The probability of causal conditionals.

By David E. Over, Constantinos Hadjichristidis, Jonathan Evans, Simon Handley, Steven A. Sloman. 2007

286 citations recorded by the source corpus.

Conditionals in natural language are central to reasoning and decision making. A theoretical proposal called the Ramsey test implies the conditional probability hypothesis: that the subjective probability of a natural language conditional, P(if p then q), is the conditional subjective probability, P(q/p). We report three experiments on causal indicative conditionals and related counterfactuals that support this hypothesis. We measured the probabilities people assigned to truth table cases, P(pq), P(p notq), P( notpq) and P( notp notq). From these ratings, we computed three independent predictors, P(p), P(q/p) and P(q/ notp), that we then entered into a regression equation with judged P(if p then q) as the dependent variable. In line with the conditional probability hypothesis, P(q/p) was by far the strongest predictor in our experiments. This result is inconsistent with the claim that causal conditionals are the material conditionals of elementary logic. Instead, it supports the Ramsey test hypothesis, implying that common processes underlie the use of conditionals in reasoning and judgments of conditional probability in decision making.

Subfields: Developmental and Educational Psychology, General Decision Sciences, History and Philosophy of Science

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Citations in the corpus

Counterfactuals in Explainable Artificial Intelligence (XAI): Evidence from Human Reasoning (2019, background): “A counterfactual’s probability may be determined by beliefs [Over et al., 2007], or by the possibilities that people envisage [Khemlani et al., 2018].”
Questions and challenges for the new psychology of reasoning (2012, background): “Conditionals have also been investigated recently with non-deductive tasks when, for example, participants are asked to judge the probability of the conditional statement given some evidence (Evans, Handley, & Over, 2003 ; Oberauer, Weidenfeld, & Fischer, 2007 ; Oberauer & Wilhelm, 2003 ; Over, H”
What makes us believe a conditional? The roles of covariation and causality (2007, background): “Over et al. (2007) found some evidence for an influence of P(qj p) on the evaluation of causal conditionals, which they interpret as reflecting pragmatic additions of the inverse, but the effect was weak.”
The conditional in mental probability logic (2010, background): “Examples are nonmonotonic reasoning, possibility theory [3], logic programming [61, 62], probabilistic approaches [41, 11, 43, 42, 37, 36, 19, 46, 47, 44] .”
Because Hitler did it! Quantitative tests of Bayesian argumentation using ad hominem (2012, background): “Alternative possibilities would be to directly ask for the subjective probability, or to ask for a judgement of confidence in the conditional: “If the policy was good, then Hitler was responsible for it,” with which ordinal predictions could be made on the recognition that participants typically rep”
Uncertainty and the de Finetti tables (2013, background): “The finding that there is not a difference between the two conditions generalizes Politzer et al. (2010). People treat questions about the truth or the falsity of the assertion of indicative conditionals as very similar to questions about winning or losing bets on conditionals.”
The psychology of inferring conditionals from disjunctions: A probabilistic study (2012, background): “…probability hypothesis was strongly supported in this way in these experiments (Evans et al., 2003; Oberauer & Wilhelm, 2003; Over & Evans, 2003; see Over et al., 2007, for confirmation of the conditional probability hypothesis for conditionals that do not refer to a known frequency distribution).”
Betting on conditionals (2010, background): “The modal response to the probability of truth question is P(BjA), and P(notBjA) to the probability of falsity question, with the two responses summing to 1 (Evans et al., 2003).”