  We prove a theorem which shows that a collection of experimental data of
probabilistic weights related to decisions with respect to situations and their
disjunction cannot be modeled within a classical probabilistic weight structure
in case the experimental data contain the effect referred to as the
'disjunction effect' in psychology. We identify different experimental
situations in psychology, more specifically in concept theory and in decision
theory, and in economics (namely situations where Savage's Sure-Thing Principle
is violated) where the disjunction effect appears and we point out the common
nature of the effect. We analyze how our theorem constitutes a no-go theorem
for classical probabilistic weight structures for common experimental data when
the disjunction effect is affecting the values of these data. We put forward a
simple geometric criterion that reveals the non classicality of the considered
probabilistic weights and we illustrate our geometrical criterion by means of
experimentally measured membership weights of items with respect to pairs of
concepts and their disjunctions. The violation of the classical probabilistic
weight structure is very analogous to the violation of the well-known Bell
inequalities studied in quantum mechanics. The no-go theorem we prove in the
present article with respect to the collection of experimental data we consider
has a status analogous to the well known no-go theorems for hidden variable
theories in quantum mechanics with respect to experimental data obtained in
quantum laboratories. For this reason our analysis puts forward a strong
argument in favor of the validity of using a quantum formalism for modeling the
considered psychological experimental data as considered in this paper.
