Abstract
The new probabilistic approaches to the natural language conditional imply that there is a parallel relation between indicative conditionals (ICs) “if s then b” and conditional bets (CBs) “I bet $1 that if s then b” in two aspects. First, the probability of an IC and the probability of winning a CB are both the conditional probability, P(s|b). Second, both an IC and a CB have a third value “void” (neither true nor false, neither wins nor loses) when the antecedent is false (¬s). These aspects of the parallel relation have been found in Western participants. In the present study, we investigated whether this parallel is also present in Eastern participants. We replicated the study of Politzer et al. (2010) with Chinese and Japanese participants and made two predictions. First, Eastern participants will tend to engage in more holistic cognition and take all possible cases, including ¬s, into account when they judge the probability of conditional: Easterners may assess the probability of antecedent s out of all possible cases, P(s), and then may focus on consequent b out of s, P(b|s). Consequently, Easterners may judge the probability of the conditional, and of winning the bet, to be P(s) ∗ P(b|s) = P(s & b), and false/losing the bet as P(s) ∗ P(¬b|s) = P(s & ¬b). Second, Eastern participants will tend to be strongly affected by context, and they may not show parallel relationships between ICs and CBs. The results indicate no cultural differences in judging the false antecedent cases: Eastern participants judged false antecedent cases as not making the IC true nor false and as not being winning or losing outcomes. However, there were cultural differences when asked about the probability of a conditional. Consistent with our hypothesis, Eastern participants had a greater tendency to take all possible cases into account, especially in CBs. We discuss whether these results can be explained by a hypothesized tendency for Eastern people to think in more holistic and context-dependent terms than Western people.
Highlights
The new Bayesian and probabilistic accounts of the natural language indicative conditional (IC) have become increasingly influential in the psychology of reasoning
There is the expected value (EV) of the conditional bets (CBs) to keep in mind, which is given by EV = P(s & b)(100) + P(s & ¬b)(−100) + P(¬s)(0) = (3/7)(100) + (1/7)(−100) = 29
The purpose of the present study was to test Bayesian accounts of the natural language conditional with Easterners by replicating the study of Politzer et al (2010). These accounts imply that there is a parallel relation between ICs and CBs: both IC and CB are related to the conditional probability, P(b|s), and both have a de Finetti table where the false antecedent cases, ¬s, are void
Summary
The new Bayesian and probabilistic accounts of the natural language indicative conditional (IC) have become increasingly influential in the psychology of reasoning. If the Equation holds, a Bayesian account of conditional reasoning will follow, with Bayesian probability theory, and not binary logic, as the new normative standard, a new paradigm, for conditional reasoning (Evans and Over, 2004; Oaksford and Chater, 2007; Pfeifer and Kleiter, 2010; Baratgin and Politzer, 2016) In this new approach, a conditional can have a third value, “neither true nor false (void),” in addition to truth or falsity, when its antecedent is false. This proposal is an important generalization that is arguably found in de Finetti himself, and it should be investigated in future research (Over and Baratgin, 2017)
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