Quantum cognition and Bell's inequality: A model for probabilistic judgment bias

Recently, quantum theory has shown its effectiveness in modeling psychological phenomena. Given the importance of Bell's inequality in the context of quantum physics, this work aims to investigate this issue in the domain of human probabilistic reasoning. Here, we present two quantum models that are able to predict the employment of the representativeness heuristic in a probabilistic task based on Bell's inequality in the Wigner-d'Espagnat format. The difference between the two models is based on the origins of the correlations achievable in conceptual combination; the first assumes incompatible variables while the second is based on quantum entanglement. From these models, two different scenarios related to three dichotomous variables (A,Ā), (B,B̄), (C,C̄) were created. Each scenario was manipulated in order to predict the violation of the inequality (Pr(A∩C̄)>Pr((A∩B̄)∪(B∩C̄))) or not (Pr(A∩C̄)≤Pr((A∩B̄)∪(B∩C̄))). Each condition was tested using two different modalities of response: Forced choice and probability rating of a single sentence. In Experiment 1, participants were randomly assigned to a single scenario, condition, and modality of response. The data showed a violation of the inequality consistent with the predictions of both models. In Experiment 2, we investigated the influence of an explicit subadditivity pattern (i.e., if Pr((A∩B̄)∪(B∩C̄))≤Pr(A∩B̄)+Pr(B∩C̄)) in our tasks, both from an empirical and theoretical point of view. Our results confirm the use of the quantum cognition approach in developing cognitive models.