In Gloms and Fizos, Massimo Fuggetta talks about a recent paper of his on Bayesian reasoning and reflects on the results of an earlier paper I co-authored with Gaelle Villejoubert on Bayesian reasoning and the inverse fallacy.

In the commentary, Massimo and I discuss the meaning of subjects’ violations of additivity for binary complements for which they are making posterior probability judgments — namely, the hypothetical creatures, Gloms and Fizos, who live on Planet Vuma.

Gaelle and I had found that the inverse fallacy could be used to predict whether mean additivity violations would be superadditive (adding to less than 1) or subadditive (adding to more than 1). We achieved this by structuring out stimuli so that the sums of the two relevant diagnostic probabilities for assessment pairs summed to more or less than one.

The discussion in Massimo’s Bayes blog focuses on whether researchers assessing Bayesian reasoning have an obligation to make various complementarity relations explicit for subjects. For instance, if we tell subjects that 98% of Gloms smoke cigarettes, must we also tell them that 2% don’t. Massimo seems quite convinced that doing so would eliminate additivity violations and correct their Bayesian assessments. I am less confident since I don’t think deviations from Bayes theorem are only due to people losing track of implicated information, although I agree that it would probably help, just as clarifying nested sets via natural sampling trees helps improve Bayesian judgement.

The other issue is whether there is any of sort of obligation to do so in experiments on probability judgment, and there I think the answer is clearly *no*. Indeed, there is no such obligation in everyday life, and the Gricean norm is to truncate redundancy. Thus, we’re not likely to say something like “I’m 95% sure I passed the exam and I’m 5% sure I didn’t.” We would either say 95% sure I passed or something like I still have a 5% doubt remaining. So the kind of truncation we used in our experiment is normative in daily life.

Reference

Villejoubert, G., & Mandel, D. R. (2002). The inverse fallacy: An account of deviations from Bayes’s theorem and the additivity principle. *Memory & Cognition*, **30**, 171-178. [PDF] [Erratum]

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