The normative decision theory in economics: a philosophy of science perspective. The case of the expected utility theory

ABSTRACT

This article analyses how normative decision theory is understood by economists. The paradigmatic example of normative decision theory, discussed in the article, is the expected utility theory. It has been suggested that the status of the expected utility theory has been ambiguous since early in its history. The theory has been treated as descriptive, normative, or both. This observation is the starting point for the analysis presented here. The text discusses various ways in which economists and philosophers of economics have conceptualized the normative status of the expected utility theory, and it shows that none is satisfactory from the point of view of philosophy of science.

KEYWORDS:

• Philosophy of economics
• philosophy of science
• normative decision theory
• the normative turn in economics
• expected utility theory
• values in science

Acknowledgments

The author is grateful to many scholars and colleagues who have commented on different versions of this article. She would like to especially thank, in alphabetical order, Vincenzo Crupi, Marion Godman, Wade Hands, Tomi Kokkonen, Luis Mireles Flores, Alain Marciano, Robert Sugden, as well as audiences of: Philosophy of Science Seminar and TINT Brown Bag Seminar at the University of Helsinki, The 4th International Conference Economics and Philosophy in Lyon, East European Network for Philosophy of Science in Bratislava, Workshop Behavioral Political Economy at Walter Eucken Institut in Freiburg, YSI Plenary Session: Piecing together a paradigm at Central European University in Budapest, ESHET Conference at Sorbonne in Paris.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes on contributor

Magdalena Małecka, in September 2018, joined the Department of Philosophy at Stanford University as Marie Skłodowska-Curie Global Fellow. Before she was an Academy of Finland post-doctoral researcher at TINT – the Centre for Philosophy of Social Science, University of Helsinki. Until July 2018, she was also a Junior Core Fellow at the Institute of Advanced Study of the Central European University in Budapest. She is a recipient of research grants and prizes (granted by the European Commission, the Academy of Finland, Poland’s National Science Centre and the Foundation for Polish Science). She publishes on a variety of topics in the philosophy of the social sciences, economic analysis of law, and philosophy of economics.

ORCID

Magdalena Małecka http://orcid.org/0000-0001-5395-9256

Notes

1 Expected utility theory was introduced to modern economic theorizing by John von Neumann and Oskar Morgenstern in 1944 in their seminal book Theory of Games and Economic Behaviour. The theory states that when making decisions under conditions of risk a decision maker compares the expected utility of options (utility value of options multiplied by the probability of getting them) and opts for the one that has the highest expected utility. Von Neumann and Morgenstern provided the mathematical, axiomatic treatment of the thus understood maximization of the expected utility. Alternative axiomatizations of EUT were proposed by Marschak (1950) and Herstein and Milnor (1953). Savage (1954) developed the axiomatization of the subjective expected utility theory under conditions of uncertainty.

2 See the review of this evidence in Schoemaker (1982). Compare with Harrison’s (1994) criticism of these experimental works. However, it should be noticed here that already in the late 1940s there were experimental works that claimed to corroborate EUT (e.g. Mosteller & Nogee, 1951).

3 Conference participants overweighed outcomes (events) which they considered to be certain. In this way, they were making choices that are not in accordance with the predictions of EUT. Allais paradox was not a proper experiment though, but it remained rather a thought experiment until researchers in the mid-1960s started testing people’s behaviour in experimental settings, inspired by Allais choice problem, as well as by so-called Ellsberg paradox (Ellsberg, 1961) that targeted Savage’s version of the utility theory (e.g. Becker and Brownson (1964), Fellner (1965), MacCrimmon (1965), for review see: Camerer and Weber (1992)).

4 The independence axiom was not present in von Neumann and Morgenstern’s formulation of EUT and was suggested, independently, by Samuelson (1947), Marschak (1950), and Nash Jr (1950). This axiom sets a requirement of separability of preferences across disjoint events for decisions under risk. Savage’s (1954) sure thing principle is its mathematical equivalent for decisions under uncertainty (see Fishburn & Wakker, 1995).

5 See the section below, in which I refer to the discussion about the normative understanding of theory in studies of judgment and decision making in cognitive psychology.

6 The work of Catherine Herfeld on the Cowles Commission Research Reports from the years 1944–54 (2018) is an illuminating example of this type of historical analysis.

7 See e.g. ‘[t]his article discusses expected utility theory as a normative theory—that is, a theory of how people should make decisions’ (Briggs, 2017, p. 1). According to Martin Peterson, normative theories of decision making, and EUT, ‘seek to yield prescriptions about what decision makers are rationally required – or ought – to do’ (2009, p. 3).

8 There is of course a vast number of studies, both theoretical and empirical, that refer to the distinction between normative and decision theory and treat EUT as a normative theory. In this section I focus on relatively prominent works – in economics, philosophy of economics, decision theory and philosophy of decision theory – in order to ensure, at least to some extent, that I reconstruct and analyse the widely accepted views.

9 EUT is often treated as a rational choice theory, but I do not discuss in which sense this view is accurate. This would require meticulous work in clarifying which theories in economics qualify as theories of rational choice and why (such an attempt has been proposed in Herfeld (2013)).

10 ‘[A] demonstration that human choices often violate the axioms of rationality does not necessarily imply any criticism of the axioms of rational choice as a normative ideal’ (Thaler, 1991, p. 138).

11 ‘utility theory lays down formal conditions that choices and preferences ought to satisfy … To define what rational preference and choice are is ipso facto to say how one ought rationally to prefer and choose’ (Hausman & McPherson, 2006, p. 49).

12 ‘The modern theory of decision making under risk (…) was conceived as a normative model of an idealized decision maker, not as a description of the behavior of real people’ (Tversky & Kahneman, 1986, p. 251).

13 ‘Expected utility theory has dominated the analysis of decision making under risk. It has been generally accepted as a normative model of rational choice, and widely applied as a descriptive model of economic behaviour. Thus, it is assumed that all reasonable people would wish to obey the axioms of the theory’ (Kahneman & Tversky, 1979, p. 263); Francesco Guala argues that the ‘‘(n)ormativists’ claim that their theories aim to describe the behaviour of an ideal rational agent, but not only because such an “ideal type” is useful in order to understand the behaviour of real agents; rather, models of rational behaviour are significant for evaluative and prescriptive purposes’ (2000, p. 67).

14 In their seminal work (1944), von Neumann and Morgenstern did not understand axioms as normative conditions with which individuals ought to comply. As noted in the historical section above, normative interpretations were proposed later.

15 The vast literature in the philosophy of action addresses to a great extent exactly this question – what is rationality, what are the definitional features of rationality, is rationality normative and, if so, in what sense? The proponents of EUT seem to take a single stand on these topics – for them EUT explicates some intuitions about rationality. They also seem to presume that rationality is a normative concept and for this reason they may be inclined to treat EUT as a normative theory. However, they mostly do not take part in the philosophical discussion and they do not bring well-argued philosophical points to support their views. In the next section I will show how the commitment to a certain notion of rationality influenced developments in decision theory. I believe that we should account for this commitment in order to understand how EUT evolved. I do not think, however, that this should lead us to defend the idea of having a normative theory in economics.

16 Sometimes it is also pointed out that EUT is a ‘model of an idealized decision maker’ (Tversky & Kahneman, 1986). The idealized character of the EUT should mean that it contains idealizations – in particular, idealized assumptions that eliminate the factors that are incidental for explanation of certain phenomena (Nowak, 1977; McMullin, 1985; Mäki, 2012). Similarly as in the case of the axiomatic character of EUT, its idealized character and normativity are not necessarily connected. In the case of EUT, idealizations, like axioms, seem to have a dual status: they are both simplifying assumptions and ideals.

17 This understanding of EUT – as the theory that can be used by individuals to guide their actions – was present in decision theory very early on. It is how Savage (1954) tried to defend and articulate the normative force of his subjective expected utility theory, as well as what Ellsberg (1961) challenged – he argued that people, in conditions of ambiguity, don’t upon reflection decide to use EUT as a guidance for their decision making. See Zappia, 2018 for a review of this discussion and of recent experimental attempts to study whether people wish to adopt EUT to make decisions, or to reason.

18 See e.g. Davidson, McKinsey, and Suppes (1955), Rabinowicz (2000), Levi (2002) on the money pump and Vineberg (2016) on the Dutch book argument.

19 Recently, Zappia (2016) and Mongin (2014/18) have subscribed to Guala’s proposal of how to make sense of the presence of a normative theory in decision theory and economics and how to apply notions of empirical testing, or falsification of it. It should be noted that Guala’s work is not the only one that intends to bring insights from the philosophy of science in order to account for the developments in decision theory and for modifications of EUT. However, neither of the existing proposals (e.g. Fishburn and Wakker’s (1995) and Mongin’s (1988)) attempts to take into account the methodological consequences of treating EUT as a normative theory (see Guala, 2000, pp. 60–61). 

20 Guala points out that the Allais paradox could be interpreted at least in two ways: it is evidence that shows it is impossible to measure classical utilities by means of von Neumann and Morgenstern’s method; it also shows that subjects’ preferences can be inconsistent with EUT axioms. The paradox was mainly interpreted in the latter way by the tradition (Guala, 2000, p. 66). See also Mongin (2014/18) on different interpretations of the paradox and his proposal of treating the paradox as ‘the normative argument’, emphasizing, like Guala, the importance of normative considerations in the discussion initiated by Allais.

21 According to Allais ‘a man will be deemed to act rationally: (1) if he pursues ends that are mutually consistent (i.e. not contradictory); (2) if he employs means that are appropriate for these ends’ (Guala, 2000, p. 71; after Allais, 1979 [1953], p. 78)

22 Guala is well aware of other developments in decision theory, for instance those that weakened the transitivity axioms (e.g. Loomes & Sugden, 1982; Fishburn, 1982), accounting for the evidence about preference reversal. For him these theories, like e.g. regret theory, were not accepted as normative (rational) though, but only as descriptive theories: they didn’t satisfy Allais’s criteria for rationality. Compare also Starmer, 2000 on other developments in non-EUT descriptive theories.

23 It remains an open question to what extent he succeeded. See e.g. Steiner, 1983; Corfield, 1997 for a discussion of Lakatos’s view on the quasi-empirical, fallible, character of mathematics.

24 See also similar remarks made by Chris Starmer, who has pointed out that ‘although economists have been prepared to relax the independence axiom in pursuit of better descriptive models, there has been an apparent reluctance to give up other normatively appealing principles such as transitivity or monotonicity’ (Starmer, 2005, p. 281).

25 A series of experiment initiated by Peter Wason demonstrating people’s inability to reason according to the rules of classical logic, especially showing the fallacy of affirming the consequent, as well as failures in applying modus tollens. For review of the early research, see Evans & Over, 2004.

26 For Chomsky (1965), competence is a structural description of abstract knowledge that is not contrasted with ‘incompetence’, but with ‘performance’ (Elqayam & Evans, 2011, p. 239).

27 They are not of course the only scholars who notice this. Most notably, researchers working with Gerd Gigerenzer have developed a similar criticism of the behavioural economics initiated by Kahneman and Tversky. Ylikoski and Kuorikoski, however, bring insights from the philosophy of science in order to account for the possible bias stemming from researching deviations from the norm of rational behaviour, often allegedly implied by EUT.

28 See also Cartwright, 2014, chapter 1; Wilkinson & Klaes, 2012, chapter 11 for concise summaries of this criticism.

Additional information

Funding

This work was supported by the Academy of Finland [grant number 308682] and by Marie Skłodowska-Curie Fellowship EPISTEMEBEHAVIOUR; European Commission.