The Conjunction Fallacy in Quantum Decision Theory

Abstract

AbstractThe conjunction fallacy is a renowned violation of classical probability laws, which is persistently observed among decision makers. Within Quantum decision theory (QDT), such deviations are the manifestation of interference between decision modes of a given choice prospect. We propose a novel QDT interpretation of the conjunction fallacy, which cures some inconsistencies of a previous treatment, and incorporates the latest developments of QDT, in particular the representation of a decision-maker’s state of mind with a statistical operator. Rather than focusing on the interference between choice options, our new interpretation identifies the origin of uncertainty and interference between decision modes to an entangled state of mind, whose structure determines the representation of prospects. Thus, on par with prospects, the state of mind can be a source of uncertainty and lead to interference effects, resulting in characteristic behavioral patterns. We present the first in-depth QDT-based analysis of an empirical study (the touchstone experimental investigations of Shafir et al. [6]), which enables a data-driven exploration of its underlying theoretical construct. We link typicality judgements to probability amplitudes of the decision modes in the state of mind, and quantify the level of uncertainty and the relative contributions of prospect’s interfering modes to its probability judgement. This enables inferences about the key QDT interference “attraction” q-factor with respect to different types of prospects—compatible versus incompatible. We propose a novel empirically motivated “QDT indeterminacy (or uncertainty) principle,” as a fundamental limit of the precision with which certain sets of prospects can be simultaneously known (or assessed) by a decision maker, or elicited by an experimental procedure. For any type of prospects, we observe a general tendency for the q-factor to converge to the same negative range \(q\in (-0.3,-0.1)\) in the presence of high uncertainty, which motivates the hypothesis of an universal “aversion” q. The “aversion” q is independent of the (un-)attractiveness of a prospect under more certain conditions, which is the main difference with the previously considered “QDT quarter law”. The universal “aversion” q substantiates the previously proposed “QDT uncertainty aversion principle” and clarifies its domain of application. The universal “aversion” q provides a theoretical basis for modelling different risk attitudes, such as aversions to uncertainty, to risk or to losses.KeywordsQuantum decision theoryConjunction fallacyInterferenceIndeterminacy principleUniversal aversion