The problem of pursuing normative theories arises because we think the cognitive system is successful. This reasoning can be summarized in something like, to the extent that cognition is so successful, whichever formal principles it is based on must be normative. But the “success” of cognition is extremely context dependent. Cognitive processing seems optimized with respect to certain types of problems (e.g., Shepard Reference Shepard, Barkow, Cosmides and Tooby1992), but, equally, it seems less so for other problems. In other words, the success of cognitive processing is context dependent. For example, it is arguable whether cognitive processing is optimal in the Wason selection task. We can use information theory to explain why people behave in the way they do in such problems, as Oaksford and Chater (Reference Oaksford and Chater1994) did, but this does not alter the fact that this is a deductive problem which has a (deductively) correct answer. Indeed, if cognitive processing were optimal across the board, the world should be problem-free (or in any case have far fewer problems than we do now). For example, people should always choose the right mortgage, they should never succumb to gambling addiction, and policy decisions should always be well-thought out and optimal in terms of their respective objectives. Equally, depending on training, experience, and so on, different observers may approach the same decision-making situation in different ways. A certain apparent cognitive flexibility in reasoning and decision making appears highly adaptive and would seem to go against an assumption of an all-inclusive, prescriptive normativism. Thus, there are some genuine concerns regarding an assumption of a general prescriptive normativism.
So far we have simply shared some of the concerns of Elqayam & Evans (E&E) regarding prescriptive normativism. But then E&E proceed to argue that the pursuit of formal cognitive theories is consistent with a rejection of prescriptive normativism. It is here that we disagree. Let us first define a formal framework as a quantitative theory based on a set of interdependent axioms, such as Bayesianism, information theory, or Quantum probability (QP). Employing a formal framework for the description of cognitive processes basically implies adopting a set of interrelated postulates. Thus, to the extent that there is a belief that postulate A is psychologically relevant, then postulate B should be psychologically relevant as well. This is undeniably elegant in the sense that the framework as a whole can be tested. In other words, once a formal framework is adopted, then implied is a claim of internal prescriptive normativism, since it is assumed that all aspects of the formal framework have psychological relevance, at least with respect to a particular range of problems. To a large extent, this is exactly what is so appealing with approaches based on formal frameworks, such as logicism, Bayesianism, and information theory.
From such a perspective, as E&E note in their target article (sect. 7), it is not surprising that Gigerenzer and Todd did not justify their heuristics research program (Gigerenzer et al. 1999) on the basis of normative considerations. An individual heuristic, such as “take the best,” while undeniably successful, is just that: an individual heuristic. Its success is measured by its ability to outperform related heuristics. But it is not possible, for example, to justify such a heuristic in terms of related, manifestly true heuristics or computational intuitions. In other words, confidence in one heuristic does not usually imply confidence in another one; from a prior theoretical point of view, individual heuristics are somewhat interchangeable, even when they are highly successful (Gigerenzer et al. 1999).
Thus, overall, it appears that the pursuit of theories based on formal frameworks necessarily implies a limited, internal prescriptive normativism. We think that there is nothing contradictory in assigning a limited prescriptive normativism to Bayesianism, within a particular range of problems, as long as it is remembered that for an alternative range of problems Bayesianism may be a suboptimal framework. For example, some researchers have argued that for a certain range of decision-making problems, human behavior exhibits strong order or context effects and in such cases the QP theory is a more appropriate framework (e.g., Busemeyer et al. Reference Busemeyer, Wang and Townsend2006; Reference Busemeyer, Pothos, Franco and Trueblood2011; Pothos & Busemeyer Reference Pothos and Busemeyer2009; Trueblood & Busemeyer, in press). QP theory is like classical probability theory, but for the fact that probability assessment is order (and context) dependent. For example, P(A∧B)≠P(B∧A). QP theory has been applied very successfully in the case of physical observables, exactly because of these properties. The QP research program in psychology aims to explore its utility in analogous psychological situations (i.e., situations which exhibit order, context dependence).
Our argument implies a piecemeal view of prescriptive normativism, which is far from the general prescriptive normativism E&E argue against. Is piecemeal prescriptive normativism problematic? In a scientific tradition arguably more successful than ours, physics, there are several normative frameworks (in a physical sense), which though very successful in their limited domains, are actually formally mutually exclusive. The most famous example is general relativity, which assumes that space is curved, and quantum mechanics, which assumes that space is flat. Unfortunately for physicists, general relativity and quantum mechanics are mutually exclusive. While this is indeed the source of quite some frustration to physicists, it does not prevent them from doing extremely successful predictive science.
Therefore, overall, we think that cognitive scientists will continue to pursue theories based on formal frameworks, because of the elegance of building theories based upon a coherent theoretical framework. We also believe that inevitably this will lead to some limited prescriptive normativism, within particular ranges of problems. The scientific objective should then be one of establishing the range of applicability of different theories and indeed assessing the representational and process convenience of employing different theories in different domains (in cases where predictions of conflicting accounts converge; cf. Kuhn Reference Kuhn1962).
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The problem of pursuing normative theories arises because we think the cognitive system is successful. This reasoning can be summarized in something like, to the extent that cognition is so successful, whichever formal principles it is based on must be normative. But the “success” of cognition is extremely context dependent. Cognitive processing seems optimized with respect to certain types of problems (e.g., Shepard Reference Shepard, Barkow, Cosmides and Tooby1992), but, equally, it seems less so for other problems. In other words, the success of cognitive processing is context dependent. For example, it is arguable whether cognitive processing is optimal in the Wason selection task. We can use information theory to explain why people behave in the way they do in such problems, as Oaksford and Chater (Reference Oaksford and Chater1994) did, but this does not alter the fact that this is a deductive problem which has a (deductively) correct answer. Indeed, if cognitive processing were optimal across the board, the world should be problem-free (or in any case have far fewer problems than we do now). For example, people should always choose the right mortgage, they should never succumb to gambling addiction, and policy decisions should always be well-thought out and optimal in terms of their respective objectives. Equally, depending on training, experience, and so on, different observers may approach the same decision-making situation in different ways. A certain apparent cognitive flexibility in reasoning and decision making appears highly adaptive and would seem to go against an assumption of an all-inclusive, prescriptive normativism. Thus, there are some genuine concerns regarding an assumption of a general prescriptive normativism.
So far we have simply shared some of the concerns of Elqayam & Evans (E&E) regarding prescriptive normativism. But then E&E proceed to argue that the pursuit of formal cognitive theories is consistent with a rejection of prescriptive normativism. It is here that we disagree. Let us first define a formal framework as a quantitative theory based on a set of interdependent axioms, such as Bayesianism, information theory, or Quantum probability (QP). Employing a formal framework for the description of cognitive processes basically implies adopting a set of interrelated postulates. Thus, to the extent that there is a belief that postulate A is psychologically relevant, then postulate B should be psychologically relevant as well. This is undeniably elegant in the sense that the framework as a whole can be tested. In other words, once a formal framework is adopted, then implied is a claim of internal prescriptive normativism, since it is assumed that all aspects of the formal framework have psychological relevance, at least with respect to a particular range of problems. To a large extent, this is exactly what is so appealing with approaches based on formal frameworks, such as logicism, Bayesianism, and information theory.
From such a perspective, as E&E note in their target article (sect. 7), it is not surprising that Gigerenzer and Todd did not justify their heuristics research program (Gigerenzer et al. 1999) on the basis of normative considerations. An individual heuristic, such as “take the best,” while undeniably successful, is just that: an individual heuristic. Its success is measured by its ability to outperform related heuristics. But it is not possible, for example, to justify such a heuristic in terms of related, manifestly true heuristics or computational intuitions. In other words, confidence in one heuristic does not usually imply confidence in another one; from a prior theoretical point of view, individual heuristics are somewhat interchangeable, even when they are highly successful (Gigerenzer et al. 1999).
Thus, overall, it appears that the pursuit of theories based on formal frameworks necessarily implies a limited, internal prescriptive normativism. We think that there is nothing contradictory in assigning a limited prescriptive normativism to Bayesianism, within a particular range of problems, as long as it is remembered that for an alternative range of problems Bayesianism may be a suboptimal framework. For example, some researchers have argued that for a certain range of decision-making problems, human behavior exhibits strong order or context effects and in such cases the QP theory is a more appropriate framework (e.g., Busemeyer et al. Reference Busemeyer, Wang and Townsend2006; Reference Busemeyer, Pothos, Franco and Trueblood2011; Pothos & Busemeyer Reference Pothos and Busemeyer2009; Trueblood & Busemeyer, in press). QP theory is like classical probability theory, but for the fact that probability assessment is order (and context) dependent. For example, P(A∧B)≠P(B∧A). QP theory has been applied very successfully in the case of physical observables, exactly because of these properties. The QP research program in psychology aims to explore its utility in analogous psychological situations (i.e., situations which exhibit order, context dependence).
Our argument implies a piecemeal view of prescriptive normativism, which is far from the general prescriptive normativism E&E argue against. Is piecemeal prescriptive normativism problematic? In a scientific tradition arguably more successful than ours, physics, there are several normative frameworks (in a physical sense), which though very successful in their limited domains, are actually formally mutually exclusive. The most famous example is general relativity, which assumes that space is curved, and quantum mechanics, which assumes that space is flat. Unfortunately for physicists, general relativity and quantum mechanics are mutually exclusive. While this is indeed the source of quite some frustration to physicists, it does not prevent them from doing extremely successful predictive science.
Therefore, overall, we think that cognitive scientists will continue to pursue theories based on formal frameworks, because of the elegance of building theories based upon a coherent theoretical framework. We also believe that inevitably this will lead to some limited prescriptive normativism, within particular ranges of problems. The scientific objective should then be one of establishing the range of applicability of different theories and indeed assessing the representational and process convenience of employing different theories in different domains (in cases where predictions of conflicting accounts converge; cf. Kuhn Reference Kuhn1962).