Full Day Tutorial on Quantum Theory in Cognitive Modeling

AbstractEven though the generally acknowledged normative and descriptive standard for modeling human inference is classical/ Bayesian probability theory (CPT), there have also been several reports which challenge CPT’s universal applicability. Some of the most influential empirical demonstrations of such so-called fallacies have been reported by Kahneman, Tversky and their collaborators. For example, consider the evocative conjunction fallacy. In the Tentori et al. (2004) demonstration of the conjunction fallacy, participants are quite happy to consider it more probable to randomly select a Scandinavian person with both blue eyes and blond hair, than just blond hair. Even though we can imagine a line-up of Scandinavian individuals (making the set theoretic structure of CPT explicit and so the impossibility of a conjunction fallacy), there just seems a persistent feeling that somehow the conjunction is more likely than the marginal (cf. Gilboa, 2000). How can our intuition be so much at odds with CPT prescription? We call quantum probability theory (QPT) the rules for how to assign probabilities to events from quantum mechanics, without any of the physics. QPT is in principle applicable in any situation where there is a need to formalize uncertainty. In psychology, one way to motivate QPT is as a bounded rationality approach to CPT: whereas in CPT we require conjunctions/ disjunctions across all possible questions (and the underlying logical structure is a Boolean algebra), in QPT (classical) conjunctions/ disjunctions are possible only for so-called compatible questions, while for incompatible ones they are undefined (they have to be computed with sequential operations; the underlying logical structure is a partial Boolean algebra).

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