Quantum Formalism for Decision-Making

Emmanuel M. Pothos, Jerome R. Busemeyer

Vikram Athalye, Emmanuel Haven

We start in this chapter arguing why quantum probability is a good candidate for modelling purposes in decision-making contexts. The quantum formalism, in this chapter, centres around the argument that such formalism can accommodate paradoxical outcomes in decision making. Quantum probability offers a response to those decision-making contexts where a consistent violation of the law of total probability occurs. Strong results have been obtained in decision-making applications and we go into some detail to discuss the so-called QQ equality and the Aumann theorem.

Hervé Zwirn C

Nicolai Friis

Taiki Takahashi

Recently, mathematical models based on quantum formalism have been developed in cognitive science. The target articles in this special issue of Topics in Cognitive Science clearly illustrate how quantum theoretical formalism can account for various aspects of human judgment and decision making in a quantitatively and mathematically rigorous manner. In this commentary, we show how future studies in quantum cognition and decision making should be developed to establish theoretical foundations based on physical theory, by introducing Taketani's three-stage theory of the development of science. Also, implications for neuroeconomics (another rapidly evolving approach to human judgment and decision making) are discussed.

Shahram Dehdashti, Lauren Fell, Peter Bruza

This article presents a general framework that allows irrational decision making to be theoretically investigated and simulated. Rationality in human decision making under uncertainty is normatively prescribed by the axioms of probability theory in order to maximize utility. However, substantial literature from psychology and cognitive science shows that human decisions regularly deviate from these axioms. Bistable probabilities are proposed as a principled and straight forward means for modeling (ir)rational decision making, which occurs when a decision maker is in "two minds". We show that bistable probabilities can be formalized by positive-operator-valued projections in quantum mechanics. We found that (1) irrational decision making necessarily involves a wider spectrum of causal relationships than rational decision making, (2) the accessible information turns out to be greater in irrational decision making when compared to rational decision making, and (3) irrational decision making is quantum-like because it violates the Bell-Wigner polytope.