Does numerical information help children in avoiding conjunction fallacy?

Traditional conjunction fallacy problems elicit a conflict between the underlying probability rule and intuitions. So conjunction fallacy is considered as a prototypical case of dual processes at work: Due to the appeal of the intuitive response offered by Type 1 processes, Type 2 processes fail to override it. Under dual-process accounts Type 1 processes are responsible for what has been termed the fundamental computational bias, i.e. the tendency for people to automatically contextualize presented information (Evans & Over, 1996; Kahneman & Frederick, 2002; Stanovich, 1999). Nevertheless, some authors (Gigerenzer, 1996; Hertwig, Benz, & Krauss, 2008; Politzer & Noveck, 1991) argue that conjunction fallacy is not actually a reasoning error but a sound inference based on subjective probability estimates (since no numerical information are offered), and consistent with linguistic ambiguity of the task. That is, conjunction fallacy represents a reasonable answer giving the above mentioned task characteristics. Several studies (Chiesi, Gronchi & Primi, 2008; Davidson, 1995; Fisk & Slattery, 2005) have documented this kind of fallacy in children. The overall results showed that the occurrence of the error depends on the task characteristics, i.e. numerical information vs. representative description. The aim of the present study was to ascertain if children’s capacity to resist to conjunction fallacy might be enhanced adding numerical information to a representative description. We predicted that numerical information should: a) highlight the mathematical meaning of the task, i.e. help in avoiding inference based on subjective probability estimates and in resolving the linguistic ambiguity of the task; b) reduce the appeal of the intuitive response, i.e. help in avoiding the fundamental computational bias. Moreover, in order to evaluate the salience of representativeness, the conjunct statement (A&B) was presented along with a representative vs. non-representative single statement (A). Primary school children (n=593, mean age=9.54yrs, SD=0.96, range 8-11yrs, 52% males) were randomly presented one of four tasks. Each participant was asked to order in likelihood (from the less likely to the more likely) the three presented options. In all the tasks, participants who ranked the option (b) as the most likely committed the conjunction fallacy. Different proportions of conjunction fallacy (X2 (3,N=586) = 207.42, p<. 001) were observed. With tasks without the single representative statement about 50% commit the fallacy when the numerical information were given, and about the 70% when no numerical information were given. With tasks containing the single representative statement, very low percentages of conjunction fallacy were observed (about 10%). The present results suggest that conjunction fallacy is less likely to occur when numerical information is provided. Nonetheless, numbers slightly reduce susceptibility to conjunction errors since numbers can only reduce but not override the appeal of the intuitive response in conflict with the rule of probability.