Quantum field inspired model of decision making: Asymptotic stabilization of belief state via interaction with surrounding mental environment

Abstract

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 R surrounding her. Such an interaction generates “dissipation of uncertainty” from Alice's belief-state ρ(t) into R and asymptotic stabilization of ρ(t) to a steady belief-state. The latter is treated as the decision state. Mathematically the problem under study is about finding constraints on 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.