Probabilising the consumer: Georgescu-Roegen, Marschak and Quandt on the modelling of the consumer in the 1950s

ABSTRACT

It is the purpose of this article to confront three attempts by economists at developing models of individual choice that go beyond standard ordinalist utility theory through introducing principles of probabilistic behaviour. We discuss first Georgescu-Roegen's neglected contributions to this subject, though he pioneered the definition of probabilistic preference in 1936 and came back on the subject intensively in the 1950s. We then present Marschak's (and his co-authors) attempts at axiomatising a probabilistic model of choice in the same period. The third contribution studied is that of Quandt, who provides a more operational style of modelling. This set of contributions is discussed against a general background of transformations of the theory of rational behaviour and of the methods proper to it.

KEYWORDS:

• Probabilistic choice theory
• Georgescu-Roegen
• Marschak
• Quandt

JEL:

• B21
• D11
• D01

Acknowledgments

Helpful comments on earlier drafts from various audiences is gratefully acknowledged, specifically from Jean Baccelli, Philippe Mongin and Ivan Moscati. I benefited also from the comments by two anonymous referees. The usual caveat applies.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ Samuelson (1950) showed that if a consumer abides by the strong axiom of revealed preferences, then theoreticians might as well use (ordinaly conceived) utility functions or revealed preference maps to model individual rational behaviour. A number of issues about integrability and correspondence between the revealed preference approach and utility theory would indeed be solved within the following 20 years. The outcome of this was Chipman et al. (1971). None of this study, however, would jeopardise the strong unity of the theory of choice.

² Friedman (1949) would follow this line in his interpretation of the Marshallian demand curve.

³ It is a complex story and we do not pretend to deal in depth with many issues that would deserve a separate investigation, such as the links with experimental psychology or the internal debates about the meaning of the axiomatics of expected utility. On both topics, see Moscati (2007), Lenfant (2012b), Heukelom (2014) and Moscati (2016).

⁴ The present research being a first step in a little known episode of the theory of choice, it is not based on archival material and instead aims at presenting three different ways to implement a probabilistic interpretation of the consumer's behaviour, trying to relate them with the background of discontent with OUT after WWII. Certainly, this first study should be a starting point for more specific inquiries into Georgescu-Roegen's and Marschak's archives.

⁵ Actually, the outcome of the Samuelson endeavour was that the use of the indifference–curve approach was eventually warranted as a theoretical construct, but not as an empirical construct (Lenfant 2012a).

⁶ The analytical examination of the conditions under which a system of axioms about the structure of individual preferences could be represented through a utility function was not addressed before Wold's 1943/1944 synthesis of demand theory, whose diffusion was rather confidential. It remained uncompleted until Debreu (1954), who gave sufficient conditions for representing a system of preferences with a real-valued utility function.

⁷ In view of Georgescu-Roegen's later considerations on time (Bobulescu 2017) in economics, which were to be central to his abandoning of the neoclassical framework, the 1936 paper lays the foundations for an opposition between a static modelling of choice against a dynamic one.

⁸ See especially Armstrong (1939, 462 and sq).

⁹ From Katona (1953, 313), we are inclined to think that every psychologist would contest the very idea of a given preference pattern before choice: “Any contradiction of a theorem derived from utility theory can always be attributed to a change of tastes, rather than to an error in the postulates or logic of the theory” (Katona 1953, 313). More generally, it is a fact that preferences are not a concept of psychological theory. It was imported only to psychology in the 1950s.

¹⁰ An indirect effect, maybe, of the comparison induced by some economists between OUT and EUT is a way of presenting consumer's theory as a generic model of rational choice adapted to every situation of choice. Alchian (1953, 32), for instance, argues that the model should deal not only with marketable commodities but also with patterns of actions (a trip to Europe, getting married). Neither Pareto nor Hicks did entrust consumer's theory with such a purpose (see Lenfant 2012a). This inflection was probably already on the way in the Chicago style of reasoning, but it was probably strengthened on this occasion.

¹¹ Interestingly, Houthakker (1961) underlines the relationship between the theory of risky decisions and the probabilistic extension of OUT.

¹² Meanwhile, the revealed preference approach reinforced the emphasis on observable data, “gradually transforming utility to an essential component of empirical research” (Houthakker 1961, 713).

¹³ One can mention a short list of scholars that would participate actively in the theory of choice and decision in economics within the period (circa 1945–1960) and that eventually contributed to the anchoring of experimental psychology and mathematical psychology at economic theory: Edwards, Katona, Mosteller, Coombs, Davidson, Davis, Estes, Lewin, Siegel, Simon, Stevens, Suppes and Luce.

¹⁴ In a similar vein, Wold pointed out that the independence axiom shall not be acceptable in a repeated choice among uncertain outcomes (Wold 1952, 663).

¹⁵ Papandreou's experiments consisted in choosing one activity in a binary choice situation (with two activities). More than 80% of the answers were in accordance with the definition of probabilistic transitivity. Actually, Moscati (2007) points that no statistical test for rejecting the null hypothesis could be carried out.

¹⁶ On this topic, we must mention Duncan Luce, a very influential mathematical psychologist, who repeatedly came on the subject of discriminatory power, that he linked with the Fechnerian tradition of psychophysics (see especially, Luce 1959b; Luce and Edwards 1958). We cannot discriminate adjacent weights, for instance, and nevertheless, we can differentiate a greater difference. Intransitivity thus “reflects the inability of an instrument to discriminate relatively to an imposed discrimination task” (Luce 1956, 179; see also Luce 1959a, 145–146). Indeed, following the idea that individuals do have an imperfect power of discrimination (represented through the notion of just noticeable differences), a specific kind of scaling of individual preferences could be obtained through an adequate set of constraints on the probability to choose one element in a set of alternatives. A few words are in order concerning Luce's contributions to the field of probabilistic choice (Luce 1956, 1958, 1959a; Luce and Edwards 1958). We have decided not to devote a full section on Luce since his contributions, important as they are for the subject at hand, are not oriented towards a reformulation and extension of the traditional model of choice and are motivated by psychological concerns (notably measurement issues). Nevertheless, Luce's work is of course at the core of the ferment of ideas of the 1950s and he contributed much to the import of concepts and methods of psychology into economics. For a presentation of Luce model (especially the axiom of choice) and a discussion within the history of random utility, see de Palma and Thisse (1987) and Lenfant (2012b).

¹⁷ Georgescu-Roegen (1950) tries to provide a model for constructing indifference curves when the consumer takes account of past experience. Among other scholars, Luce (1959b) would again discuss the influence of learning in relation with the axiom of choice. Learning is also a central theme of Simon's (Simon 1955) reconstruction of the theory of rational behaviour.

¹⁸ A related issue is whether what is called random behaviour is a conscious strategy of the agent or if it is a projected interpretation of the theoretician. It will always be difficult to disentangle conscious random behaviour from errors of choice on the part of the consumer, and from errors in the experimental setting.

¹⁹ “We can arrive in this way at the formulation of a necessary and sufficient set of assumptions for handling the problem, and thus obtain a kind of measure of the extent to which our mental experiment may diverge from a similar actual investigation. For maintaining further this parallelism between the mental and actual experiment, the formulation of our postulates in such a way as to outline in a straightforward fashion the corresponding physical investigation is undoubtedly the most advisable procedure (Georgescu-Roegen 1936, 546–547).

²⁰ The axiom also implies that there is no saturation (for any good in the commodity space), and the agent gets the bare necessities in any good.

²¹ The difference with Luce's model now appears more clearly. In Luce's model, the threshold in choice is defined as a sensorial threshold only. Georgescu-Roegen (1958, 160) indicates also that Luce's axiomatic of preference is intrinsically discontinuous, whereas the threshold model is inherently stochastic.

²² We may wonder whether this axiom is still compatible with the idea to develop a pure binary choice model. It implies some structure upon the preference pattern implying three goods. It seems that there is some similarity between this axiom and the WARP.

²³ This leads to discussing how to obtain information on multiple choices from binary choices.

²⁴ Marschak (1950, 1955, 1959), Block and Marschak (1960) and Davidson and Marschak (1959).

²⁵ Marschak is much more assertive in 1955: “It is important that at least people whose decisions involve the welfare of many others should fulfil certain norms of consistency, should know, for example, how ‘to make up their minds’” (Marschak 1955, 46).

²⁶ Block and Marschak (1960) contain most of the content of Marschak (1959).

²⁷ Irrelevance of additional (contextual might be better) alternatives means that whether x is or is not worse than y is independent of whether z (or any other) belongs to the set of alternatives. Transitivity means that if x is not worse than y, and y not worse than z, then x is not worse than z.

²⁸ This does not prevent from identifying and theorising the possible implications of observations errors on the part of the experimenter and other variations in the decisional context that might affect the subject's behaviour.

²⁹ The idea, pioneered by Thurstone (1927), is that to each stimulus x one can ascribe a basic random variable u(x) formalising all the neural attributes of the stimulus. Each subject is supposed to have some discrimination abilities, expressed by discrimination probabilities, leading to p_xy = H[u(x) − u(y)]. Various discussions about the forms of the functions H(.) and u(.) were addressed in the 1970s. It also led to various extensions, notably Luce's logistic model (see Luce 1959c; Falmagne 2002, chap. 5); de Palma and Thisse 1987; McFadden 2001).

³⁰ For instance, binary choices are more easily observable than more complex rankings. Also, the size of the set of alternatives shall not be too large, since some conditions imply a complete simultaneous observation of probabilities on all possible binary choices.

³¹ Notably, Davidson, Suppes, and Siegel (1957, 31) have defined a stochastically continuous set of alternatives. Davidson and Marschak (1959) have shown that stochastic continuity is equivalent to the quadruple condition. Nevertheless, one may wonder whether stochastic continuity is more plausible that the quadruple condition since it assumes condition (ii). . See also Debreu (1958).

³² A weaker transitivity condition is studied by Georgescu-Roegen (1958) and Chipman (1960).

³³ See also Georgescu-Roegen (1936, 587).

³⁴ “The assumption of knowledge and of comparability of alternatives is widespread in economics. The assumption of knowledge is composed of two distinct assumptions. First, it is assumed that the consumer knows the available alternatives. Secondly, it is assumed that he is familiar with the methods of finding a set of strategies which will maximize his chances of attaining his goals”. (Quandt 1956, 508).

³⁵ This phrasing comes from the fact that in supermarkets, when people are in state of ignorance or hesitation regarding two or more similar products, they buy brands located on the top shelves rather than on bottom shelves.

³⁶ “A is preferred to B (in the present sense of the word ‘preferred’) if the sum of the probabilities of considering pairs of characteristics for which the A characteristic has higher utility is greater than .5” (Quandt 1956, 522).

³⁷ In the first example, there is a hypothesis of absence of independence, meaning that the characteristics considered as significant for evaluating one commodity will impact the relevant characteristics for the other commodity. In another example, Quandt removes this assumption, and constructs a hypothetical joint probability distribution in the case when there is independency, such that intransitivity holds again (Quandt 1956, Table III, 522). It is to be noted that in this case, the pattern of probability can exhibit the cases enhanced either by Georgescu-Roegen (that the consumer takes account of all relevant characteristics) or Simon's idea that only some characteristics are taken into account.