Throughout the target article, Rahnev & Denison (R&D) employ the likelihood function, prior, cost function, and decision rule (LPCD) framework, as they analyze the (sub)optimality of perceptual decision making in terms of the likelihood of the world state (i.e., stimulus) given the internal “signal” (i.e., perceptual experience); the prior probability of that world state; the cost function of an action given the world state; and the decision rule used to determine what action to take in light of the other three components. This framework is mathematically derived from models of Bayesian decision making and mirrors much of the language – mathematical and conceptual – used by proponents of optimality in perceptual decision making. Over the course of their target article, however, R&D shift between two different interpretations of this mathematical framework and thereby provide a positive proposal that does not follow from their empirical survey.
For the first four sections of the target article, R&D use the LPCD framework as an analytical tool to decompose the complex behavioral functions identified in the many experiments that they survey. In general, people's decisions are a complicated function of the current environment, task demands, internal constraints (e.g., memory or attention), perceptual history, and more. R&D briefly discuss the complexity, and so possible computational intractability, of the optimal function, but of course, our actual perceptual decision functions are also incredibly complicated. The LPCD framework provides a way to decompose this complicated behavioral function into tractable, interpretable components.
This use of the LPCD framework is analogous to a Fourier decomposition of a complex waveform into a set (possibly infinite) of component sine waves of varying frequency and amplitude. Importantly, those component sine waves need not correspond to any underlying causal or generative processes; they are simply a more tractable way to understand the input waveform. Similarly, we can use the LPCD framework as an analytical tool to decompose people's perceptual decision functions into those four components, without thereby thinking that the LPCD components correspond to anything in the perceptual or cognitive system. Those mathematical components are only relatively simpler functions that jointly provide accurate (and sometimes, rationally defensible) predictions.
In section 5.1, however, R&D shift to using LPCD in a very different way. In particular, they start to interpret the four components realistically, as elements that are really present in the mind/brain. For example, they propose that we should search for hypotheses about the content, functional form, or source of particular LPCD components, where those are understood to be represented internally (LPC) or actually used to make a decision (D). That is, R&D no longer use LPCD solely as an analytical tool, but rather interpret the components as psychologically real. For example, many of the hypotheses in their Table 1 treat the LPCD components as discrete psychological or neurally encoded elements that can be independently measured and manipulated by researchers. They are not simply a useful way of mathematically decomposing a complex behavioral function, but are presumed to be legitimate targets of direct scientific inquiry.
R&D might well be right that the LPCD components are psychologically real and can be shaped or influenced in various ways. For example, some of the cited papers that develop optimality models of perceptual decision making also provide evidence for the psychological reality (and modularity) of one or another element in a Bayesian model. However, R&D do not base their realist commitments on those studies, but rather on extrapolation from the structure they propose for observer models. But if we do not have a background assumption of optimality (or near optimality), then we need not assume that perceptual decision making decomposes, in any realist sense, into the LPCD components. Mathematical decompositions do not necessarily provide a guide to underlying causal or psychological processes. For example, the function f(x, y) = x 2 − y 2 can be mathematically decomposed into x 2 and y 2 “modules,” but that does not imply that the underlying system actually computes x 2 and y 2 in distinct components and then subtracts the results. The system could just as easily have components that compute (x + y) and (x – y) and then multiply the results. Or the function could be actually computed in many other ways.
Moreover, the realist commitments in section 5 are not idle, but rather can have real impacts. As R&D note, there are many different types of models that we might consider, not only Bayesian or LPCD-based models. Nonetheless, R&D's positive proposal involves viewing all of these proposals through the LPCD lens and, therefore, privileging that particular decomposition of the complex perceptual decision-making function, even if the mind/brain does not actually work that way. Of course, all science requires some theoretical commitments, but there is well-known value in having variation across the scientific community. In contrast, R&D propose that the LPCD components, in the form of standard observer models, should be the default theoretical framework for this research domain.
R&D demonstrate the utility of the LPCD framework as a tool for identifying suboptimal behaviors. They do not, however, provide reason to prefer substantive psychological hypotheses that are expressed with LPCD components, and so their positive proposal about how to advance the science risks placing unnecessary constraints on our theorizing.
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Throughout the target article, Rahnev & Denison (R&D) employ the likelihood function, prior, cost function, and decision rule (LPCD) framework, as they analyze the (sub)optimality of perceptual decision making in terms of the likelihood of the world state (i.e., stimulus) given the internal “signal” (i.e., perceptual experience); the prior probability of that world state; the cost function of an action given the world state; and the decision rule used to determine what action to take in light of the other three components. This framework is mathematically derived from models of Bayesian decision making and mirrors much of the language – mathematical and conceptual – used by proponents of optimality in perceptual decision making. Over the course of their target article, however, R&D shift between two different interpretations of this mathematical framework and thereby provide a positive proposal that does not follow from their empirical survey.
For the first four sections of the target article, R&D use the LPCD framework as an analytical tool to decompose the complex behavioral functions identified in the many experiments that they survey. In general, people's decisions are a complicated function of the current environment, task demands, internal constraints (e.g., memory or attention), perceptual history, and more. R&D briefly discuss the complexity, and so possible computational intractability, of the optimal function, but of course, our actual perceptual decision functions are also incredibly complicated. The LPCD framework provides a way to decompose this complicated behavioral function into tractable, interpretable components.
This use of the LPCD framework is analogous to a Fourier decomposition of a complex waveform into a set (possibly infinite) of component sine waves of varying frequency and amplitude. Importantly, those component sine waves need not correspond to any underlying causal or generative processes; they are simply a more tractable way to understand the input waveform. Similarly, we can use the LPCD framework as an analytical tool to decompose people's perceptual decision functions into those four components, without thereby thinking that the LPCD components correspond to anything in the perceptual or cognitive system. Those mathematical components are only relatively simpler functions that jointly provide accurate (and sometimes, rationally defensible) predictions.
In section 5.1, however, R&D shift to using LPCD in a very different way. In particular, they start to interpret the four components realistically, as elements that are really present in the mind/brain. For example, they propose that we should search for hypotheses about the content, functional form, or source of particular LPCD components, where those are understood to be represented internally (LPC) or actually used to make a decision (D). That is, R&D no longer use LPCD solely as an analytical tool, but rather interpret the components as psychologically real. For example, many of the hypotheses in their Table 1 treat the LPCD components as discrete psychological or neurally encoded elements that can be independently measured and manipulated by researchers. They are not simply a useful way of mathematically decomposing a complex behavioral function, but are presumed to be legitimate targets of direct scientific inquiry.
R&D might well be right that the LPCD components are psychologically real and can be shaped or influenced in various ways. For example, some of the cited papers that develop optimality models of perceptual decision making also provide evidence for the psychological reality (and modularity) of one or another element in a Bayesian model. However, R&D do not base their realist commitments on those studies, but rather on extrapolation from the structure they propose for observer models. But if we do not have a background assumption of optimality (or near optimality), then we need not assume that perceptual decision making decomposes, in any realist sense, into the LPCD components. Mathematical decompositions do not necessarily provide a guide to underlying causal or psychological processes. For example, the function f(x, y) = x 2 − y 2 can be mathematically decomposed into x 2 and y 2 “modules,” but that does not imply that the underlying system actually computes x 2 and y 2 in distinct components and then subtracts the results. The system could just as easily have components that compute (x + y) and (x – y) and then multiply the results. Or the function could be actually computed in many other ways.
Moreover, the realist commitments in section 5 are not idle, but rather can have real impacts. As R&D note, there are many different types of models that we might consider, not only Bayesian or LPCD-based models. Nonetheless, R&D's positive proposal involves viewing all of these proposals through the LPCD lens and, therefore, privileging that particular decomposition of the complex perceptual decision-making function, even if the mind/brain does not actually work that way. Of course, all science requires some theoretical commitments, but there is well-known value in having variation across the scientific community. In contrast, R&D propose that the LPCD components, in the form of standard observer models, should be the default theoretical framework for this research domain.
R&D demonstrate the utility of the LPCD framework as a tool for identifying suboptimal behaviors. They do not, however, provide reason to prefer substantive psychological hypotheses that are expressed with LPCD components, and so their positive proposal about how to advance the science risks placing unnecessary constraints on our theorizing.