Conditionals and conditional probability.

Abstract

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 not q, not pq, and not p not q (where not = not). Three hypotheses were compared: (a) that people equate the probability with that of the material conditional, 1 - P(p not 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 Probability of Conditionals

“…One mystery for both the theories to explain is the variety of estimates of conditional probabilities themselves. Evans et al (2003) also interpret their results as supporting the conditionalprobability hypothesis. In one study, for example, the participants were given the description of a pack of 30 cards, containing yellow circles, yellow diamonds, red circles, red diamonds.…”

“…This view, which we refer to as the "conditional-probability" hypothesis, was formulated by Adams (1975), it has been defended by Stevenson and Over (1995, pp. 617-618), and has received some empirical support in recent studies (e.g., Evans, Handley, & Over, 2003;Hadjichristidis, Stevenson, Over, Sloman, Evans, & Feeney, 2001;Oberauer & Wilhelm, 2003).…”

Mental models and the suppositional account of conditionals.

“…It can also be noted that the model p q is not part of the initial representation because all the disjunctions are not true in this case. cases and p cases or the conjunctive probability if they consider simply the proportion of cases in which the conditional is true among all the possible cases (Evans et al, 2003;Girotto & Johnson-Laird, 2004). This explains also why, as Evans et al (2005) noted, the probability of a conditional is never judged to be equal to not p or q.…”

The modulation of conditional assertions and its effects on reasoning

“…Other theorists have maintained the notion of validity, but postulated a probabilistic semantics for conditionals: "In everyday contexts it seems to be more plausible to interpret conditionals not by material implications, but by much weaker conditional probabilities" (Pfeifer & Kleiter, 2005). Likewise, many theorists have proposed that the probability of a conditional is the corresponding conditional probability of its consequent given its antecedent (e.g., Evans, Handley, Neilens, & Over, 2007;Evans, Handley, & Over, 2003;Hadjichristidis et al, 2001;Over, Hadjichristidis, Evans, Handley, & Sloman, 2007;Oberauer & Wilhelm, 2003). Oberauer and his colleagues have argued that the model theory needs to be revised in order to explain their participants' judgements of the probabilities of conditionals, which usually corroborated the conditional probability hypothesis (Oberauer, Geiger, Fischer, & Weidenfeld, 2007).…”