  In recent years, quantum mechanics has been actively used in areas outside of
physics, such as psychology, sociology, theory of decision-making, game theory,
and others. In particular, quantum mechanics is used to explain the paradoxes
arising in cognitive psychology and decision making. Wang and Busemeyer
invented a quantum model and approach as well as non-parametric equality
(so-called QQ-equality), explaining the questions order effect. The primary
objective of this note is to test the possibility to expand the Wang-Busemeyer
model by considering questions which are mathematically represented by positive
operator valued measures. We found that, for such observables, the QQ-equality
can be violated. But, we also showed that, in principle, it is possible to
reduce expanded model to the original Wang-Busemeyer model by expanding the
context of the questions. This version of preprint is aimed to point out to
annoying miscalculation in version 1. This miscalculation might mislead a
reader who is not experienced in operating with POVMs. Otherwise the main line
of construction and reasoning presented in version 1 is right and it can be
easily completed by the reader on the basis of version 1 and the correction
remark in version 2.
