Modeling behavior of decision makers with the aid of algebra of qubit creation–annihilation operators

We present a general model of the process of decision making based on the representation of the basic behavioral variables with the aid of an algebra of qubit creation–annihilation operators, adopted from the quantum information theory. In contrast to the genuine quantum physical systems, which are divided into either bosons or fermions and modeled with the aid of operators, satisfying canonical commutation or anti-commutation relations, decision makers preferences for possible actions are constructed with the aid of operators satisfying the so-called qubit commutation relations. Systems described by operators, satisfying such commutation relations, combine the features of bosons and fermions. Thus, one of the basic consequences of the presented model is that decision makers mimic the combined bosonic–fermionic behavior. By using the algebra of qubit creation–annihilation operators, we proceed with the construction of the concrete operators, describing the process of decision making. In particular, the generators of the quantum Markov dynamics, which is used for modeling human decision making process, are expressed as polynomials of the qubit creation–annihilation operators. The devised coefficients have a natural cognitive and social meaning.