The Mind under the Axioms

Decision-Theory Beyond Revealed Preferences

Sacha Bourgeois-Gironde

• Editorial: Academic Press
• Año: 2019
• ISBN:
  9780128151327
• Categoría: Économie
• Categoría: Économétrie

The Mind under the Axioms reviews two basic ingredients of our understanding of human decisions – conative aspects (preferences) and cognitive aspects (beliefs). These ingredients are axiomatized in modern decision theory in the view to obtain a formally and empirically tractable representation of the decision-maker. The main issue developed in this book is the connection between realistic and testable psychological features and the descriptive component of abstract axioms of rationality. It addresses three main topics for which the interaction between axiomatization and psychology leads to potential new developments in experimental decision-theory and puts strictures on the standard revealed preference methodology prevailing in that field. The possibility of a cardinal representation of preferences is discussed. Different ways of accounting for incomplete preferences, and in which sense, are analysed. Finally, the conditions of separability between preferences and beliefs, such as prescribed by axioms of state-independence, are submitted to actual and potential tests. The book offers a bridge between the disciplines of decision-theory, psychology, and neuroeconomics. It is thus relevant for those, in psychology and cognitive sciences, who are sometimes put off by the high degree of formalism and abstraction in decision-theory, that seems to lie beyond the reach of psychological realism. It also aims to convince those in decision-theory for whom psychological realism and empirical testability should not constrain the modelling enterprise that conceptual clarification can come from attempted experimentation.

• Addresses open and evolving theoretical issues in decision-theory, especially from experimental perspectives
• Helps researchers understand the psychological and neuroscientific mechanisms for decision-making
• Considers how preferences shape beliefs and how beliefs shape preferences
• Uncovers the very formal and abstract psychological and behavioral implications that are actually made in contemporary decision-theory

Chapter 1

Cardinalism

Abstract

Cardinalism has been dismissed by neoclassical economics, leading to an impoverished view of the nature of preferences. In this chapter, we analyze how to ground cardinalism in a classical representational strategy, possibly richer than von Neumann-Morgenstern cardinal utility functions specific to the expected utility framework. We also investigate the possibility of an enriched informational basis allowing, besides choice-data, reliable introspective judgments. We analyze different possible levels of cardinalism, trying to assign a subjective signification to utility functions. We analyze, in particular, the tension between considering utility functions as being induced from axiomatic structures of preferences and taking them as primitive entities. Utility functions and their properties, when taken as primitives, allow for the description of the psychology of an individual in a different way than when we are confined to the representational framework. In this chapter, we also discuss and analyze neuroeconomic attempts to probe the neurobiologically underpinnings of some utility functions.

Keywords

Cardinalism; ordinalism; vNM-utility; hedonimetry; introspection; Allais’s cardinalism; neuroeconomics of utility; utility functions as psychologies; prospect theory; episodes

1.1 The need for cardinal utility

1.1.1 Cardinalism and subjectivity

In economics, thanks to the concept of utility, we can compare not only between apples and between apples and pears but also between apples and clothes and apples and poetry or a good sleep. On the other hand, it is a controversial issue as to whether we can compare between such several comparisons. To do so, we would need a precise scale and measure of subjective utility that would in fact be objective enough to apply across individuals. What permits such inter-individual comparisons of utility is—the general saying goes—that the utility function is not subjective after all, that it does not capture real subjective aspects of the individual utility but nevertheless yields an objective indication of what this subjective utility is. Freed of essentially individual aspects in its construction, the standard (i.e., not significant in subjective terms) utility functions that represent individual preferences can be exported to social choice-theory and concerns.

Many issues to be disentangled will constitute the successive topics of this chapter and determine its progressive inclination not only toward cardinalism but toward a significantly subjective admission of this doctrine. The first issue is to remember a clear definition of what counts as a cardinal utility function and what its relationship with respect to the subjective experience of utility is. Because the two notions are not equivalent (Section 1.1.1). The second issue is whether we can adopt a subjective conception of a cardinal utility function and yet pursue the significant goals that an apparently more parsimonious ordinal function achieves in decision-theory and economics (the rest of Section 1.1). Finally, we can wonder how sound the theoretical foundations of decision-theory can be when we adopt such a cardinalist and subjectivist point of view (Sections 1.2 and 1.3 will dwell on these issues). In particular, can we obtain a representation theorem—that is, the main conceptual link between preference orderings and utility—when we accept, in our informational basis a cardinal (and subjective) notion of preference intensities (Section 1.3)? Or should we and can we dispense in decision-theory with representation theorems as foundational moves of the discipline (Section 1.3.3 in particular)? Finally, in our “To-the-lab” experimental Section 1.4, we suggest protocols that tackle psychological issues motivating the resort to a cardinal subjective utility function and the admissibility of introspective data in relation to a choice-based decision-theoretical paradigm.

The first ambiguity to dispel is that the standard von Neumann-Morgenstern (vNM) utility function is cardinal, not ordinal. To recall, the expected utility hypothesis that these authors have developed means that an individual having some preferences and exerting some choices on a space of risky objects (a set of lotteries) and satisfying a series of sufficiently intuitive axioms (see Fig. 1.1) can be described in terms of the maximization of the expected value of a utility function that is cardinal. It is cardinal in the sense that it is unique up to a positive affine transformation. It means that the properties we assigned to the preference relation represented in this way can be preserved through changes of interval scales (the “up to positive affine transformations” of an initial function). By contrast, an ordinal utility function is unique up to an increasing monotone transformation. A cardinal utility function is then by default ordinal, but the reverse is not true. A cardinal utility function is more demanding in terms of its informational basis, since it supposes that there are possible valuations of options on a cardinal space and not simply an ordering of these options. It more exactly supposes that the ordering of the options preserves the cardinal valuation of options and that we can continue to perform comparisons of preferences themselves in the form of “I prefer x to y more than I prefer w to z” [(x

y)>(w

z)], implying that the intensity of preferences is preserved under the cardinal utility function (which it is not under a strict ordinal function). Cardinalism, in this sense, means that we do not simply order options by a preference relation (which, with no more informational basis, yields an ordinal utility function) but that we can rank the instances of that preference relation themselves.

Figure 1.1 vNM axioms.

The main difficulty is not to distinguish cardinality and ordinality but to agree on what we call a “cardinal utility function.” The problem lies in the extent to which we want the cardinal utility function that represents the preferences of an individual to reflect her subjective experience. A classical statement in economics (see Baumol, 1951, 1958) holds that the vNM utility function has nothing to do with the neoclassical utilitarian idea that utility is the measure of the subjective satisfaction (let alone welfare or happiness) of the individual when she expresses her preferences through her choices. Suppose that an hedonimeter could measure degrees of satisfaction and that we obtain an objective measure of that subjective experience, it still would have nothing to do with what vNM utility measures or indicates. If this position is to be accepted, it would amount to saying that vNM utility is an indirect index of subjective utility, not a measure of it and that it therefore conveys richer information than ordinal utility functions. Many applied economists understand and use vNM utility in that way.

Yet this position leaves an impression of ambiguity and dissatisfaction, and we may want a vNM utility function to have more subjective significance and correlate more directly with the experience of the decision-maker. Ng (1984) identifies a psychological postulate that prevents a more subjective interpretation. It is worth analyzing Ng’s contribution in some details, as it forms a paradigmatic example of how axioms and the provability of a utility representation encapsulate implicit “psychologies,” that is, underlying views of the mind. Ng points out that the assumption of infinite sensitivity—the perfect ability to discriminate between the finest levels of subjective experience—is implicitly contained in vNM axioms. If we add to that unmodified list of axioms a psychologically more realistic postulate of imperfect experiential discrimination, we can grant the vNM utility function the subjective significance that classical utilitarianism associates with the very concept of utility.

Classical utilitarianism suggests that the human perceptual apparatus is endowed with limited discriminative capacities but that it is possible to calibrate minimal perception thresholds and construct units of utility on this minimum. This is, of course, a postulate subject to objection and experimentation, but we postpone this discussion for now. Minimal sensitivity to differences i...