Pothos & Busemeyer (P&B) make clear that quantum probability (QP) theory offers a rich array of theoretical constructs, such as superposition, entanglement, incompatibility, and interference, which can help explain human judgment. The authors illustrate how these concepts, which are strongly contrasted with the basic tenets of classical probability (CP) theory, can be used to accommodate aspects of human choice that deviate from normative CP accounts. For example, the conjunction fallacy is explained in terms of incompatible questions requiring sequential evaluation, which induces an interference effect.
Although new frameworks can provide novel insights, one worry is that QP will recapitulate some of the shortcomings of rational CP approaches by sticking to a computational-level analysis. To the authors' credit, they acknowledge how notions of optimality in CP approaches can be impoverished and not match the goals of the decision maker. However, these criticisms largely serve to question CP's status as the preferred normative account rather than question the wisdom of eschewing process-level considerations in favor of a computational-level analysis.
In a recent article with Jones (Jones & Love Reference Jones and Love2011), we, too, critiqued rational (Bayesian) CP approaches to explaining human cognition, but our critique was broader in scope. Although many of our points are particular to the rational Bayesian program (which we refer to as “Bayesian Fundamentalism”), some of the central critiques apply equally well to any approach largely formulated at the computational level. The basic issue is that such accounts wall off a tremendous amount of related data and theory in the cognitive sciences, including work in attention, executive control, embodiment, and cognitive neuroscience, as well as any study using response time measures. It seems unlikely that a complete theory of cognition or decision making can be formulated when neglecting these insights and important constraints.
The suggestion offered in Jones and Love (Reference Jones and Love2011), which we referred to as “Bayesian Enlightenment,” is to integrate probability and mechanistic approaches. In the context of QP, one could imagine construing operations, such as projections to subspaces, as psychological operations that unfold in time, may have brain correlates, be limited in capacity, and change over development. Such an approach would retain the distinctive characteristics of QP while linking to existing theory and data.
Grounding QP in mechanism may offer a number of other advantages, such as better motivating the assumptions (that are psychological in nature) that make QP successful. Many of the effects considered in the target article require assumptions on the order in which statements are considered and the role context plays. These topics may be addressed in a principled manner when situated within a mechanism that aims to explain shifts in focus or attention. Such mechanistic models would also make clear what role QP plays in accounting for the results, as opposed to the ancillary assumptions.
The authors note that one key challenge is to anticipate new findings rather than simply accommodate existing data. Grounding QP ideas in mechanism may facilitate making a priori predictions. Once the move to mechanism is made, second generation questions can be asked, such as which QP model best accounts for human judgment. My guess is that moving away from evaluating general frameworks to testing specific proposals will hasten progress. As the authors note, it is very difficult to invalidate an entire framework, as ancillary assumptions can always be made (e.g., CP models can be modified to account for the main findings in the target article). In contrast, particular models can be evaluated using model selection procedures.
My prediction is that moving toward evaluating particular models grounded in mechanism will lead to a rapprochement between QP and CP approaches. For a view that allows for superposition, many aspects of the QP are very rigid. For example, according to the approach advocated by the authors, statements are either compatible or incompatible. One possibility is that successful models will be more fluid and include a mixture of states, which is a notion from CP. Given the complexities of human cognition and decision making, it would be surprising if one unadulterated formalism carried the day. Although physics undergraduates may complain about how confusing QP is, human cognition will likely prove more vexing.
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Pothos & Busemeyer (P&B) make clear that quantum probability (QP) theory offers a rich array of theoretical constructs, such as superposition, entanglement, incompatibility, and interference, which can help explain human judgment. The authors illustrate how these concepts, which are strongly contrasted with the basic tenets of classical probability (CP) theory, can be used to accommodate aspects of human choice that deviate from normative CP accounts. For example, the conjunction fallacy is explained in terms of incompatible questions requiring sequential evaluation, which induces an interference effect.
Although new frameworks can provide novel insights, one worry is that QP will recapitulate some of the shortcomings of rational CP approaches by sticking to a computational-level analysis. To the authors' credit, they acknowledge how notions of optimality in CP approaches can be impoverished and not match the goals of the decision maker. However, these criticisms largely serve to question CP's status as the preferred normative account rather than question the wisdom of eschewing process-level considerations in favor of a computational-level analysis.
In a recent article with Jones (Jones & Love Reference Jones and Love2011), we, too, critiqued rational (Bayesian) CP approaches to explaining human cognition, but our critique was broader in scope. Although many of our points are particular to the rational Bayesian program (which we refer to as “Bayesian Fundamentalism”), some of the central critiques apply equally well to any approach largely formulated at the computational level. The basic issue is that such accounts wall off a tremendous amount of related data and theory in the cognitive sciences, including work in attention, executive control, embodiment, and cognitive neuroscience, as well as any study using response time measures. It seems unlikely that a complete theory of cognition or decision making can be formulated when neglecting these insights and important constraints.
The suggestion offered in Jones and Love (Reference Jones and Love2011), which we referred to as “Bayesian Enlightenment,” is to integrate probability and mechanistic approaches. In the context of QP, one could imagine construing operations, such as projections to subspaces, as psychological operations that unfold in time, may have brain correlates, be limited in capacity, and change over development. Such an approach would retain the distinctive characteristics of QP while linking to existing theory and data.
Grounding QP in mechanism may offer a number of other advantages, such as better motivating the assumptions (that are psychological in nature) that make QP successful. Many of the effects considered in the target article require assumptions on the order in which statements are considered and the role context plays. These topics may be addressed in a principled manner when situated within a mechanism that aims to explain shifts in focus or attention. Such mechanistic models would also make clear what role QP plays in accounting for the results, as opposed to the ancillary assumptions.
The authors note that one key challenge is to anticipate new findings rather than simply accommodate existing data. Grounding QP ideas in mechanism may facilitate making a priori predictions. Once the move to mechanism is made, second generation questions can be asked, such as which QP model best accounts for human judgment. My guess is that moving away from evaluating general frameworks to testing specific proposals will hasten progress. As the authors note, it is very difficult to invalidate an entire framework, as ancillary assumptions can always be made (e.g., CP models can be modified to account for the main findings in the target article). In contrast, particular models can be evaluated using model selection procedures.
My prediction is that moving toward evaluating particular models grounded in mechanism will lead to a rapprochement between QP and CP approaches. For a view that allows for superposition, many aspects of the QP are very rigid. For example, according to the approach advocated by the authors, statements are either compatible or incompatible. One possibility is that successful models will be more fluid and include a mixture of states, which is a notion from CP. Given the complexities of human cognition and decision making, it would be surprising if one unadulterated formalism carried the day. Although physics undergraduates may complain about how confusing QP is, human cognition will likely prove more vexing.