Vittorio Girotto

Relevance theory explains the selection task

We propose a general and predictive explanation of the Wason Selection Task (where subjects are asked to select evidence for testing a conditional rule). Our explanation is based on a reanalysis of the task, and on Relevance Theory. We argue that subjects selections in all true versions of the Selection Task result from the following procedure. Subjects infer from the rule directly testable consequences. They infer them in their order of accessibility, and stop when the resulting interpretation of the rule meets their expectations of relevance. Subjects then select the cards that may test the consequences they have inferred from the rule. Order of accessibility of consequences and expectations of relevance vary with rule and context, and so, therefore, does subjects performance. By devising appropriate rule-context pairs, we predict that correct performance can be elicited in any conceptual domain. We corroborate this prediction with four experiments. We argue that past results properly reanalyzed confirm our account. We discuss the relevance of the Selection Task to the study of reasoning.

Solving probabilistic and statistical problems: a matter of information structure and question form

Is the human mind inherently unable to reason probabilistically, or is it able to do so only when problems tap into a module for reasoning about natural frequencies? We suggest an alternative possibility: naive individuals are able to reason probabilistically when they can rely on a representation of subsets of chances or frequencies. We predicted that naive individuals solve conditional probability problems if they can infer conditional probabilities from the subset relations in their representation of the problems, and if the question put to them makes it easy to consider the appropriate subsets. The results of seven studies corroborated these predictions: when the form of the question and the structure of the problem were framed so as to activate intuitive principles based on subset relations, naive individuals solved problems, whether they were stated in terms of probabilities or frequencies. Otherwise, they failed with both sorts of information. The results contravene the frequentist hypothesis and the evolutionary account of probabilistic reasoning.

The effect of premise order in conditional reasoning: A test of the mental model theory

The difference in difficulty between modus ponens (if p then q; p; therefore q) and modus tollens (if p then q; not-q; therefore not-p) arguments has been traditionally explained by assuming that the mind contains a rule for modus ponens, but not for modus tollens. According to the mental model theory, modus tollens is a more difficult deduction than modus ponens because people do not represent the case not-q in their initial model of the conditional. On the basis of this theory, we predicted that conditions in which reasoners are forced to represent the not-q case should improve correct performance on modus tollens. In particular, we predicted that the presentation of the minor premise (not-q) as the initial premise should produce facilitation. Experiment 1 showed that this is the case: whereas the inversion of the premise order did not affect modus ponens, it produced a significant increase of valid conclusions for modus tollens. Experiment 2 showed that this facilitation does not depend on the negative form (contrary vs. contradictory) of the minor premise. Experiments 3 and 4 (and/or some of their replications) demonstrated that facilitation also occurs when participants are asked to find the cases compatible with not-q or to evaluate a p conclusion. No premise order effect was found for sentences which make explicit the not-q case right from the start, i.e. p only if q conditionals and biconditionals (Experiments 5 and 6). Finally, Experiments 7 and 8 showed that the conditional fallacies are not significantly affected by the premise order.

Children's understanding of posterior probability

Do young children have a basic intuition of posterior probability? Do they update their decisions and judgments in the light of new evidence? We hypothesized that they can do so extensionally, by considering and counting the various ways in which an event may or may not occur. The results reported in this paper showed that from the age of five, childrens decisions under uncertainty (Study 1) and judgments about random outcomes (Study 2) are correctly affected by posterior information. From the same age, children correctly revise their decisions in situations in which they face a single, uncertain event, produced by an intentional agent (Study 3). The finding that young children have some understanding of posterior probability supports the theory of naive extensional reasoning, and contravenes some pessimistic views of probabilistic reasoning, in particular the evolutionary claim that the human mind cannot deal with single-case probability.

Inept reasoners or pragmatic virtuosos? Relevance and the deontic selection task

Most individuals fail the selection task, selecting P and Q cases, when they have to test descriptive rules of the form If P, then Q. But they solve it, selecting P and not-Q cases, when they have to test deontic rules of the form If P, then must Q. According to relevance theory, linguistic comprehension processes determine intuitions of relevance that, in turn, determine case selections in both descriptive and deontic problems. We tested the relevance theory predictions in a within-participants experiment. The results showed that the same rule, regardless of whether it is tested descriptively or deontically, can be made to yield more P and Q selections or more P and not-Q selections. We conclude that the selection task does not provide a tool to test general claims about human reasoning.

Use or misuse of the selection task? Rejoinder to Fiddick, Cosmides, and Tooby.

Sperber, Cara, and Girotto (Cognition 52 (1995) 3) argued that, in Wasons selection task, relevance-guided comprehension processes tend to determine participants performance and pre-empt the use of other inferential capacities. Because of this, the value of the selection task as a tool for studying human inference has been grossly overestimated. Fiddick, Cosmides, and Tooby (Cognition 77 (2000) 1) argued against Sperber et al. that specialized inferential mechanisms, in particular the social contract algorithm hypothesized by Cosmides (Cognition 31 (1989) 187), pre-empt more general comprehension abilities, making the selection task a useful tool after all. We rebut this argument. We argue and illustrate with two new experiments, that Fiddick et al. mix the true Wason selection task with a trivially simple categorization task superficially similar to the Wason task, yielding methodologically flawed evidence. We conclude that the extensive use of various kinds of selection tasks in the psychology of reasoning has been quite counter-productive and should be discontinued.

Chances and frequencies in probabilistic reasoning: rejoinder to Hoffrage, Gigerenzer, Krauss, and Martignon

Do individuals unfamiliar with probability and statistics need a specific type of data in order to draw correct inferences about uncertain events? Girotto and Gonzalez (Cognition 78 (2001) 247) showed that naive individuals solve frequency as well as probability problems, when they reason extensionally, in particular when probabilities are represented by numbers of chances. Hoffrage, Gigerenzer, Krauss, and Martignon (Cognition 84 (2002) 343) argued that numbers of chances are natural frequencies disguised as probabilities, though lacking the properties of true probabilities. They concluded that we failed to demonstrate that naive individuals can deal with true probabilities as opposed to natural frequencies. In this paper, we demonstrate that numbers of chances do represent probabilities, and that naive individuals do not confuse numbers of chances with frequencies. We conclude that there is no evidence for the claim that natural frequencies have a special cognitive status, and the evolutionary argument that the human mind is unable to deal with probabilities.

Judgements of deontic relevance in reasoning: A reply to Jackson and Griggs

Facilitation on abstract versions of the selection task can be produced by deontic content. Jackson and Griggs (1990) claimed that this finding depends on the presence of an explicit negative on the not-q card. We hypothesized that the removal of the explicit negative from this card made its deontic status ambiguous. Experiment 1 demonstrated that a not-q card presenting implicit negative is not selected, and most subjects select the only card that appears to be relevant from a deontic point of view (i.e. the p card). Experiments 2 and 3 showed that the presence of the explicit negative on the not-q card is not necessary for producing facilitation, provided that the form of this card makes it clear that the not-q individual is a potential violator. Experiment 4 showed that a high success rate can be obtained even with a not-q card presenting an implicit negative. The results are discussed in terms of the specificity of reasoning in the deontic domain.

How We Detect Logical Inconsistencies

How do individuals detect inconsistencies? According to the theory described in this article, they search for a possibility represented in a mental model, in which each proposition in a description is true. If they find such a possibility, the description is consistent; otherwise, it is inconsistent. Evidence corroborates the theory. The evaluation of consistency is easy when the first possibility generated from the start of a description fits later propositions in the description; it is harder when this possibility does not fit later propositions, and individuals have to look for an alternative possibility. The theory postulates that models represent what is true, not what is false. As a result, individuals succumb to systematic illusions of consistency and of inconsistency.

Hypothesis testing in a rule discovery problem: when a focused procedure is effective.

We investigated individuals’ ability to use negative evidence in hypothesis testing. We compared performance in two versions of Wasons (1960) rule discovery problem. In the original version, a triple of numbers- {2, 4, 6}- was presented as an example of a rule that the experimenter had in mind (i.e., “increasing numbers”). Participants had to discover the rule by proposing new triples. In the other version, the same triple was presented as a counterexample to the experimenters rule (i.e., “decreasing numbers”). We predicted that, in both conditions, participants would form hypotheses based on the features of the triple, and test only instances of the hypothesized rule. However, in the counter-example condition, such focused testing would invariably produce negative evidence. As a consequence, participants would be forced to revise their hypotheses. The reported results corroborated our predictions: Participants solved the counter-example version significantly better than the original problem.