a The Akerlof–Kranton Initiative

Until Akerlof and Kranton’s “Economics and Identity” paper imported the concept of social group identity from social psychology into economics (2000; see also Akerlof and Kranton, Reference Akerlof and Kranton2002, Reference Akerlof and Kranton2005, Reference Akerlof and Kranton2010), the concept of identity was hardly employed at all in economics.Footnote ¹ Psychology, sociology, and anthropology had long employed social identity concepts in decades of empirical research devoted to determining the conditions under which people’s social relationships influence their behavior. In psychology’s social identity theory, people were shown to often change their behavior when influenced by the social groups to which they belonged. From an agency perspective, group interests then supplant or modify individual interests, and individuals accordingly do not always act as distinct and independent agents. Thus, importing the identity concept into economics came with significant challenges to the mainstream’s long-standing commitment to the idea that only individuals are agents.

Akerlof and Kranton creatively addressed these challenges by saying a person’s individual identity is their utility function, and then arguing that how people’s social group identities mattered to them influenced how they individually maximized utility (Akerlof and Kranton, Reference Akerlof and Kranton2000; Davis, Reference Davis2007a). People could indeed be concerned about and influenced in their choices by their social identities, or by the different social identity categories they believed applied to them (what Akerlof and Kranton called a person’s “sense of self”), but this was simply another individual concern, or type of preference, that could be traded off against others they had in maximizing individual utility. Having social identities could have a place in economics, but in contrast to psychology’s social identity theory individuals still always made all their own choices. In identity terms, maximizing one’s utility was what identified a person as an individual agent.

In this respect, Akerlof and Kranton followed a well-established path earlier adopted in the social preferences literature that in a similar way had added a variety of different types of social preferences – for example, inequality aversion (Engelmann and Strobel, Reference Engelmann and Strobel2004) – to the utility function alongside the traditional self-regarding ones. However, this literature makes no special claims about the nature of individual identity. Akerlof–Kranton went further in implicitly making an ontological claim that people still had independent individual identities even when their social relationships significantly affected their behavior. Faced with the possibility that people could be strongly socially embedded, they simply fit the identity concept into the individual utility function – a bold, strategic move securing economics’ traditional domain of investigation.Footnote ²

Yet surely this does not fully capture how the world works since there are many well-recognized circumstances in which people make other people’s choices for them, even when they say those choices are their own. Trivially, parents often make “choices” for their children, who learn to take them as their own. More importantly, across a whole range of social settings people make choices for others when they act as their delegates, representatives, and agents. Economics generally explains this in a way that assumes people still make all their own choices, such as in heroic interpretations of principal–agent theory that dismisses the idea that agents substitute their preferences for their principles’ preferences. But in a world of specialized skills in which expertise is unevenly distributed, it seems there are many occasions when people identify with others who they allow to make decisions replacing their own.

Thus, in regarding an individual’s utility function as a person’s individual identity – or as their personal identity – Akerlof and Kranton open the door to our asking whether the utility function as a conception of individual identity successfully identifies people as distinct and independent individuals. Does being a utility maximizer make one an individual? Why many mainstream economists seem to assume so is because utility maximizers by definition always maximize only their own individual preferences, not someone else’s preferences. Yet notice that groups of individuals such as firms are also often said to maximize objective functions akin to utility functions. How, then, can utility maximization name and refer to single individuals and groups of individuals at the same time? Does utility maximization identify both individuals and groups, or either … or neither?

b The Fallacy of Self-Reference

This calls for us to be clear about how the utility function individual identity conception needs to be stated if it is at least to identify single persons as distinct and independent individuals. Given that in many circumstances, people make choices for others, to say having a utility function makes a person a distinct and independent individual can only mean that their preferences and the utility function a person acts on are always that person’s own preferences and utility function, not someone else’s.Footnote ³

However, this leads to a problem. To say that what distinguishes a person as an independent individual is something specific to that person, which is what using the word “own” does, simply assumes in a circular way the conclusion that needs to be shown. That is, in saying what distinguishes a person as an independent individual is what is specific to that person just says what distinguishes that person as an independent individual is what makes them an independent individual. There are two ways, then, of seeing what the problem is here.

First, the underlying reasoning constitutes an example of a well-known form of fallacious inference known as affirming the consequent. Affirming the consequent occurs when for “If P, then Q” where Q is assumed to be true, we mistakenly infer that P must also be true.Footnote ⁴

For the “own utility function” conception of the person, the fallacious inference is given in Box 2.1. We may hold that [2] is true, and that people can act as independent individuals. However, [3] does not follow. Why is straightforward. What inferences that affirm the consequent do wrong is exclude other possibilities that might explain why we might hold something like [2]. For that reason, such inferences are fallacious and are to be avoided. At the same time, this does not mean that we cannot infer something like [2], as I will show below in connection with an example of a valid inference taken from Ronald Coase.

Second, what else is problematic here is that the “own utility function” conception commits a version of what is known as the self-reference problem (Bolander, Reference Bolander2017). In philosophy, logic, and mathematics, self-reference occurs when a concept or conceptual system reflexively refers only to itself rather than what it is supposed to be about and thus fails to generate any explanation of what it is supposed to be about. An example from economics is J.M. Keynes’s (Reference Keynes1936) famous “beauty contest” where speculators try to determine the value of an investment based on what other speculators think about it. All one gets is a circular set of expectations empty of any determination of value of the investment. Another example from game theory is the “Holmes–Moriarty” problem in which two hyperrational players circularly refer to each other’s strategies in determining their own strategies (Koppl and Rosser, Reference Koppl and Rosser2002). Holmes’ strategy is based on Moriarty’s strategy, but Moriarty’s is based on Holmes’ strategy, etc. Self-reference problems, then, not only fail to explain what subjects they are about, but can also generate sparadoxes, such as the famous Cretan liar paradox and “intractability” or “insolvability” of Gödel’s incompleteness-type problems.Footnote ⁵

Generally, then, the names we use refer to things other than themselves. A self-referential expression, however, refers not to something in the world but in a circular way to itself. When we speak of a person’s utility function as their own utility function what are we referring to? We are just referring to the idea of a utility function. While the expression is meant to refer to real-world individuals and explain something about them in the content it ascribes to them as utility maximizers, it only refers to that idea itself.

A consequence of self-referentiality is that nothing essentially constrains us from arbitrarily applying this expression to anything in the world that one might like to claim has utility maximizing behavior regardless of whether it does. I suggest this partly underlies the tremendous versatility and appeal of utility function reasoning in mainstream economics. Since the idea does not hook onto the world, it can be applied to whatever economists might want to call an agent: individual people, parts of people, groups of people, other animals, machines, nations, organizations, governments, communities, etc.

As Simon said more generally of rationality theory: “It is a gun for hire that can be employed in the service of any goals we have, good or bad” (Simon, Reference Simon1983, pp. 7–8). What such expressions in economics need to do to avoid the self-reference problem, then, is be formulated in such a way as to instead refer to things other than themselves. Then, we may ask whether those expressions as they are formulated also successfully identify distinct and independent things. As an example of where this is done successfully, consider how Ronald Coase formulated and defined the firm as a distinct and independent thing.

For Coase, a firm is not defined as a collection of its own characteristics, say, its own assets as some might assume, but rather as a “collection of nonmarket exchanges” (Coase, Reference Coase1937) – an expression that does not refer in a self-referencing way to what it defines. Instead, the idea of “nonmarket exchanges” – how people trade with one another without going through markets – describes something we can observe about the world without referring to firms to do so. Then we can observe there appear to exist distinct and independent collections of nonmarket exchanges, associate some of them with what economists call business firms based on the activities they exhibit, and name these particular collections as distinct and independent firms.

The inference involved in Coase’s case is not the fallacious affirming the consequent inference, but rather the mainstay of inferential reasoning, the valid modus ponens inference that affirms the antecedent (Box 2.2): Here, we affirm the antecedent, not the consequent, and thus validly infer [6] from [4] and [5]. We can of course debate whether we observe distinguishable collections of nonmarket exchanges and also the merits of Coase’s definition of the firm as such a collection. However, in identity terms he provides a good example of a definition of an independent individual (indeed a multi-person one) that avoids the self-reference problem.

Coase’s example tells us something important about successful individual conceptions in economics. To avoid self-reference, they cannot be formulated strictly in terms of individual or “own” characteristics. It follows that they need to make some sort of reference to people’s nonindividual or social characteristics. Coase’s “collections of nonmarket exchanges” definition does this by interpreting the individual firm as essentially a kind of social network. Firms are independent (multi-person) single individuals because they are certain kinds of distinct and independent networks of people. The same reasoning can also be applied to other kinds of things made up of many individuals, such as institutions, communities, governments, etc.

I hold, then, that this lesson applies to single persons as well as to collections of individuals. A non–self-referential definition of individuals which successfully identifies them as single persons needs to define them in terms of other than strictly individual characteristics. Like Coase’s firms, we might say persons are “collections of relationships” that are different and distinguishable from one another that we can observe in examining the world. When we use the name individual to refer to a person and identify them through these relationships, ontologically speaking we employ a relational conception of individual identity, not an atomistic one, that makes individuals socially embedded, not unembedded beings. I lay out such a conception for economics in Chapter 4.

One reason perhaps why the “own utility function” individual conception has had so much appeal in economics – an epistemological one – is that it eases construction of formalized explanations and modeling in economics (as discussed in Chapter 1). Since it is formulated only in terms of the concept of preference, it is comparatively simple logically to work out a complete account of behavior based upon elaborating a set of consistent logical axioms governing it. This was done relatively early in the development of formal utility reasoning, culminating in the “von Neumann–Morgenstern utility function theorem” which states that if the axioms of completeness, transitivity, independence, and continuity are all satisfied, any set of preferences is “well ordered” and can be represented by a distinct (monotonic) individual utility function (von Neumann and Morgenstern, Reference von Neumann and Morgenstern1944).

In contrast, a socially embedded individual explanation is more complicated because it needs to be formulated in terms of two different types of characteristics of people – their individual and social characteristics. How these two types of characteristics are related cannot be explained in a purely abstract, logical “well-ordered” way, and calls for empirical as well as theoretical investigation. This is one way to think about the emergence of experimental economics, which has investigated empirical disconfirmations of the standard axioms underlying the utility function individual conception.Footnote ⁶ But we still need a theoretical understanding of how people’s individual and social interests or characteristics relate to one another. A possible pathway that may address this is representative agent theory. In fact, the concept of a representative agent is employed in both mainstream economics and social identity theory, which I compare in Section c.

c Representative Agents in Social Identity Theory and Mainstream Economics

Social identity theorists argue that, as members of social groups, people may appear to act as individuals and appear to behave independently, but instead often act as others would have them act and as the interests of those groups dictate. They thus act and choose from the perspective of those groups, engage in “in-group” behavior, and function as representative agents of those groups (Tajfel and Turner, Reference Tajfel, Turner, Worchel and Austin1986). They are still nominally independent individuals, but in acting as representative agents of social groups they put social interests ahead of their individual interests. Empirical research on this dates back in the early postwar period to the famous 1950s “Robbers Cave” experiment, which showed that especially when individuals find themselves in uncertain, zero-sum-type situations, they can act in the interest of social groups rather than as independent individuals (Sherif et al., Reference Sherif, Harvey, Jack White, Hood and Sherif1954/1961; Baumeister and Vohs, Reference Baumeister and Vohs2007; Schofield, Reference Schofield, Levine and Hogg2010). Research since then has shown that “in-group” behavior is common and widespread. Compare this thinking, then, to how mainstream economics employs the representative agent concept.

Mainstream macroeconomics’ dynamic stochastic general equilibrium (DSGE) model’s representative agent concept treats the choices of many individuals as identical and equivalent to the choice of one single representative individual (Lucas, Reference Lucas, Brunner and Meltzer1976), and heterogeneous agent New Keynesian (HANK) models do the same only with multiple representative agents (Kaplan and Violante, Reference Kaplan and Violante2018; Kaplan, Moll, and Violante, Reference Kaplan and Violante2018). Similarly, mainstream microeconomics theory of the firm assumes that firms act as a single agent representing all the individuals that make them up, and the theory of the household assumes that households act as a single agent representing all their family members (Becker, Reference Becker1981).Footnote ⁷

This representative agent thinking is quite different from that employed in social identity theory. The mainstream concept is primarily a model-simplifying device that aggregates together many particular individuals in order to treat them together as a scaled-up or generalized utility maximizing agent. No reference to social groups or social interests is then needed, because the collection of individuals which the representative agent stands for is simply replaced by that agent. Moreover, because representative agents are taken to adequately stand for many particular individuals, this assumes that these collections of individuals have no properties over and above those of the representative individual.

The rationale for this is that if all individuals are essentially alike, aggregating them as a single representative individual is only a formal simplification without substantive meaning. Yet, the evidence we have from “Robbers Cave” and social identity theory research is that sometimes when a collection of real-world individuals perceive they share social group identities, and do not behave as independent individuals. Then these collections of individuals have additional social group properties that the aggregative representative agent concept does not capture, and it would not be the case that independent individuals can be represented as a single representative agent with the same characteristics. So, although the mainstream takes the representative agent idea to be a model-simplifying device, behaviorally speaking it is more a means of blocking off the idea that like individuals have social interests that go along with their individual interests.

The issue of whether aggregations of individuals should be understood in this reductionistic way has not been entirely ignored in the mainstream, as shown, for example, by the literature on how information cascades operate across individuals (e.g., Banerjee, Reference Banerjee1992; Bikhchandani et al., Reference Bikhchandani, Hirschleifer and Welch1998). In that literature, if real-world individuals are assumed to be like one another in some important way and also know this, this can result in social group or “herd” behaviors when they take others’ choices into account in making their own choices. Yet, in contrast to social identity theory where people identify with others, cascade theory maintains the Akerlof–Kranton assumption that people’s individual identities are solely their utility functions. They accordingly do not identify with others but instead draw on other individuals’ information. That is, cascades are information cascades, not identity cascades.

Thus, while there are social aspects to what the representative agent literature models, like the social preference and Akerlof and Kranton’s initiatives, those aspects still presuppose the standard self-referential individual conception. How, then, can we make individuals’ social involvements and interests a factor in explaining individual behavior or what individuals are? In Section d, I discuss how Amartya Sen goes about doing this.

d Sen’s Alternative Account of Individual Identity

Sen first advances his conception of individual identity in his “Goals, Commitment, and Identity” paper (Sen, Reference Sen1985), published fifteen years before Akerlof–Kranton’s first paper. As the latter point out (Akerlof and Kranton, Reference Akerlof and Kranton2000, ftn. 1), Sen did not make identity an argument in the individual utility function but used the identity concept in a different way. He allows that people can act on utility functions – and distinguishes three types of utility functions in terms of their degrees of “privateness” – but also says people can make commitments to others that ignore personal gain or loss. Commitment to others for him involves identifying with them as that idea is understood in social identity theory (Davis, Reference Davis, Peter and Schmid2007b). Indeed, Sen’s concept of commitment includes identification not only with social groups but also with other individuals through one’s social relationships such as friends, family members, coworkers, etc.Footnote ⁸

Sen thus divides the individual into four different types of selves that a person has and can act on. The three utility function types progress from narrower to wider forms of individual interest or self-regardingness: self-centered welfare, self-welfare goal, and self-goal choice. Commitment goes beyond the last in replacing even the broadest individual interest with social interest. For Sen, acting on social interests also takes us into the domain of ethics which deals with what people believe they ought to do rather than what they want or prefer to do.Footnote ⁹

If people have multiple selves, can they nonetheless still be regarded as single individuals? I argue that Sen’s reasoning parallels Coase’s. Coase’s premise was that if can we distinguish different collections of nonmarket exchanges, we can refer to them as independent firms (Box 2.2). Sen’s premise is that if we can distinguish different collections of selves, we can refer to them as independent individual persons (Box 2.3). Both Coase and Sen say we can distinguish such collections, and conclude we can refer to them as independent firms/individual persons.

This of course leaves open for both why we would want to refer to these different collections as independent firms/individual persons, and this is where their theories of individuality come into play. For Coase, arguably implicit in his argument is that what makes different collections of nonmarket exchanges independent firms is that people are involved in managing and organizing them as such. There is no circularity in this inference since it does not employ the firm’s own characteristics to say what firms are. Rather, the idea that people engage in such activities and exhibit what might be called a capacity to do so comes from thinking about people generally.

If a capacity is what Coase has in mind, he is not explicit about it. However, Sen is explicit about the sort of capacity involved, and thus about why we should think different collections of selves can function as independent individual persons. The capacity human beings possess to manage and organize the different kinds of selves people exhibit is what he calls a “reasoning and self-scrutiny” capacity (Sen, Reference Sen2002, p. 36). Then, the single “self” is what reasons about and scrutinizes these selves. As he puts it:

That is, Sen simply holds that human beings possess a specific kind of cognitive capacity which goes beyond simple instrumental calculation, and involves how any person can take a stance toward their different goals and compare and relate them to one another. That is, what makes this specifically a human capacity is its reflexive character. If animals have capacities to recognize objects in their environments, people also have that capacity including being able to examine their different goals as objects in their environments. Again, there is no circularity in this inference since it does not employ the individual person’s own characteristics to say what individuals are. Rather what underlies the inference is a capacity human beings are said to have.Footnote ¹⁰

Simply being able to exercise this reflexive capacity, then, even if a person does not always do so, is what in Sen’s multiple selves individual conception individuates and identifies people as distinct and independent individuals. We are as human beings in principle always able to “ask what we want to do and how, and in that context also examine what we should want and how.” But does Sen’s individual conception also allow us to reidentify individuals through change? If people have a capacity to manage and organize their different selves, but over time fail to use it, then we cannot reidentify them as distinct and independent individuals.

For Sen, then, this is a difference between what people can be and do in terms of their capacities, and what capabilities they develop based on their capacities for what they are and do. As argued above, it means that individuality is not just something we explain analytically, but is also something that needs to be realized employing a normative analysis that investigates how societies are organized to influence what people can be and do. In effect, while Sen’s conceptual analysis explains what individuals are by describing how they stand outside and evaluate themselves, a normative analysis emphasizing realization of individuality focuses on our standing outside how societies function and evaluating how they succeed or fail in promoting this realization.

Sen does not make significant use of the idea of individuals being adaptive in regard to how people move back and forth between their different individual selves. Nonetheless, that on one occasion a person might be self-regarding in some way and on another occasion instead be other-regarding tells us that the circumstances people face influence them and they can be seen to adapt to them. To say people are adaptive is basically just to say that their environments affect their choices and behavior. In terms of rationality theory, context matters implying we must give up the standard independence axioms if we are to replace Homo economicus with a more realistic conception of the individual in economics. Section 3 turns to this issue.

a The Incoherence of the Independence of Irrelevant Alternative Riskless Choice Axiom

There are different formulations of the IIA axiom, but an often-used, clear way of stating it is: If x is preferred to y, introducing a third option z cannot make y preferred to x. Consider what the axiom requires. If we rule out that the introduction of some z changes the comparison of x and y, then that comparison has to stand no matter how the world might be organized. This implies either that people just subjectively stick with their comparisons no matter what, or that they factor in all imaginable effects of additional possible options being introduced. Both responses ignore the evidence that how choices are “framed” influences choice, as illustrated by how the ordering of food items in cafeteria lines often changes what people prefer (Thaler and Sunstein, Reference Thaler and Sunstein2008), or what has been called the decoy effect (or asymmetric dominance effect) studied in business marketing, where a person, say, selling something can manipulate another’s choice buying something, by structuring a menu of choices in the former’s favor (Angner, Reference Angner2012, pp. 38–42).

At the heart of the IIA assumption is the idea that people determine their preferences in a completely private way without any reference to factors external to them. My argument that this is incoherent is adapted from Ludwig Wittgenstein’s famous critique of the idea of a private language (Wittgenstein, Reference Wittgenstein1953, §§243–271; see Candlish and Wrisley, Reference Candlish and Wrisley2014). Before he advanced it, many philosophers had believed that the way people understood language was to associate the meanings of words with sensations they privately experienced. One knew that “dog” referred to what people called dogs because one associated this with the private sensation one had of seeing dogs when the term “dog” was used. Language thus worked through a kind of private–public interaction – private sensations and public language working together through some sort of associational psychology. Wittgenstein argued, however, that this view made no sense.

That is, if sensations are truly private, then they cannot be associated with public meanings, and an “inner” private psychology provides no basis for language.

With the IIA axiom, then, subjective preferences are essentially private sensations since the axiom requires that the comparison of any x and y must occur apart from the presence of anything external to this comparison in the form of another option z. These comparisons must thus constitute a “private language” that is neither meaningful nor language. More generally, from a contemporary philosophical point of view, the whole idea of private sensations and an “inner” private psychology on which the subjective preference idea is modeled is a throwback to a now discredited theory of perception built around the private “sense data” concept (Hatfield, Reference Hatfield2021). Indeed, the modern concept of preference not only solidified in the 1930s ordinalist neoclassical economics, but also in disregard to any attention to what its philosophical foundations might be.

Yet, concern about the problematic nature of the private preference concept has not been entirely absent from economics and found prewar expression in Paul Samuelson’s insistence that choice theory should be “freed from any vestigial traces of the utility concept” (1938, p. 71). In his alternative revealed preference theory, any particular bundle of goods a person selects only needed to be seen to be “revealed preferred” to any other bundle they could select (see Hands, Reference Hands2014). Samuelson was skeptical that a theory of choice based on a psychology of the unobservable workings of the mind was scientific. He did not argue in the manner of Wittgenstein that the idea of private preference is incoherent, but his emphasis on observability has the same basis as Wittgenstein’s understanding of language as shared meaning.Footnote ¹¹

Since the 1970s, the revealed preference theory has been a research workhorse of economics’ demand theory. Oddly, until the 1980s and 1990s emergence of new behavioral economics’ emphasis on reference dependence, the IIA axiom and context-independent choice remained a mainstay of traditional utility function reasoning and economics instruction as if it were consistent with revealed preference theory and its underlying assumptions were unproblematic.

Consider, then, how the concept of context operates in Wittgenstein’s argument. For him, language meaning must be socially shared meaning. He expressed this in his definition of meaning in terms of use.

The concept of use has an ancient but straightforward understanding. What has a use and is useful are the means people employ to achieve their goals. Yet, whether something works well in achieving a given goal also depends on the context in which it is applied. Thus, to say the meaning of a word or an expression is its use in language presupposes both shared experience about how meanings are used and incorporating how the context of application influences the meaning of a word or an expression. That is, how a system of socially shared meanings is tied to their use is always context-dependent.

Any choice over some x and y, then, since it is motivated by the goal of utility maximization, considers their comparative usefulness for that goal. That is, the meaning x and y have is their use. But on Wittgensteinian argument above, use presupposes both socially shared experience about what usefulness means in regard to achieving any goal and also an ability to incorporate how the context of application influences what usefulness means in regard to that goal. Yet, the context independence principle limits choice to the comparative usefulness of x and y, ignoring how any contextual z may influence their comparative usefulness.

Thus, the IIA axiom misrepresents the nature of choice and relies on incoherent conceptual foundations. Wittgenstein’s critique of private language allows us to diagnose its failing as deriving from a confused understanding of subjectivity as intrinsically private. This does not imply nor would we want to say that people do not have subjective experiences. It only implies that the meanings they use to describe them which make it possible for them to choose between options are socially shared, where that comes with a sensitivity to the contexts on which they depend.Footnote ¹²

b The Unrealisticness of Expected Utility Theory’s Risky Choice Independence Axiom

A different argument regarding why context matters applies to risky choices (or gambles) and the independence axiom (IA), or “sure thing” principle, underlying expected utility theory (EUT). A serious challenge to the IA was mounted early on by Maurice Allais who designed a choice problem counterexample to the IA showing that how people were likely to make choices is inconsistent with the axiom and EUT predictions (Allais, Reference Allais1953; see Heukelom, Reference Heukelom2015). Allais presented the problem to Leonard Savage, whose The Foundations of Statistics (1954) had codified EUT. When Savage failed to choose as his theory predicted, he responded that one ought to adopt a normative stance toward the IA, where to be rational people ought to choose in such a way as to avoid the sorts of choices Allais described (Moscati, Reference Moscati2018, pp. 294ff). What Savage believed important was explaining the world in terms of rational behavior.

Most commentators on the “Allais paradox” have interpreted Allais’ argument in epistemological–methodological terms as potentially an empirical falsification of the IA and in some respects rationality theory itself. However, Philippe Mongin (Reference Mongin2019) showed that Allais was also skeptical about the IA and EUT on ontological grounds, because this assumed a “rational man” individual conception he believed did not represent the “real man” individual conception he thought economics should employ. Mongin argues that whereas a “rational man” makes choices in an all-things-considered kind of way that ignores context, for Allais a “real man” is a “reasonable and prudent” person who answers for his choices however they may turn out and respects general rules of conduct. Allais did not further develop his view of the person, but the idea of answering for one’s choices and paying attention to general rules of conduct is like Sen’s emphasis on reasoning and self-scrutiny and the idea that one can stand outside oneself and reflexively evaluate one’s individual interests and commitments to others.

What lies behind the difference between Allais’ “real man” who sometimes sees a need to answer for past choices and Savage’s “rational man” who does not? Savage follows Frank Ramsey (Reference Ramsey, Ramsey and Braithwaite1926) and Bruno de Finetti (Reference de Finetti1937) in seeing probability judgments as thoroughly subjective. They consequently cannot be second-guessed. Therefore, people ought to choose as the theory has rational people choose. It follows that a “rational man” is a person who is always unhesitatingly willing to undertake gambles. Allais agrees people make subjective bets on the future when they make choices, but since he assumes they sometimes see a need to answer for them, he injects a principle of caution into what is involved in taking risky gambles.

At issue here are two conceptions of subjectivity and action. Note that whereas the riskless choice IIA axiom concerns the nature of people’s preferences, the Allais–Savage exchange over the IA risky choice axiom focuses on individuals’ subjective willingness to act. This understanding of subjectivity avoids the private language incoherence problem that applies to the preference-based IIA axiom, because it is not built upon an inner world private psychology. Instead, subjective willingness to act concerns how individuals see their life chances in light of their choices. Allais emphasizes caution and the need to be able to second-guess our choices. Contemporary Bayesian decision theory that derives from Savage offers one response to Allais in how decision-makers can adjust to unexpected circumstances through updating their prior probabilities to generate posterior ones as new information becomes available. Does this sufficiently address Allais’ concern?

At issue is whose view provides a more realistic understanding of human action. That issue is inseparable from the issue of what the world is like – also an ontological matter. How people make decisions and act depends on the possibilities the world creates for them. People have a capacity to act and achieve goals, but it is not unlimited. Bayesian theory’s response to this is its information updating principle. Yet this principle does not address circumstances in which a Keynes–Knight-type uncertainty prevails, where there is no way of knowing many things about the future, and people may have no grounds at all for assigning probabilities to future events (Keynes, Reference Keynes1921; Knight, Reference Knight1921).

Savage recognized that Keynes–Knight uncertainty did not fit his risky choice theory. He differentiated between “small” worlds where his theory applies and “large” ones where it does not. Allais could then say that we were often in “small” worlds but that we are not always in them means we ought to be cautious, be prepared to second-guess ourselves, and perhaps pay attention to general rules of conduct. Savage did not accept this, because he argued when we encounter “large” worlds we can figure out how to treat them as “small” worlds. He referred to two proverbs – “look before you leap” and “you can cross that bridge when you get to it” – and essentially argued that when decision-makers encounter circumstances which were not immediately like small worlds, they can reconstruct them as small ones. After all, assigning probabilities to future events was a subjective matter, and it was thus up to the decision-maker to determine how the circumstances encountered should be valued.

Thus for Savage, and for most Bayesians today, large worlds really do not exist. Savage might have moved toward Allais had he not died young since his treatment of the two proverbs was informal. Kenneth Binmore (Reference Binmore2009) suggests this and argues Bayesianism has become an unbounded philosophical principle extending Bayesian decision theory in ways Savage would not have intended. Indeed, it is hard to ignore the evidence that decision-makers often fail dramatically to anticipate unexpected events – especially in cases such as “black swans” (Taleb, Reference Taleb2007) in the 2007/2008 financial crisis. In those sorts of circumstances, decision-makers, practically speaking, find they need to put aside exclusive focus on scenarios they believe possible, and try – counterfactually – to imagine what they thought all but impossible (Feduzi, et. al., Reference Feduzi, Faulkner, Runde, Cabantous and Loch2022). Then, for example, they might reconstruct the small/large world distinction by forming analogies to past cases (Gilboa and Schmeidler, Reference Gilboa and Schmeidler2001). Or in game theory terms, they might adopt different “frames” for interpreting their shared circumstances – a “variable frame” theory (Bacharach, Reference Bacharach, Gold and Sugden2006) – where which frames people adopt are determined by salience cues (Larrouy and Lecouteux, Reference Larrouy and Lecouteux2018).Footnote ¹³

It consequently seems fair to say that there are two implications of all this: Context matters and individuals are adaptive. The IA axiom neither shows choice is context-independent nor provides a realistic understanding of human action. That is, it fails in both epistemological and ontological terms. The IIA and IA axioms raise different philosophical issues, but put together those issues make the argument that context independence is not a reasonable foundation for explaining choice behavior nor supposing people are Homo economicus individuals. What can we say, then, about what embedded individuals are?