Why do we need quantum probability (QP) in place of classical probability (CP)? According to Pothos & Busemeyer (P&B), we need the QP technique to model “incompatible” questions, that is, when the states of the world are “potential” states that would collapse into concrete ones in light of interaction with other variables. This is similar to the famous Schrödinger's cat: The state of the cat is both dead and alive in the potential state, which becomes concrete only with further interaction. But if the questions are “compatible,” the CP technique would suffice.
P&B apply QP to the “context effect” as illustrated in the questions about happiness and employment. These questions are incompatible because the evaluation of one interferes with the evaluation of the other.
P&B, in turn, apply QP to the “order effect” and other biases such as the conjunction fallacy, similarity judgment, and Wason selection task. In these biases, incompatibility again arises because a particular appearance of a question influences the answer.
But is a particular appearance – as in the “order effect” – the same as the “context effect”? The order effect and other biases definitely share similarities with the context effect – which seem to justify the use of the same technique, namely, the QP technique in their case.
However, there is problem: What if the similarities between the appearance effect, such as the order effect, and the context effect are analogies rather than homologies, to use the familiar biological distinction? If they are analogies, the use of the same technique (whether CP or QP) for the analysis of both effects would amount to an “identificational slip” (Khalil Reference Khalil2000). One would commit an identificational slip if one mistakes an analogy for a homology – such as identifying the forearms of dolphins as “fins” or the forearms of bats as “wings” (Khalil Reference Khalil2000). To recall, the forearms of dolphins and bats are homologous because of common mammalian origin. In contrast, the forearms of dolphins and fish, or the forearms of bats and birds, are analogous because of common functions. One would commit an identification slip if one used the fin or the wing technique to describe how, respectively, dolphins swim or how bats fly. Therefore, do P&B commit an identificational slip when they use the QP technique to describe the order effect (and other biases)?
First, what is the initial intuition behind QP? It is designed to model potentiality in nature, with implications with regard to the specification of meaning of what is observed by the sense, including the meaning of observed actions in relation to goals. The latter has ramifications for the understanding of internal motivation, self-esteem, and entrepreneurship (see Khalil Reference Khalil1997a; Reference Khalil1997b; Reference Khalil2010). Such potentiality is a “context,” which becomes concrete with interaction.
Do the biases marshaled by P&B as candidates for QP involve potentiality; a potentiality found in the context effect? With respect to the order effect, do we have a potentiality issue?
When subjects are presented with A and B – for example, “Is Clinton honest?” and “Is Gore honest?” – they give different answers, depending on the order of A and B. The questions A and B invoke symmetrical and independent information. Information with regard to each question can be evaluated without the appeal to the other. But this is not the case with the employment and happiness questions. If you ask if one is happy, the evaluation must depend on another question, such as employment, because one must be happy about something. But if you ask “Is Clinton honest?” the evaluation need not depend on the honesty of Gore. Insofar as the Gore question exercises influence on how to assess Clinton (i.e., the order effect), it must have acted as a fast and frugal metric. Therefore, A and B cannot be “incompatible” questions: The presence of A does not act as a context for B. There is no potentiality that becomes concrete once the other piece is present.
It is simply that each metric has its own memories or heuristics. P&B dismiss such an explanation, but it can be related to Herbert Simon's “bounded rationality.” For Simon, the person has limited cognitive resources, and hence has to use rules of thumb to make decisions. Such rules of thumb are fast ways to look at a problem when the stakes are not high. That is, such rules of thumb are actually efficient, which explains why standard economists welcome Simon's notion of bounded rationality. To wit, if the stakes are high, people usually review and replace the existing rule of thumb (Baron Reference Baron2008, Ch. 6). People are even ready to correct their errors of logical reasoning, as in the Wason selection task or the famous Linda in the conjunction fallacy, once they are given extra time for reflection and cognition.
Such correction would not be possible if the order effect were similar to the context effect in a substantial (homologous) sense. But what is “context”? It is the outcome of the neural principle when it specifies the background, which allows the comprehension of the foreground data; similar to how the brain selects the background in Rubin's vase. The principle that specifies the background cannot be “corrected” by data because it is not a datum. The background acts as a context that affords “meaning” or, as discussed earlier, a “potentiality” of what the observed thing can become.
An example of the context effect is the “gain frame” versus the “loss frame” in the Asian disease experiment: Two medical remedies are presented to deal with an Asian disease: one remedy has a certain outcome in terms of saved lives or prevention from death, whereas the other has uncertain outcomes. The uncertain remedy has an expected value equal to the certain remedy. Subjects usually chose the certain remedy if the results were couched as “saving lives” rather than “preventing death,” that is, using the “gain frame,” but subjects usually chose the uncertain remedy if the results were couched in the other way, that is, using the “loss frame.”
LeBoeuf and Shafir (Reference LeBoeuf and Shafir2003) showed that subjects, once exposed to a context, would not generally “correct” the choice if given more time to reflect, even if such subjects had scored high on the “need for cognition” test, that is, enjoyed cognitive pursuits (Cacioppo & Petty Reference Cacioppo and Petty1982). This confirms that context is not a datum to be corrected. The context is rather a background that provides meaning to the foreground, content. The context and content are asymmetrical, that is, stand dependently on each other. This is contrary to the Gore/Clinton test in which A and B are symmetrical, that is, stand independently of each other. Therefore, the context effect is radically different from the order effect.
Therefore, P&B commit an identificational slip: they confuse analogies with homologies. The same technique (whether CP or QP) cannot apply to the context effect, on the one hand, and to the order effect and its associated biases, on the other.
Why do we need quantum probability (QP) in place of classical probability (CP)? According to Pothos & Busemeyer (P&B), we need the QP technique to model “incompatible” questions, that is, when the states of the world are “potential” states that would collapse into concrete ones in light of interaction with other variables. This is similar to the famous Schrödinger's cat: The state of the cat is both dead and alive in the potential state, which becomes concrete only with further interaction. But if the questions are “compatible,” the CP technique would suffice.
P&B apply QP to the “context effect” as illustrated in the questions about happiness and employment. These questions are incompatible because the evaluation of one interferes with the evaluation of the other.
P&B, in turn, apply QP to the “order effect” and other biases such as the conjunction fallacy, similarity judgment, and Wason selection task. In these biases, incompatibility again arises because a particular appearance of a question influences the answer.
But is a particular appearance – as in the “order effect” – the same as the “context effect”? The order effect and other biases definitely share similarities with the context effect – which seem to justify the use of the same technique, namely, the QP technique in their case.
However, there is problem: What if the similarities between the appearance effect, such as the order effect, and the context effect are analogies rather than homologies, to use the familiar biological distinction? If they are analogies, the use of the same technique (whether CP or QP) for the analysis of both effects would amount to an “identificational slip” (Khalil Reference Khalil2000). One would commit an identificational slip if one mistakes an analogy for a homology – such as identifying the forearms of dolphins as “fins” or the forearms of bats as “wings” (Khalil Reference Khalil2000). To recall, the forearms of dolphins and bats are homologous because of common mammalian origin. In contrast, the forearms of dolphins and fish, or the forearms of bats and birds, are analogous because of common functions. One would commit an identification slip if one used the fin or the wing technique to describe how, respectively, dolphins swim or how bats fly. Therefore, do P&B commit an identificational slip when they use the QP technique to describe the order effect (and other biases)?
First, what is the initial intuition behind QP? It is designed to model potentiality in nature, with implications with regard to the specification of meaning of what is observed by the sense, including the meaning of observed actions in relation to goals. The latter has ramifications for the understanding of internal motivation, self-esteem, and entrepreneurship (see Khalil Reference Khalil1997a; Reference Khalil1997b; Reference Khalil2010). Such potentiality is a “context,” which becomes concrete with interaction.
Do the biases marshaled by P&B as candidates for QP involve potentiality; a potentiality found in the context effect? With respect to the order effect, do we have a potentiality issue?
When subjects are presented with A and B – for example, “Is Clinton honest?” and “Is Gore honest?” – they give different answers, depending on the order of A and B. The questions A and B invoke symmetrical and independent information. Information with regard to each question can be evaluated without the appeal to the other. But this is not the case with the employment and happiness questions. If you ask if one is happy, the evaluation must depend on another question, such as employment, because one must be happy about something. But if you ask “Is Clinton honest?” the evaluation need not depend on the honesty of Gore. Insofar as the Gore question exercises influence on how to assess Clinton (i.e., the order effect), it must have acted as a fast and frugal metric. Therefore, A and B cannot be “incompatible” questions: The presence of A does not act as a context for B. There is no potentiality that becomes concrete once the other piece is present.
It is simply that each metric has its own memories or heuristics. P&B dismiss such an explanation, but it can be related to Herbert Simon's “bounded rationality.” For Simon, the person has limited cognitive resources, and hence has to use rules of thumb to make decisions. Such rules of thumb are fast ways to look at a problem when the stakes are not high. That is, such rules of thumb are actually efficient, which explains why standard economists welcome Simon's notion of bounded rationality. To wit, if the stakes are high, people usually review and replace the existing rule of thumb (Baron Reference Baron2008, Ch. 6). People are even ready to correct their errors of logical reasoning, as in the Wason selection task or the famous Linda in the conjunction fallacy, once they are given extra time for reflection and cognition.
Such correction would not be possible if the order effect were similar to the context effect in a substantial (homologous) sense. But what is “context”? It is the outcome of the neural principle when it specifies the background, which allows the comprehension of the foreground data; similar to how the brain selects the background in Rubin's vase. The principle that specifies the background cannot be “corrected” by data because it is not a datum. The background acts as a context that affords “meaning” or, as discussed earlier, a “potentiality” of what the observed thing can become.
An example of the context effect is the “gain frame” versus the “loss frame” in the Asian disease experiment: Two medical remedies are presented to deal with an Asian disease: one remedy has a certain outcome in terms of saved lives or prevention from death, whereas the other has uncertain outcomes. The uncertain remedy has an expected value equal to the certain remedy. Subjects usually chose the certain remedy if the results were couched as “saving lives” rather than “preventing death,” that is, using the “gain frame,” but subjects usually chose the uncertain remedy if the results were couched in the other way, that is, using the “loss frame.”
LeBoeuf and Shafir (Reference LeBoeuf and Shafir2003) showed that subjects, once exposed to a context, would not generally “correct” the choice if given more time to reflect, even if such subjects had scored high on the “need for cognition” test, that is, enjoyed cognitive pursuits (Cacioppo & Petty Reference Cacioppo and Petty1982). This confirms that context is not a datum to be corrected. The context is rather a background that provides meaning to the foreground, content. The context and content are asymmetrical, that is, stand dependently on each other. This is contrary to the Gore/Clinton test in which A and B are symmetrical, that is, stand independently of each other. Therefore, the context effect is radically different from the order effect.
Therefore, P&B commit an identificational slip: they confuse analogies with homologies. The same technique (whether CP or QP) cannot apply to the context effect, on the one hand, and to the order effect and its associated biases, on the other.