Johnson, Bilovich, and Tuckett set out a framework for thinking about how humans make decisions under radical uncertainty. We confront radical uncertainty when there is no objective basis for attaching probabilities to different outcomes of decisions or where these outcomes are themselves subject to vagueness or ambiguity. They explicitly contrast their framework to “classical decision theory, [where] the currency of thought is probability and the driver of action is expected utility maximization” (target article, Fig. 1 legend). This description of classical decision theory is common but inaccurate.
Classical decision theory presents utility maximisation as a representation that can be made given the relevant axioms are met, not as the criteria by which choices are actually made. It is not so much a theory of decision-making as a theory about decision-making. In particular, these theories take it as axiomatic that the individual already knows what they want to do in every situation. The other axioms do not influence their choices but only constrain them.
Expected Utility Theory's (von Neumann & Morgenstern, Reference von Neumann and Morgenstern1953) axiom (3:A:a) is “the statement of the completeness of the system of individual preferences” over lotteries, which are “combinations of events with stated [i.e., objective] probabilities.” Savage (Reference Savage1954) developed a similar theory for subjective beliefs about probabilities.
Savage's axiom P1 states that there is “a simple ordering among acts.” Pfanzagl's (Reference Pfanzagl and Shubik1967) order axiom similarly assumes a complete order over wagers. Anscombe and Aumann (Reference Anscombe and Aumann1963) allow for both objective and subjective probabilities and state “we share with him [Savage] explicitly P1.” Schmeidler (Reference Schmeidler1989) allows subjective non-additive probabilities; his first axiom is a weak order over all acts. In all these utility theories maximising some function of utility is not “the driver of action”; decision-makers are assumed to already know what they want to do in any situation. We have criticised this assumption elsewhere (Kay & King, Reference Kay and King2020) and Aumann (Reference Aumann1962) shows formally how these theories become silent when it is dropped.
In contrast, Prospect Theory (Kahneman & Tversky, Reference Kahneman and Tversky1979) is represented as a theory of how decisions are made; prospects are valued by combining a decision weight (a function of objective or subjective probability) and the subjective value attached to a change from a reference level for each potential outcome. Although decision-makers are assumed to be able to value any prospect through this mechanism, Prospect Theory purports to explain how these values are reached, rather than merely representing them. (One could also claim that Prospect Theory is just a representation of an even more complex process.)
Many other theories of decision-making claim to deduce, or perhaps recommend, courses of action by assuming a particular goal for the decision-maker. Markowitz (Reference Markowitz1952) asserts that an optimal portfolio is constructed by finding the optimal point (for a subjective but consistently employed risk tolerance) on an efficient frontier of return-variance tradeoffs; various growth-optimal approaches assume the growth rate of wealth will be maximised. Elsewhere we have shown that in real situations growth optimality requires further psychological assumptions to actually predict behaviour (Ford & Kay, Reference Ford and Kay2022). Still other theories, such as minimax, assume an even simpler goal, for example, choose such that the worst-possible outcome is as good as it can be.
Still other theories are explicitly behavioural and thus describe only particular observed characteristics of real decision-making. For example, the anchoring effect – exposure to a particular, seemingly irrelevant number influences a subsequent decision – seems to demand a psychological explanation. Many such “biases” (or apparent violations of the axioms of subjective utility theory, as they are often defined in contrast to the predictions of a utility theory) have been posited.
With this taxonomy (Table 1), we see that the central economic theory of decision-making under uncertainty draws on no theory of psychology (beyond the naïve “people already know exactly what they want”). Given that assumption, the theory merely shows that, with certain restrictions, decision-making can be expressed in a mathematically tractable form. Other theories, often more influenced by psychology, do introduce assumptions about how decisions are actually made, albeit often retaining the assumptions that outcomes can be exhaustively listed and assigned probability-type measures.
Table 1. A comparison of different theories of decision-making under uncertainty
Thus the authors do both less and more than it appears. Less, in that their account of affective evaluation of outcomes is not so far removed from the theories they critique; more, in that by providing a psychological framework for how such evaluation occurs, they are providing an explanation for a process that some of those theories assume but are silent upon, and others cannot fully account for.
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Johnson, Bilovich, and Tuckett set out a framework for thinking about how humans make decisions under radical uncertainty. We confront radical uncertainty when there is no objective basis for attaching probabilities to different outcomes of decisions or where these outcomes are themselves subject to vagueness or ambiguity. They explicitly contrast their framework to “classical decision theory, [where] the currency of thought is probability and the driver of action is expected utility maximization” (target article, Fig. 1 legend). This description of classical decision theory is common but inaccurate.
Classical decision theory presents utility maximisation as a representation that can be made given the relevant axioms are met, not as the criteria by which choices are actually made. It is not so much a theory of decision-making as a theory about decision-making. In particular, these theories take it as axiomatic that the individual already knows what they want to do in every situation. The other axioms do not influence their choices but only constrain them.
Expected Utility Theory's (von Neumann & Morgenstern, Reference von Neumann and Morgenstern1953) axiom (3:A:a) is “the statement of the completeness of the system of individual preferences” over lotteries, which are “combinations of events with stated [i.e., objective] probabilities.” Savage (Reference Savage1954) developed a similar theory for subjective beliefs about probabilities.
Savage's axiom P1 states that there is “a simple ordering among acts.” Pfanzagl's (Reference Pfanzagl and Shubik1967) order axiom similarly assumes a complete order over wagers. Anscombe and Aumann (Reference Anscombe and Aumann1963) allow for both objective and subjective probabilities and state “we share with him [Savage] explicitly P1.” Schmeidler (Reference Schmeidler1989) allows subjective non-additive probabilities; his first axiom is a weak order over all acts. In all these utility theories maximising some function of utility is not “the driver of action”; decision-makers are assumed to already know what they want to do in any situation. We have criticised this assumption elsewhere (Kay & King, Reference Kay and King2020) and Aumann (Reference Aumann1962) shows formally how these theories become silent when it is dropped.
In contrast, Prospect Theory (Kahneman & Tversky, Reference Kahneman and Tversky1979) is represented as a theory of how decisions are made; prospects are valued by combining a decision weight (a function of objective or subjective probability) and the subjective value attached to a change from a reference level for each potential outcome. Although decision-makers are assumed to be able to value any prospect through this mechanism, Prospect Theory purports to explain how these values are reached, rather than merely representing them. (One could also claim that Prospect Theory is just a representation of an even more complex process.)
Many other theories of decision-making claim to deduce, or perhaps recommend, courses of action by assuming a particular goal for the decision-maker. Markowitz (Reference Markowitz1952) asserts that an optimal portfolio is constructed by finding the optimal point (for a subjective but consistently employed risk tolerance) on an efficient frontier of return-variance tradeoffs; various growth-optimal approaches assume the growth rate of wealth will be maximised. Elsewhere we have shown that in real situations growth optimality requires further psychological assumptions to actually predict behaviour (Ford & Kay, Reference Ford and Kay2022). Still other theories, such as minimax, assume an even simpler goal, for example, choose such that the worst-possible outcome is as good as it can be.
Still other theories are explicitly behavioural and thus describe only particular observed characteristics of real decision-making. For example, the anchoring effect – exposure to a particular, seemingly irrelevant number influences a subsequent decision – seems to demand a psychological explanation. Many such “biases” (or apparent violations of the axioms of subjective utility theory, as they are often defined in contrast to the predictions of a utility theory) have been posited.
With this taxonomy (Table 1), we see that the central economic theory of decision-making under uncertainty draws on no theory of psychology (beyond the naïve “people already know exactly what they want”). Given that assumption, the theory merely shows that, with certain restrictions, decision-making can be expressed in a mathematically tractable form. Other theories, often more influenced by psychology, do introduce assumptions about how decisions are actually made, albeit often retaining the assumptions that outcomes can be exhaustively listed and assigned probability-type measures.
Table 1. A comparison of different theories of decision-making under uncertainty
Thus the authors do both less and more than it appears. Less, in that their account of affective evaluation of outcomes is not so far removed from the theories they critique; more, in that by providing a psychological framework for how such evaluation occurs, they are providing an explanation for a process that some of those theories assume but are silent upon, and others cannot fully account for.
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This research received no specific grant from any funding agency, commercial or not-for-profit sectors.
Competing interest
None.