  This paper is devoted to justification of quantum-like models of the process
of decision making based on the theory of open quantum systems, i.e. decision
making is considered as decoherence. This process is modeled as interaction of
a decision maker, Alice, with a mental (information) environment ${\cal R}$
surrounding her. Such an interaction generates "dissipation of uncertainty"
from Alice's belief-state $\rho(t)$ into ${\cal R}$ and asymptotic
stabilization of $\rho(t)$ to a steady belief-state. The latter is treated as
the decision state. Mathematically the problem under study is about finding
constraints on ${\cal R}$ guaranteeing such stabilization. We found a partial
solution of this problem (in the form of sufficient conditions). We present the
corresponding decision making analysis for one class of mental environments,
the so-called "almost homogeneous environments", with the illustrative
examples: a) behavior of electorate interacting with the mass-media
"reservoir", b) consumers' persuasion. We also comment on other classes of
mental environments.
