Updating: A Psychologically Basic Situation of Probability Revision

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

Is the mind Bayesian? The case for agnosticism

This paper aims to make explicit the methodological conditions that should be satisfied for the Bayesian model to be used as a normative model of human probability judgment. After noticing the lack of a clear definition of Bayesianism in the psychological literature and the lack of justification for using it, a classic definition of subjective Bayesianism is recalled, based on the following three criteria: An epistemic criterion, a static coherence criterion and a dynamic coherence criterion. Then it is shown that the adoption of this framework has two kinds of implications. The first one regards the methodology of the experimental study of probability judgment. The Bayesian framework creates pragmatic constraints on the methodology that are linked to the interpretation of, and the belief in, the information presented, or referred to, by an experimenter in order for it to be the basis of a probability judgment by individual participants. It is shown that these constraints have not been satisfied in the past, and the question of whether they can be satisfied in principle is raised and answered negatively. The second kind of implications consists of two limitations in the scope of the Bayesian model. They regard (i) the background of revision (the Bayesian model considers only revising situations but not updating situations), and (ii) the notorious case of the null priors. In both cases Lewis' rule is an appropriate alternative to Bayes' rule, but its use faces the same operational difficulties

Not only base rates are neglected in the Engineer-Lawyer problem: An investigation of reasoners' underutilization of complementarity

The standard Engineer-Lawyer problem (Kahneman & Tversky, 1973) points to reasoners' failure to integrate mentioned base rate information as they arrive at likelihood estimates. Research in this area nevertheless presupposes that reasoners respect complementarity (i.e., participants ensure that competing estimates add up to 100%). A survey of the literature lends doubt to this presupposition. We propose that participants' non-normative performance on the standard problem reflects a reluctance to view the task probabilistically and that normative responses become more prominent as probabilistic aspects of the task do. Three Experiments manipulated two kinds of probabilistic cues and determined the extent to which a) base rates were integrated and b) the complementarity constraint was respected. Experiment 1 presented six versions of an Engineer-Lawyer-type problem (that varied 3 Levels of cue-to-complementarity and 2 base rates). Results showed that base-rate integration increased as cues-to-complementarity did. Experiment 2 confirmed that Gigerenzer, Hell & Blank's (1988) random draw paradigm facilitates base rate integration; a second measure revealed that it also prompts respect for complementarity. Experiment 3 replicated two of our main findings in one procedure while controlling for the potential influence of extraneous task features. Approaches that describe how probabilistic cues might prompt normative responding are discussed

New Psychological Paradigm for Conditionals and General de Finetti Tables

International audienceThe new Bayesian paradigm in the psychology of reasoning aims to integrate the study of human reasoning, decision making, and rationality. It is supported by two findings. One, most people judge the probability of the indicative conditional, P(if A then B), to be the conditional probability, P(B|A), as implied by the Ramsey test. Two, they judge if A then B to be void when A is false. Their three-valued response table used to be called 'defective', but should be termed the de Finetti table. We show how to study general de Finetti truth tables for negations, conjunctions, disjunctions, and conditionals

The psychology of indicative conditionals and conditional bets

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

Cooperation in Online Conversations: The Response Times as a Window Into the Cognition of Language Processing

Measuring the cognitive cost of interpreting the meaning of sentences in a conversation is a complex task, but it is also at the core of Sperber and Wilson's Relevance Theory. In cognitive sciences, the delay between a stimulus and its response is often used as an approximation of the cognitive cost. We have noticed that such a tool had not yet been used to measure the cognitive cost of interpreting the meaning of sentences in a free-flowing and interactive conversation. The following experiment tests the ability to discriminate between sentences with a high cognitive cost and sentences with a low cognitive cost using the response time of the participants during an online conversation in a protocol inspired by the Turing Test. We have used violations of Grice's Cooperative Principle to create conditions in which sentences with a high cognitive cost would be produced. We hypothesized that response times are directly correlated to the cognitive cost required to generate implicatures from a statement. Our results are coherent with the literature in the field and shed some new light on the effect of violations on the humanness of a conversational agent. We show that violations of the maxim of Relation had a particularly important impact on response times and the perceived humanness of a conversation partner. Violations of the first maxim of Quantity and the fourth maxim of Manner had a lesser impact, and only on male participants

Coherence, not conditional meaning, accounts for the relevance effect

Missing-link conditionals like “If bats have wings, Paris is in France” are generally felt to be unacceptable even though both clauses are true. According to the Hypothetical Inferential Theory, this is explained by a conventional requirement of an inferential connection between conditional clauses. Bayesian theorists have denied the need for such a requirement, appealing instead to a requirement of discourse coherence that extends to all ways of connecting clauses. Our experiment compared conditionals (“If A, C”), conjunctions (“A and C”), and bare juxtapositions (“A. C.”). With one systematic exception that is predicted by prior work in coherence theory, the presence or absence of an inferential link affected conditionals and other statement types in the same way. This is as expected according to the Bayesian approach together with a general theory of discourse coherence

Betting on conditionals

A study is reported testing two hypotheses about a close parallel relation between indicative conditionals, if A then B, and conditional bets, I bet you that if A then B. The first is that both the indicative conditional and the conditional bet are related to the conditional probability, P(B|A). The second is that de Finetti's three-valued truth table has psychological reality for both types of conditional – true, false, or void for indicative conditionals and win, lose or void for conditional bets. The participants were presented with an array of chips in two different colours and two different shapes, and an indicative conditional or a conditional bet about a random chip. They had to make judgments in two conditions: either about the chances of making the indicative conditional true or false or about the chances of winning or losing the conditional bet. The observed distributions of responses in the two conditions were generally related to the conditional probability, supporting the first hypothesis. In addition, a majority of participants in further conditions chose the third option, “void”, when the antecedent of the conditional was false, supporting the second hypothesis