theories, we would not have made progress in various empirical sciences. In the past decades, the important role of causal knowledge has been discovered in many areas of cognitive (...) psychology. Despite the ubiquity of causal reasoning, textbooks of cognitive psychology have neglected this growing field. The goal of The Oxford Handbook of Causal Reasoning is to fill this gap. The handbook brings together the leading researchers in the field of causal reasoning and offers state-of-the-art presentations of theories and research. It provides introductions of competing theories of causal reasoning, and discusses its role in various cognitive functions and domains. The final section presents research from neighboring fields. 1. Causal Reasoning: An Introduction Michael R. Waldmann Part I: Theories of Causal Cognition 2. Associative Accounts of Causal Cognition Mike E. Le Pelley, Oren Griffiths, and Tom Beesley 3. Rules of Causal Judgment: Mapping Statistical Information Onto Causal Beliefs José C. Perales, Andrés Catena, Antonio Cándido, and Antonio Maldonado 4. The Inferential Reasoning Theory of Causal Learning: Toward a Multi- Process Propositional Account Yannick Boddez, Jan De Houwer, and Tom Beckers 5. Causal Invariance as an Essential Constraint for Creating a Causal Representation of the World: Generalizing the Invariance of Causal Power Patricia W. Cheng and Hongjing Lu 6. The Acquisition and Use of Causal Structure Knowledge Benjamin Margolin Rottman 7. Formalizing Prior Knowledge in Causal Induction Thomas L. Griffiths 8. Causal Mechanisms Samuel G. B. Johnson and Woo-kyoung Ahn 9. Force Dynamics and Causation Phillip Wolff and Robert Thorstad 10. Mental Models and Causation P. N. Johnson- Laird and Sangeet S. Khemlani 11. Pseudocontingencies Klaus Fiedler and Florian Kutzner 12. Singular Causation David Danks 13. Cognitive Neuroscience of Causal Reasoning Joachim T. Operskalski and Aron K. Barbey Part II: Basic Cognitive Functions 14. Visual Impressions of Causality Peter White 15. Goal-Directed Actions Bernhard Hommel 16. Planning and Control Magda Osman 17. Reinforcement Learning and Causal Models Samuel J. Gershman 18. Causation and the Probability of Causal Conditionals David E. Over 19. Causal Models and Conditional Reasoning Mike Oaksford and Nick Chater 20. Concepts as Causal Models: Categorization Bob Rehder 21. Concepts as Causal Models: Induction Bob Rehder 22. Causal Explanation Tania Lombrozo and Nadya Vasilyeva 23. Diagnostic Reasoning Björn Meder and Ralf Mayrhofer 24. Inferring Causal Relations by Analogy Keith J. Holyoak and Hee-Seung Lee 25. Causal Argument Ulrike Hahn, Roland Bluhm, and Frank Zenker 26. Causality in Decision- Making York Hagmayer and Philip M. Fernbach Part III: Domains of Causal Reasoning 27. Intuitive Theories Tobias Gerstenberg and Joshua B. Tenenbaum 28. Space, Time, and Causality Marc J. Buehner 29. Causation in Legal and Moral Reasoning David A. Lagnado and Tobias Gerstenberg 30. The Role of Causal Knowledge in Reasoning About Mental Disorders Woo-kyoung Ahn, Nancy S. Kim, and Matthew S. Lebowitz 31. Causality and Causal Reasoning in Natural Language Torgrim Solstad and Oliver Bott 32. Social Attribution and Explanation Denis Hilton Part IV: Development, Phylogeny, and Culture 33. The Development of Causal Reasoning Paul Muentener and Elizabeth Bonawitz 34. Causal Reasoning in Non-Human Animals Christian Schloegl and Julia Fischer 35. Causal Cognition and Culture Andrea Bender, Sieghard Beller, and Douglas L. Medin. (shrink)

Psychological research on people’s understanding of natural language connectives has traditionally used truth table tasks, in which participants evaluate the truth or falsity of a compound sentence given the truth or falsity of its components in the framework of propositional logic. One perplexing result concerned the indicative conditional if A then C which was often evaluated as true when A and C are true, false when A is true and C is false but irrelevant“ (devoid of value) when A is (...) false (whatever the value of C). This was called the “psychological defective table of the conditional.” Here we show that far from being anomalous the “defective” table pattern reveals a coherent semantics for the basic connectives of natural language in a trivalent framework. This was done by establishing participants’ truth tables for negation, conjunction, disjunction, conditional, and biconditional, when they were presented with statements that could be certainly true, certainly false, or neither. We review systems of three-valued tables from logic, linguistics, foundations of quantum mechanics, philosophical logic, and artificial intelligence, to see whether one of these systems adequately describes people’s interpretations of natural language connectives. We find that de Finetti’s (1936/1995) three-valued system is the best approximation to participants’ truth tables. (shrink)

The Monty-Hall Problem ($MHP$) has been used to argue against a subjectivist view of Bayesianism in two ways. First, psychologists have used it to illustrate that people do not revise their degrees of belief in line with experimenters' application of Bayes' rule. Second, philosophers view $MHP$ and its two-player extension ($MHP2$) as evidence that probabilities cannot be applied to single cases. Both arguments neglect the Bayesian standpoint, which requires that $MHP2$ (studied here) be described in different terms than usually applied (...) and that the initial set of possibilities be stable (i.e., a focusing situation). This article corrects these errors and reasserts the Bayesian standpoint; namely, that the subjective probability of an event is always conditional on a belief reviser's specific current state of knowledge. (shrink)

The poor performances of typically developing children younger than 4 in the first-order false-belief task “Maxi and the chocolate” is analyzed from the perspective of conversational pragmatics. An ambiguous question asked by an adult experimenter (perceived as a teacher) can receive different interpretations based on a search for relevance, by which children according to their age attribute different intentions to the questioner, within the limits of their own meta-cognitive knowledge. The adult experimenter tells the child the following story of object-transfer: (...) “Maxi puts his chocolate into the green cupboard before going out to play. In his absence, his mother moves the chocolate from the green cupboard to the blue one.” The child must then predict where Maxi will pick up the chocolate when he returns. To the child, the question from an adult (a knowledgeable person) may seem surprising and can be understood as a question of his own knowledge of the world, rather than on Maxi's mental representations. In our study, without any modification of the initial task, we disambiguate the context of the question by (1) replacing the adult experimenter with a humanoid robot presented as “ignorant” and “slow” but trying to learn and (2) placing the child in the role of a “mentor” (the knowledgeable person). Sixty-two typical children of 3 years-old completed the first-order false belief task “Maxi and the chocolate,” either with a human or with a robot. Results revealed a significantly higher success rate in the robot condition than in the human condition. Thus, young children seem to fail because of the pragmatic difficulty of the first-order task, which causes a difference of interpretation between the young child and the experimenter. (shrink)

In this paper, Knetsch's exchange paradigm is analyzed from the perspective of pragmatics and social norms. In this paradigm the participant, at the beginning of the experiment, receives an object from the experimenter and at the end, the same experimenter offers to exchange the received object for an equivalent object. The observed refusal to exchange is called the endowment effect. We argue that this effect comes from an implicature made by the participant about the experimenter's own expectations. The participant perceives (...) the received item as a gift, or as a present, from the experimenter that cannot be exchanged as stipulated by the social norms of western politeness common to both the experimenter and the participant. This implicature, however, should not be produced by participants from Kanak culture for whom the perceived gift of a good will be interpreted as a first act of exchange based on gift and counter-gift. This exchange is a natural, frequent, balanced, and indispensable act for all Kanak social bonds whether private or public. Kanak people also know the French social norms that they apply in their interactions with French people living in New Caledonia. In our experiment, we show that when the exchange paradigm takes place in a French context, with a French experimenter and in French, the Kanak participant is subject to the endowment effect in the same way as a French participant. On the other hand, when the paradigm is carried out in a Kanak context, with a Kanak experimenter and in the vernacular language, or in a Kanak context that approaches the ceremonial of the custom, the endowment effect is no longer observed. The same number of Kanak participants accept or refuse to exchange the endowed item. These results, in addition to providing a new explanation for the endowment effect, highlight the great flexibility of decisions according to social-cultural context. (shrink)

Ranking theory is one of the salient formal representations of doxastic states. It differs from others in being able to represent belief in a proposition (= taking it to be true), to also represent degrees of belief (i.e. beliefs as more or less firm), and thus to generally account for the dynamics of these beliefs. It does so on the basis of fundamental and compelling rationality postulates and is hence one way of explicating the rational structure of doxastic states. Thereby (...) it provides foundations for accounts of defeasible or nonmonotonic reasoning. It has widespread applications in philosophy, it proves to be most useful in Artificial Intelligence, and it has started to find applications as a model of reasoning in psychology. (shrink)

The technique of imaging was first introduced by Lewis, in order to provide a novel account of the probability of conditional propositions. In the intervening years, imaging has been the object of significant interest in both AI and philosophy, and has come to be seen as a philosophically important approach to probabilistic updating and belief revision. In this paper, we consider the possibility of generalising imaging to deal with uncertain evidence and partial belief revision. In particular, we introduce a new (...) logical criterion that any update rule should satisfy, and use it to evaluate a range of different approaches to generalising imaging to situations involving uncertain evidence. We show that none of the currently prevalent approaches to imaging allow for such a generalisation, although a lesser known version of imaging, introduced by Joyce, can be generalised in a way that mitigates these problems. (shrink)