Ever since Tversky and Kahneman's influential research exposing the failures of classical probability theory to describe human reasoning under uncertainty (1974), decision researchers gave up almost all hope to find an axiomatic foundation for understanding human judgments and decisions. Instead, they turned to the idea of using tool boxes of heuristics to explain myriad decision bias and errors. The project will further develop a new theoretical application of quantum probability theory (the mathematical foundation of quantum theory) to human judgment and decision making. Quantum probability theory fundamentally differs from classical probability theory. The critical question is which set of probability rules provides a better description of human judgment and decision. In the Principal Investigators' past several years of research supported by NSF, they have shown that quantum probability theory provides an innovative, coherent, and mathematically principled approach to account for many paradoxical findings in judgment and decision research (i.e., conjunction and disjunction errors, interference effects, question order effects). The current project will further develop and test a consistent quantum probability account of violations of classic probability rules found in question order effects. The investigators will extend the quantum model for order effects to make a priori predictions about the direction of order effects and also to be able to account for measures with multiple ordinal levels.
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. This project will study whether it matters in what order questions are asked on a survey. The investigators regularly organize workshops on quantum probability models of cognition at annual meetings of Cognitive Science Society and Society for Mathematical Psychology. They have organized two special journal issues on the topic: one appeared in the Journal of Mathematical Psychology (2009) and the other is forthcoming in Topics in Cognitive Science. Their work has been cited across disciplines, ranging from cognitive science, decision science, economics, engineering, to mathematics, physics, and astronomy.
Ever since Kahneman and Tversky’s extremely influential research (1974) exposing the failures of classical probability to describe human reasoning and decision making under uncertainty, researchers gave up almost all hope to find an axiomatic foundation for understanding human judgments and decisions. Separate and disconnected heuristic explanations have been proposed using variants of classical decision theory to explain a number of paradoxical findings, such as violations of the classical probability laws of commutativity and distributivity. The paradoxical findings have resisted explanation under a common classical theoretical framework. Our past research supported by NSF applies mathematical principles from quantum theory to cognitive and decision sciences. Our findings demonstrate that quantum theory provides a viable new direction toward the possibility of accounting for paradoxical findings from decision research using a unified and principled theoretical framework. The broad and long term goal of this research program is to provide a new foundation for constructing probabilistic-dynamic systems from principles based on quantum as opposed to classical probability theory. To be clear, we are not interested in physics, and neither do we claim the brain is a quantum computer. Our interest lies solely in the application of mathematical principles from quantum theory to cognitive and decision sciences. Our recent research demonstrates that quantum theory provides a viable new direction for organizing and accounting for paradoxical findings from decision research using a unified and principled theoretical framework. Our specific goals for this particular NSF grant were to (1) develop and test a quantum model of question order effects with surveys. The first goal was to develop a general a priori, exact, and parameter-free theoretical test from our quantum theory of judgment and decision. Rarely are such predictions tested in social sciences. (2) A second goal was to develop a quantum model of similarity judgments. This theory describes how people judge the similarity of different types of objects. These similarity judgments are complicated because they are highly contextual and they violate the axioms of distance theory. However it is important to understand them because they play an important role in human categorization and decision making. (3) A third goal was to provide a rigorous quantitative comparison of our new quantum decision model with one of the most successful previous models from past research using a state of the art Bayesian model comparison methods. We found the following results: (1) Large and significant question order effects in the large ensemble data sets that we collected (70 national representative surveys with 651-3006 participants in each survey, and two lab experiments). Most importantly, the test of the quantum model for question order effects provided surprisingly accurate predictions. The results of the test strongly supported the quantum model for question order effects with survey research. (2) We also succeeded in developing a quantum model of similarity judgments that accounts for a variety of puzzling findings in the field of similarity judgments (such as asymmetric similarity judgments). (3) Finally, our quantitative Bayesian model comparison of our quantum decision model versus a model based on prospect theory with respect to each model's capability of explaining a fundamental violation of rational decision theory called dynamic inconsistency provided overwhelming support for the quantum model. Our findings have been written up for publication in major journals and we have presented our results at major scientific meetings. We have developed web sites for the public to learn about our new theory and its applications and accomplishments. We have trained scientists on our new theory by presenting workshops at major scientific meetings. We have also trained graduate students to conduct scientific research at academic universities on this new theory.
