  In the present article we consider the conjunction fallacy, a well known
cognitive heuristic experimentally tested in cognitive science, which occurs
for intuitive judgments in situations of bounded rationality. We show that the
quantum formalism can be used to describe in a very simple way this fallacy in
terms of interference effect. We evidence that the quantum formalism leads
quite naturally to violations of Bayes' rule 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 \textit{quantum regime}, the bounded-rationality
regime, where the cognitive heuristics are valid.
