Behavioural Paradoxes and Behavioural Economics
Debate on von Neumann and Morgenstern’s work mainly concerned the assumption of rationality underlying the system of axioms. In this respect we can distinguish two streams: rationality understood in a descriptive sense, as a characteristic perhaps not perfectly present in all agents but nevertheless endowed with sufficient general validity, so that the theory based on it can contribute to our interpretation of the real world (and the failure to adopt rational behaviour constitutes an imperfection of the agent); and rationality understood as a prescriptive norm, i.e. the behaviour that agents should adopt in order to obtain optimal results.
The two interpretations, the normative and the descriptive one, constitute a useful distinctive element for the various positions present in the subsequent debate, involving psychologists and economists. The distinction is adopted by Savage, after a debate in which he and Friedman were opposed to Allais, Baumol and Samuelson, who supported a descriptive interpretation of the axioms. In this respect, Maurice Allais (1911-2010, Nobel Laureate 1988) found some counterexamples: when submitted to a few persons - high-ranking economists and probability scholars, among them Savage, hence persons one may assume to be capable of rational reasoning - their choices were quite often different from those prescribed by the von Neumann- Morgenstern theory.  If we interpret expected utility theory as describing the agents’ behaviour, then the ‘Allais paradox’ in itself constitutes destructive criticism of this theory, showing that rational agents violate its postulates. (An analogous critique, aimed at the postulate of independence of individual preference sets, considering not risk aversion but aversion to uncertainty, was proposed by Daniel Ellsberg (b. 1931) in 1961.) According to the normative interpretation, though, violations of the postulates may be interpreted as a deviation of individual agents from the optimal choice path, which remains the one described by the theory.
Such developments intersect with the parallel developments in mathematical and experimental psychology, concerning the two aspects - normative and descriptive - of decision theory. These research fields also received substantial funding, partly connected to military research.11 In this context, research on decisional processes developed at the University of Michigan, in the Institute for Social Research founded in 1947 and mainly staffed by psychologists, followed in 1949 by the Mathematical Psychology Group, the Mental Health Research Institute in 1955 and the Human Performance Center in 1958. Ward Edwards (1927-2005), stimulated by the von Neumann-Morgenstern work, proposed a fusion of mathematical and experimental psychology, giving rise to the field of behavioural decision theory (the title ofhis influential 1961 article). Expected utility analysis was interpreted as a theory of measurement and as the basis for an understanding of the behaviour of the rational agent when confronted with uncertainty.
According to subjective probability theory, proposed by De Finetti and taken up by Savage, each agent has her/his own evaluation - not necessarily a correct one - of probabilities and outcomes (i.e. of expected utility) of events, and this evaluation determines the agent’s choices. Errors in the agent’s behaviour consist in violations of her own system of preferences and probabilities and may be attributed to causes such as the scarcity of time, decision taken under stress and the like. A different problem, specifically considered by Kahneman and Tversky in the 1970s, concerned the fact that agents systematically make ‘wrong’ decisions, differing from those considered optimal by decision theory, as a consequence of their incapacity for rational reasoning.
Amos Tversky’s (1937-1996) work at the end of the 1960s focused on verification of the transitivity axiom, a necessary condition for the existence of an ordinal scale of utility. Of course, each violation of the axiom may be attributed to a change in the agent’s preferences; however, when this justification becomes recurrent, it must be considered ad hoc. Daniel Kahneman (b. 1934, Nobel Laureate 2002), on the other hand, studied how agents deviate from the rational norm of behaviour and was convinced that human beings often commit cognitive errors. The issue thus became how to simplify and reorganize the decisional problem so that even an unsophisticated agent would be able to tackle and solve it. Collaboration between Kahneman and Tversky began along this line of research at the end of the 1960s, leading to what is known as prospect theory.12 This theory took as reference an S-shaped utility curve, defined by considering the distance from the status quo: due to risk aversion, the loss (disutility) corresponding to a negative deviation from the status quo is greater than the gain (utility) stemming from a positive deviation of equal magnitude. Kahneman and Tversky concluded that expected utility theory interpreted as a descriptive theory is falsified by this result.
These conclusions opened the way to what may be called behavioural paternalism: economic agents are sufficiently but not fully rational; the scientist engaged in a human engineering programme, and more specifically in efforts to improve their decisional processes, is better able to locate the optimal choices and to point them out to the agents. 
Kahneman and Tversky’s theory differed from the mainstream less than the theory developed by Herbert Simon (1916-2001), who stressed the distance between the mainstream notion ofrationality and the agents’ actual behaviour. Simon (1957, 1979) proposed the notion of bounded rationality, abandoning the assumptions of a predefined set of alternative actions among which to choose, of knowledge of the outcomes of the different actions and of a given utility function to be maximised. Confronted with a multiplicity of objectives, it is reasonable to adopt a satisficing behaviour, aiming at reaching an acceptable result for each of the different objectives, rather than maximising a function that embodies all of them, adequately weighted.
Relative to the notion of rationality we then have a series of specifications. The first, already implicit in von Neumann-Morgenstern’s work and in the subsequent debate, concerns the distinction between rationality understood as internal consistency of the system of choices, or as systematic pursuit of self-interest on the part of the agent. We then have the distinction between substantive rationality, understood as the pursuit of a personal interest defined in an objective way, i.e. independently of the individual’s own choices, and instrumental rationality, when the agent pursues a target however it is chosen; on many counts this distinction is connected to, but does not coincide with, the first one. Within a new field of research, neuroeconomics, some authors suggested the need to consider as distinct fields of thinking the short and the long period, the latter being more rational-dominated, the former more sentiment-dominated (McClure et al. 2004). Both neuroeconomics, and the bioeconomics that preceded it, rely in their analyses of the agents’ behaviour on the assumption of rational behaviour, considered as the result of a natural process of evolutionary selection (cf. for instance Vromen 2007).
Another recent stream of research aims to extend the von Neumann- Morgenstern utility functions to include in them aspects such as the importance for the agent of identities (sex, religion, nationality and so on): the choices implying adhesion to or refusal of the identity entail positive or negative effects both for the agent concerned and (externalities) for other agents (Akerlof and Kranton 2000). Multiple equilibriums may derive from this, depending on the values of the parameters. The assumption that the outcomes of the choices may be measured on a one-dimensional scale remains in any case essential, since it allows for addition to or subtraction from the utility directly expected from the act of choice the utility indirectly stemming from the strengthening or weakening of the identity: precisely the assumption that, as we saw in Chapter 8, John Stuart Mill criticised with respect to Bentham’s utilitarianism.
Finally, in the most recent stage, a series of interdisciplinary research, with the collaboration of anthropologists, psychologists and economists, tend to render endogenous the formation of preferences (see the important work by Henrich et al., Foundations of Human Sociality, 2004). This research implies superseding the original von Neumann-Morgenstern approach; hence the tendency to exclude it from the field of economics, or at least from the field of mainstream economics.
-  This dichotomy differs from the one concerning the ambit of positive science and thenormative ambit of ethics proposed by Friedman 1953: even in its ‘normative’ meaning,von Neumann and Morgenstern’s theory is ‘objective’, in the sense that its results automatically stem from the assumptions of the theory without recourse to any value judgment. Like Savage, von Neumann and Morgenstern considered their axioms as at thesame time an abstract but realistic representation of human behavior and as a norm forrational decision making. For a history ofbehavioural economics, cf. Heukelom 2014.
-  For an account of Allais’s experiments, conducted by mail (with Savage and others) or atthe occasion of international conferences such as the one held in Paris in May 1952, cf.Heukelom 2014, pp. 44 ff. For an illustration, cf. Allais 1953.
-  Mirowski 2002 and Heukelom 2014 provide various examples in this respect.
-  Cf. for instance Kahneman and Tversky 1979.
-  Experimental economics as originated by Vernon Smith (b. 1927, Nobel Laureate in2002) mainly concerns the behavior of the markets, which according to Smith functionwell, in the sense that they show convergence to what mainstream theory indicates.The techniques ofexperimental economics, widely utilised in the past couple ofdecades,may in any case be utilised regardless of Vernon Smith’s free market views.