The conjunction fallacy and interference effects

In the present article we consider the conjunction fallacy, a well known cognitive fallacy experimentally tested in cognitive science, which occurs for intuitive judgments. We show that the quantum formalism can be used to describe, in a very simple way, this fallacy, in terms of interference effect. We provide evidence that the quantum formalism leads quite naturally to violations of the joint probability rule of classic probability when considering the estimated probability of the conjunction of two events. By defining the concept of maximal conjunction error, we find a good agreement with experimental results. Thus we suggest that in cognitive science the formalism of quantum mechanics can be used to describe a quantum regime, where the cognitive fallacies and heuristics are valid.