Quantum probability theory provides a new formalism for constructing probabilistic and dynamic systems of cognition and decision. The purpose of this chapter is to introduce psychologists to this fascinating theory. This chapter is organized into six sections. First, some of the basic psychological principles supporting a quantum approach to cognition and decision are summarized; second, some notations and definitions needed to understand quantum probability theory are presented; third, a comparison of quantum and classical probability theories is presented; fourth, quantum probability theory is used to account for some paradoxical findings in the field of human probability judgments; fifth, a comparison of quantum and Markov dynamic theories is presented; and finally, a quantum dynamic model is used to account for some puzzling findings of decision-making research. The chapter concludes with a summary of advantages and disadvantages of a quantum probability theoretical framework for modeling cognition and decision.
Quantum probability theory provides a new formalism for constructing probabilistic and dynamic systems of cognition and decision. The purpose of this chapter is to introduce psychologists to this fascinating theory. This chapter is organized into six sections. First, some of the basic psychological principles supporting a quantum approach to cognition and decision are summarized; second, some notations and definitions needed to understand quantum probability theory are presented; third, a comparison of quantum and classical probability theories is presented; fourth, quantum probability theory is used to account for some paradoxical findings in the field of human probability judgments; fifth, a comparison of quantum and Markov dynamic theories is presented; and finally, a quantum dynamic model is used to account for some puzzling findings of decision-making research. The chapter concludes with a summary of advantages and disadvantages of a quantum probability theoretical framework for modeling cognition and decision.
Why should you be interested in quantum theory applied to Cognition and decision? Perhaps you are a physicist who is curious whether or not quantum principles can be applied outside of physics. In fact, that is one purpose of this book. Perhaps you are a cognitive scientist who is interested in representing concepts by vectors in a multidimensional feature space. This is essentially the way quantum theory works too. Perhaps you are a decision scientist who is trying to understand how people make decisions under uncertainty. Quantum theory could provide some interesting new answers. Generally speaking, quantum theory is a new theory for constructing probabilistic and dynamic systems , and in this book we apply this new theory to topics in cognition and decision. Later in this chapter we will give some specific examples, but let us step back at this point and try to understand the more general principles that support a quantum approach to cognition and decision. Six reasons for a quantum approach to cognition and decision Quantum physics is arguably the most successful scientific theoretical achievement that humans have ever created. It was created to explain puzzling findings that were impossible to understand using the older classical physical theory, and it achieved this by introducing an entirely new set of revolutionary principles. The older classical physical theory is now seen as a special case of the more general quantum theory. In the process of creating quantum mechanics, physicists also created a new theory of probabilistic and dynamic systems that is more general than the previous classic theory (Pitowski, 1989).
How can we use quantum theory to model other phenomena of interest to researchers in cognition and decision making? Quantum theory is not easy for researchers in cognition and decision making to accept. In fact, quantum mechanics was not easy for physicists to accept either, but it was forced on them by several paradoxical findings that could not be explained using classical physics. We have a similar problem in cognition and decision making – there are numerous paradoxical findings that just seem irrational according to classic probability theory. For example, under some conditions, people judge the probability of event A and B to be greater than the probability of event B , which is called the conjunction fallacy (Tversky & Kahneman, 1983). Also, under the same conditions, they judge the probability of A or B to be less than the probability of event A (Carlson & Yates, 1989), which is called the disjunction fallacy. In this chapter we examine how quantum probability theory explains these and other puzzling results from human probability judgment research. This chapter has two main parts. In the first part, we use a quantum model to derive qualitative predictions for conjunction errors, disjunction errors, and other closely related findings. The first section provides a general set of predictions that do not depend on specific assumptions about the features used to represent events, and the predictions are parameter free. In the second part, we examine the quantitative predictions of the quantum model for a Bayesian inference task, which we use to explain order effects on inference.
The quantum cognition research programme concerns the application of quantum probability theory(the rules for how to assign probabilities to events from quantum mechanics, without the physics) tocognitive modeling. We review quantum cognitive models in several areas of psychology, includingconjunction/ disjunction fallacies in probabilistic judgment, conceptual combinations, similarity, order effects on judgments, causal inference, the disjunction effect in decision making, measurement and interference effects on judgments and decisions, memory, perception, and other judgment anddecision-making applications. For each area, we first present the empirical findings that have motivated the application of quantum models, emphasizing any characteristics which are particularly puzzling or have resisted coherent theoretical explanations previously; we then discuss the quantum cognitive models, noting the key features of the models that help explain the empirical data; we finally cast a critical eye on the models and explore comparisons with non-quantum models.
Quantum theory has inspired many new ideas for understanding Cognition and decision making. Given the nascent state of this field, many new challenges still remain. What are the strengths and unique contributions of these ideas? What are likely next steps in its development? How can it be applied to practical problems in cognitive science? Is this a rational or an irrational system of reasoning? What, if any, are its connections to neuroscience? Should the hard problem of consciousness be considered? These are questions that we try to address in this chapter, albeit at times in a limited way. We end with a debate with a fictitious skeptic (actually previous reviewers) of these ideas. Let us start by reviewing what we have covered so far. Contributions to cognition and decision We begin by summarizing the conclusions reached in previous chapters regarding the usefulness of quantum theory for modelling phenomena in cognition and decision. Chapter 1 provided some motivation and Chapter 2 provided a theoretical introduction to quantum theory. Chapter 3 presented a quantum model to account for question order effects on survey research. An exact and parameter-free test was derived from the model, which produced surprisingly accurate predictions for results obtained from three different large Gallup poll survey studies. Chapter 4 described a quantum model of probability judgments to account for findings that produce violations of classic probability theory, including conjunction and disjunction fallacies and order effects on inference.
Quantum cognition (QC) is a rapidly growing research program in the field of cognitive science, which provides potentially important applications to better understand human communication processes. QC takes the basic mathematical principles from quantum theory, particularly quantum probability theory, and applies them to human reasoning, judgment, and decision-making, perception, attention, memory, and attitude, among other cognitive processes and observed behaviors. This chapter presents reasons for applying QC models to study communication processes and effects. Then the chapter reviews some basic QC concepts relevant to communication and provides an illustrative example where QC concepts are used to guide hypotheses for psychophysiological research on communication and decision processes. This introduction to QC is a conceptual summary of general principles that does not require any background in quantum theory.
Quantum cognition is a new research program that uses mathematical principles from quantum theory as a framework to explain human cognition, including judgment and decision making, concepts, reasoning, memory, and perception. This research is not concerned with whether the brain is a quantum computer. Instead, it uses quantum theory as a fresh conceptual framework and a coherent set of formal tools for explaining puzzling empirical findings in psychology. In this introduction, we focus on two quantum principles as examples to show why quantum cognition is an appealing new theoretical direction for psychology: complementarity, which suggests that some psychological measures have to be made sequentially and that the context generated by the first measure can influence responses to the next one, producing measurement order effects, and superposition, which suggests that some psychological states cannot be defined with respect to definite values but, instead, that all possible values within the superposition have some potential for being expressed. We present evidence showing how these two principles work together to provide a coherent explanation for many divergent and puzzling phenomena in psychology.