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)

According to the weak version of linguistic relativity, also called the Sapir-Whorf hypothesis, the features of an individual’s native language influence his worldview and perception. We decided to test this hypothesis on the sufficient conditional and the necessary conditional, expressed differently in Chinese and French. In Chinese, connectors for both conditionals exist and are used in everyday life, while there is only a connector for the sufficient conditional in French. A first hypothesis follows from linguistic relativity: for the necessary conditional, (...) better logic performance is expected in Chinese participants rather than French participants. As a second hypothesis, for all participants, we expect performance on the sufficient conditional to be better than on the necessary conditional. Indeed, despite the isomorphism of the two conditionals, they differ in how information is processed for reasoning. We decided to study reasoning under uncertainty as it reflects reality more accurately. To do so, we analyzed the coherence of participants using de Finetti’s theory for deduction under uncertainty. The results of our study show no significant difference in performance between Chinese and French participants, neither on the sufficient conditional nor on the necessary conditional. Thus, our first hypothesis derived from the weak version of linguistic relativity is not confirmed. In contrast, our results confirm the second hypothesis in two out of three inference schemas. (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)

ABSTRACTThe new paradigm in the psychology of reasoning redirects the investigation of deduction conceptually and methodologically because the premises and the conclusion of the inferences are assumed to be uncertain. A probabilistic counterpart of the concept of logical validity and a method to assess whether individuals comply with it must be defined. Conceptually, we used de Finetti's coherence as a normative framework to assess individuals' performance. Methodologically, we presented inference schemas whose premises had various levels of probability that contained non-numerical (...) expressions and, as a control, sure levels. Depending on the inference schemas, from 60% to 80% of the participants produced coherent conclusions when the premises were uncertain. The data also show that except for schemas involving conjunction, performance was consistently lower with certain than uncertain premises, the rate of conjunction fallacy was consistently low (not exceeding 20%,.. (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)

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)

The Bayesian model is used in psychology as the reference for the study of dynamic probability judgment. The main limit induced by this model is that it confines the study of revision of degrees of belief to the sole situations of revision in which the universe is static (revising situations). However, it may happen that individuals have to revise their degrees of belief when the message they learn specifies a change of direction in the universe, which is considered as changing (...) with time (updating situations). We analyze the main results of the experimental literature with regard to elementary qualitative properties of these two situations of revision. First, the order effect phenomenon is confronted with the commutative property. Second, an apparent new phenomenon is presented: the redundancy effect that is confronted with the idempotence property. Finally, results obtained in this kind of experimental situations are reinterpreted in the light of pragmatic analysis. (shrink)

A conceptual and mathematical model of a social community behavior in a choice situation under a veil of ignorance, where two alternative policies—Rawlsian maximin and Harsanyian utilitarianism—can be implemented through the aggregation of individual preferences over these two policies, is constructed and investigated. We first incorporate in our conceptual model psychological features such as risk-aversion and prosocial preferences that likely underlie choices of welfare policies. We secondly develop and select the mathematical model presented it by means of an autonomous system (...) of ordinary differential equations. A qualitative analysis of this system global phase-plane behavior shows possible tendencies of community development under social choices over Rawlsian or utilitarian societies depending on psychological parameters such as risk aversion and prosocial preferences. (shrink)

The Bayesian model has been used in psychology as the standard reference for the study of probability revision. In the first part of this paper we show that this traditional choice restricts the scope of the experimental investigation of revision to a stable universe. This is the case of a situation that, technically, is known as focusing. We argue that it is essential for a better understanding of human probability revision to consider another situation called updating (Katsuno & Mendelzon, 1992), (...) in which the universe is evolving. In that case the structure of the universe has definitely been transformed and the revision message conveys information on the resulting universe. The second part of the paper presents four experiments based on the Monty Hall puzzle that aim to show that updating is a natural frame for individuals to revise their beliefs. (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 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)

There is a new Bayesian, or probabilistic, paradigm in the psychology of reasoning, with new psychological accounts of the indicative conditional of natural language. In psychological experiments in this new paradigm, people judge that the probability of the indicative conditional, P(if A then C), is the conditional probability of C given A, P(C | A). In other experiments, participants respond with what has been called the 'de- fective' truth table: they judge that if A then C is true when A (...) holds and C holds, is false when A holds and C does not, and is neither true nor false when A does not hold. We argue that these responses are not 'defective' in any negative sense, as many psychologists have implied. We point out that a number of normative researchers, including de Finetti, have proposed such a table for various coherent interpretations of the third value. We review the relevant general tables in the normative literature, in which there is a third value for A and C and the logically compound forms of the natural language conditional, negation, conjunction, disjunction, and the material conditional. We describe the results of an experiment on which of these tables best describes ordinary people's judgements when the third value is interpreted as indicating uncertainty. (shrink)