Summary: This paper is devoted to a 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 \(\mathcal{R}\) surrounding her. Such an interaction generates “dissipation of uncertainty” from Alice’s belief-state \(\rho(t)\) into \(\mathcal{R}\) 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 \(\mathcal{R}\) 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.