Quantum-like model of cognitive decision making and information processing

In this paper we offer the quantum-like (QL) representation of the Shafir–Tversky statistical effect which is well known in cognitive psychology. We apply the so-called contextual approach. We consider the Shafir–Tversky effect to result from mixing statistical data obtained in incompatible contexts which are involved, e.g. in Prisoner’s Dilemma or in more general games in which the disjunction effect can be found. As a consequence, the law of total probability is violated for the experimental data obtained in experiments on cognitive psychology by Shafir and Tversky [Shafir, E., Tversky, A., 1992. Thinking through uncertainty: nonconsequential reasoning and choice. Cogn. Psychol. 24, 449–474] as well as Tversky and Shafir [Tversky, A., Shafir, E., 1992. The disjunction effect in choice under uncertainty. Psychol. Sci. 3, 305–309]. Moreover, we can find a numerical measure of contextual incompatibility (the so-called coefficient of interference) as well as represent contexts which are involved in Prisoner’s Dilemma (PD) by probability amplitudes—normalized vectors (“mental wave functions”). We remark that statistical data from Shafir and Tversky [Shafir, E., Tversky, A., 1992. Thinking through uncertainty: nonconsequential reasoning and choice. Cogn. Psychol. 24, 449–474] and Tversky and Shafir [Tversky, A., Shafir, E., 1992. The disjunction effect in choice under uncertainty. Psychol. Sci. 3, 305–309] experiments differ crucially from the point of view of mental interference. The second one exhibits the conventional trigonometric (cos?$\cos ?$-type) interference while the first one exhibits even the so-called hyperbolic (cosh?$\cosh ?$-type) interference. We discuss the QL processing of information by cognitive systems, especially, the QL decision making and both classical and QL rationality and ethics.