Quantum-like Description of Probabilistic Data from Shafir-Tversky Experiments: evidence of trigonometric and hyperbolic (!) interference

TL;DR

This paper models the Shafir-Tversky experimental data using quantum-like frameworks, revealing both trigonometric and hyperbolic interference effects, and introduces measures of contextual incompatibility in cognitive decision processes.

Contribution

It presents a quantum-like representation of probabilistic data from cognitive experiments, identifying hyperbolic interference and providing a new measure of contextual incompatibility.

Findings

Identification of trigonometric and hyperbolic interference in data

Introduction of a coefficient of interference as a measure of contextual incompatibility

Representation of mental states using probability amplitudes or wave functions

Abstract

In this paper we present quantum-like (QL) representation of the Shafir-Tversky statistical effect. We apply so called contextual approach. The Shafir-Tversky effect is considered as a consequence of combination of a number of incompatible contexts which are involved e.g. in Prisoner's Dilemma or in more general games inducing the disjunction effect. As a consequence, the law of total probability is violated for experimental data obtained by Shafir and Tversky (1992) as well as Tversky and Shafir (1992). Moreover, we can find a numerical measure of contextual incompatibility (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 (1992) and Tversky and Shafir (1992) experiments differ crucially from the point of view of mental interference. The second one exhibits the conventional trigonometric ($\cos$-type) interference, but the first one exhibits so called hyperbolic ($\cosh$-type) interference. We discuss QL processing of information by cognitive systems, in particular, QL decision making as well as classical and QL rationality.