The probability of conditionals: A review (original) (raw)
Related papers
The meaning(s) of conditionals: Conditional probabilities, mental models, and personal utilities
Journal of Experimental Psychology: Learning, Memory, and Cognition, 2003
Five experiments were conducted to test the hypothesis that people understand conditional statements ("if p then q") as indicating a high conditional probability P(q͉p). Participants estimated the probability that a given conditional is true (Experiments 1A, 1B, and 3) or judged whether a conditional was true or false (Experiments 2 and 4) given information about the frequencies of the relevant truth table cases. Judgments were strongly influenced by the ratio of pq to p¬q cases, supporting the conditional probability account. In Experiments 1A, 1B, and 3, judgments were also affected by the frequency of pq cases, consistent with a version of mental model theory. Experiments 3 and 4 extended the results to thematic conditionals and showed that the pragmatic utility associated with believing a statement also affected the degree of belief in conditionals but not in logically equivalent quantified statements.
The Probability of Conditionals: The Psychological Evidence
Mind and Language, 2003
The two main psychological theories of the ordinary conditional were designed to account for inferences made from assumptions, but few premises in everyday life can be simply assumed true. Useful premises usually have a probability that is less than certainty. But what is the probability of the ordinary conditional and how is it determined? We argue that people use a two stage Ramsey test that we specify to make probability judgements about indicative conditionals in natural language, and we describe experiments that support this conclusion. Our account can explain why most people give the conditional probability as the probability of the conditional, but also why some give the conjunctive probability. We discuss how our psychological work is related to the analysis of ordinary conditionals in philosophical logic.
On the provenance of judgments of conditional probability
2009
In standard treatments of probability, Pr (A| B) is defined as the ratio of Pr (A& B) to Pr (B), provided that Pr (B)> 0. This account of conditional probability suggests a psychological question, namely, whether estimates of Pr (A| B) arise in the mind via implicit calculation of Pr (A& B)/Pr (B). We tested this hypothesis (Experiment 1) by presenting brief visual scenes composed of forms, and collecting estimates of relevant probabilities. Direct estimates of conditional probability were not well predicted by Pr (A&B)/Pr (B).
Conditional Probability and the Cognitive Science of Conditional Reasoning
Mind and Language, 2003
This paper addresses the apparent mismatch between the normative and descriptive literatures in the cognitive science of conditional reasoning. Descriptive psychological theories still regard material implication as the normative theory of the conditional. However, over the last 20 years in the philosophy of language and logic the idea that material implication can account for everyday indicative conditionals has been subject to severe criticism. The majority view is now apparently in favour of a subjective conditional probability interpretation. A comparative model fitting exercise is presented that shows that a conditional probability model can explain as much of the data on abstract indicative conditional reasoning tasks as psychological theories that supplement material implication with various rationally unjustified processing assumptions. Consequently, when people are asked to solve laboratory reasoning tasks, they can be seen as simply generalising their everyday probabilistic reasoning strategies to this novel context.
Journal of Experimental Psychology: Learning, Memory, & Cognition, 2003
- proffered a Bayesian model in which conditional inferences are a direct function of conditional probabilities. In the current article, the authors first considered this model regarding the processing of negatives in conditional reasoning. Its predictions were evaluated against a large-scale meta-analysis (W. J. Schroyens, W. . This evaluation shows that the model is flawed: The relative size of the negative effects does not match predictions. Next, the authors evaluated the model in relation to inferences about affirmative conditionals, again considering the results of a meta-analysis (W. J. Schroyens, W. . The conditional probability model is countered by the data reported in literature; a mental models based model produces a better fit. The authors conclude that a purely probabilistic model is deficient and incomplete and cannot do without algorithmic processing assumptions if it is to advance toward a descriptively adequate psychological theory.
The Probabilities of Conditionals Revisited
Cognitive Science, 2013
According to what is now commonly referred to as "the Equation" in the literature on indicative conditionals, the probability of any indicative conditional equals the probability of its consequent of the conditional given the antecedent of the conditional. Philosophers widely agree in their assessment that the triviality arguments of Lewis and others have conclusively shown the Equation to be tenable only at the expense of the view that indicative conditionals express propositions. This study challenges the correctness of that assessment by presenting data that cast doubt on an assumption underlying all triviality arguments.
Conditionals and Conditional Probability
JOURNAL …, 2003
The authors report 3 experiments in which participants were invited to judge the probability of statements of the form if p then q given frequency information about the cases pq, p¬q, ¬pq, and ¬p¬q (where ¬ ϭ not). Three hypotheses were compared: (a) that people equate the probability with that of the material conditional, 1 Ϫ P(p¬q); (b) that people assign the conditional probability, P(q/p); and (c) that people assign the conjunctive probability P(pq). The experimental evidence allowed rejection of the 1st hypothesis but provided some support for the 2nd and 3rd hypotheses. Individual difference analyses showed that half of the participants used conditional probability and that most of the remaining participants used conjunctive probability as the basis of their judgments.
The Mental Model Theory of Conditionals: A Reply to Guy Politzer
Topoi, 2009
This paper replies to criticisms of the mental model theory of conditionals. It argues that the theory provides a correct account of negation of conditionals, that it does not provide a truth-functional account of their meaning, though it predicts that certain interpretations of conditionals yield acceptable versions of the 'paradoxes' of material implication, and that it postulates three main strategies for estimating the probabilities of conditionals.
Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment
Psychological Review, 1983
Perhaps the simplest and the most basic qualitative law of probability is the conjunction rule: The probability of a conjunction, P(A&B), cannot exceed the probabilities of its constituents, P(A) and .P(B), because the extension (or the possibility set) of the conjunction is included in the extension of its constituents. Judgments under uncertainty, however, are often mediated by intuitive heuristics that are not bound by the conjunction rule. A conjunction can be more representative than one of its constituents, and instances of a specific category can be easier to imagine or to retrieve than instances of a more inclusive category. The representativeness and availability heuristics therefore can make a conjunction appear more probable than one of its constituents. This phenomenon is demonstrated in a variety of contexts including estimation of word frequency, personality judgment, medical prognosis, decision under risk, suspicion of criminal acts, and political forecasting. Systematic violations of the conjunction rule are observed in judgments of lay people and of experts in both between-subjects and within-subjects comparisons. Alternative interpretations of the conjunction fallacy are discussed and attempts to combat it are explored.