On the Irrationality of Being in Two Minds

Abstract

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.

Bistable Probabilities: A Unified Framework for Studying Rationality and Irrationality in Classical and Quantum Games

“…In addition, it is worthwhile to mention that application of quantum games in cognitive science have been generalized to contextuality scenarios, for example see [44,45,46,47], in which intransitive and transitive preferences have been studied. In fact, the bistable framework exhibits some potential to model contextuality [29] and future work will be directed to the modelling of contextuality in games. Another future direction involves extending our quantum treatment of incentivised games beyond two agents which opens the possibility of modelling agents with varying levels of entanglement.…”

“…If System 2, and monetary gain, is seen to be the rational process and choice in a certain situation, we introduce irrationality as the deviation from that choice if System 1 preferences conflict with System 2. We introduce the bistable parameter k to represent the level of disagreement between System 1 and System 2 in a similar way as in [29]. It should be noted at this point that we can just as easily flip the explanation under the assumption that System 1 produces a choice that maximises the agent's utility, and where System 2 is seen to deviate from this by a factor defined by k. In terms of the interaction between System 1 and System 2, there are various views about how this might occur, for example, in parallel or with System 1 acting as a default for which System 2 can intervene [30].…”

Modeling Human Behavior Part II -- Cognitive approaches and Uncertainty

“…For relevant survey papers and related, please refer to [1,20,47,76,83] 4.1.2 Principles and Definitions. It has been argued that traditional probabilistic representations do not fully represent the reasoning of humans [81] or can require exponentially more complex representations [76,83].…”

Bistable probabilities: a unified framework for studying rationality and irrationality in classical and quantum games

“…If system 2, and monetary gain, is seen to be the rational process and choice in a certain situation, we introduce irrationality as the deviation from that choice if system 1 preferences conflict with system 2. We introduce the bistable parameter k to represent the level of disagreement between systems 1 and 2 in a similar way as in [29]. It should be noted at this point that we can just as easily flip the explanation under the assumption that system 1 produces a choice that maximizes the agent's utility, and where system 2 is seen to deviate from this by a factor defined by k. In terms of the interaction between systems 1 and 2, there are various views about how this might occur; for example, in parallel or with system 1 acting as a default for which system 2 can intervene [30].…”