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Behavioral and Brain Sciences

Is quantum probability rational?

Alasdair Ian Houston, Karoline Wiesner

Published May 14, 2013• 2 citations
Publisher

Abstract

We concentrate on two aspects of the article by Pothos & Busemeyer (P&B): the relationship between classical and quantum probability and quantum probability as a basis for rational decisions. We argue that the mathematical relationship between classical and quantum probability is not quite what the authors claim. Furthermore, it might be premature to regard quantum probability as the best practical rational scheme for decision making.

DOI
10.1017/s0140525x12002993

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We concentrate on two aspects of the article by Pothos & Busemeyer (P&B): the relationship between classical and quantum probability and quantum probability as a basis for rational decisions. We argue that the mathematical relationship between classical and quantum probability is not quite what the authors claim. Furthermore, it might be premature to regard quantum probability as the best practical rational scheme for decision making.
There has been a growing trend to develop cognitive models based on the mathematics of quantum theory. A common theme in the motivation of such models has been findings which apparently challenge the applicability of classical formalisms, specifically ones based on classical probability theory. Classical probability theory has had a singularly important place in cognitive theory, because of its (in general) descriptive success but, more importantly, because in decision situations with low, equivalent stakes it offers a multiply justified normative standard. Quantum cognitive models have had a degree of descriptive success and proponents of such models have argued that they reveal new intuitions or insights regarding decisions in uncertain situations. However, can quantum cognitive models further benefit from normative justifications analogous to those for classical probability models? If the answer is yes, how can we determine the rational status of a decision, which may be consistent with quantum theory, but inconsistent with classical probability theory? In this paper, we review the proposal from Pothos, Busemeyer, Shiffrin, and Yearsley (2017), that quantum decision models benefit from normative justification based on the Dutch Book Theorem, in exactly the same way as models based on classical probability theory.
We are sympathetic to the general ideas presented in the article by Pothos & Busemeyer (P&B): Heisenberg's uncertainty principle seems naturally relevant in the social and behavioral sciences, in which measurements can affect the people being studied. We propose that the best approach for developing quantum probability models in the social and behavioral sciences is not by directly using the complex probability-amplitude formulation proposed in the article, but rather, more generally, to consider marginal probabilities that need not be averages over conditionals.
This comment suggests that Pothos & Busmeyer (P&B) do not provide an intuitive rational foundation for quantum probability (QP) theory to parallel standard logic and classical probability (CP) theory. In particular, the intuitive foundation for standard logic, which underpins CP, is the elimination of contradictions - that is, believing p and not-p is bad. Quantum logic, which underpins QP, explicitly denies non-contradiction, which seems deeply counterintuitive for the macroscopic world about which people must reason. I propose a possible resolution in situation theory.