Research on human judgment and decision making has revealed a number of paradoxical findings that have resisted explanation under a common theoretical framework. These include violations of the sure thing axiom of decision making, interactions between inferences and decisions, violations of the reduction axiom of decision making, violations of the conjunctive and disjunctive axioms of probability theory, and order effects on judgments. In the past, separate and disconnected explanations have been proposed using variants of classic decision theory. This research proposes a unifying explanation for all of these paradoxical results based on a new quantum decision theory. Classic decision theory is based on classic probability theory. Probabilities are assigned to events defined as subsets of a universal set, which obey all the laws of Boolean algebra. Quantum decision theory is based on quantum probability theory. Probabilities are assigned to events defined as subspaces of a Hilbert space, which obey all the laws of Boolean algebra except the distributive axiom. Following from the distributive axiom, classic probability theory adheres to one of its most important theorems, the law of total probability. Because quantum logic does not have to obey the distributive law, quantum probabilities do not have to obey the law of total probability. Instead, quantum probability theory must obey another law called the doubly stochastic law, which the classic probability model does not obey. Hence, the two probability theories are fundamentally different and the critical question is which set of rules provides a better description of human behavior. The immediate goal of this research is to rigorously compare decision models built upon classical probability theory with those built from quantum probability theory. To rigorously compare quantum versus classical probability models of decision making, a series of experiments will be conducted. The experiments focus on tests of the law of total probability and tests of the law of double stochasticity, where the two classes of models make major and qualitatively different predictions. The research will accomplish three objectives: (1) develop a new quantum theory of human inference and decision making, (2) conduct new empirical tests of the fundamental laws of total probability and double stochasticity using human inference and decision behavior, and (3) rigorously compare and contrast classic versus quantum models of decision making with respect to the new empirical findings. A quantum or classic model will be preferred only if it provides a superior scientific explanation of the phenomena with respect to both accuracy and parsimony.
The broad and long-term goal of this research program is to break new ground and pioneer a new path by building probabilistic and dynamic systems for social and behavioral sciences from quantum rather than classical probability principles. Previously, theorists in these fields have relied on mathematical models (e.g. stochastic differential equations) based on fundamental assumptions borrowed from classical physics. What are these fundamental assumptions? Are they overly restrictive? Social and behavioral scientists also face findings that remain paradoxical from a classic probability point of view. These paradoxes suggest that measurements in these fields may not always obey the law of total probability and entail different assumptions. This program of research also will contribute to the training of students at the undergraduate, graduate, and post doctoral levels at two major state universities. In addition to student training, the investigators will make an effort to train scientists in the area quantum cognition. They have conducted a full day tutorial at the annual Cognitive Science meeting and they plan to continue these tutorials in the future. They also plan to organize a special issue on Quantum Cognition in the Journal of Mathematical Psychology. New graduate courses on quantum cognition and decision making will be prepared and presented at the graduate level, and finally, a resource web site will be developed with tutorial and reference information on quantum theory for social and behavioral sciences.
