Rationality in reproduction models¹

Vivian Walsh

Introduction

Rationality claims, in the original classics, primarily concerned what they regarded as the reasonable, responsible use of the surplus in the accumulation of capital. These claims were made in the French or English of their period, calling upon the rich resources of such natural languages for characterizing, and advocating, what was reasonable, wise and (emphatically!) natural. Neoclassical theory, on the contrary, developed a formal characterization of ‘rationality’ as a choice or action that satisfied an axiom set. Rationality claims were (naively) asserted to be ‘value-free’. Despite loudly proclaimed ‘rigour’, a number of distinguishable versions of what counted as ‘rationality’ were used, some of which were inconsistent with others. Thus neoclassical theorists kept several sets of books. During the Augustan age of Arrow “Debreu models (roughly 1950–75), this formalized analysis greatly impressed the less mathematical social sciences and spread widely. However, with the Balkanization of general equilibrium theory, an increasingly severe critique of the neoclassical axioms for ‘rationality’ has been growing, even from within the neoclassical economic and decision-theory establishment.

Meanwhile, classical theorists would be ill advised to buy this used neoclassical concept of rationality, though it is going cheap and has been recommended by rational choice Marxists. Classical theory, however, does need to develop its own analysis of what counts as rational choice in a present-day classical model, with transformational growth, technical innovation, and irrevocable changes in effectual demand.² Strategic choices may also be unavoidable, but the seductive sirens of game theory have hitherto sung a profoundly neoclassical song.

Increasingly serious and far-reaching critiques of the various (often inconsistent) formulations of the neoclassical concept of rationality have been appearing for a number of years with growing frequency. These criticisms come from younger theorists trained in the neoclassical tradition, as well as from present-day classical economists, and from philosophers. (For a survey of some of the extensive literature, see Walsh, 1996). The most important task now is to proceed to ‘the more constructive discussion of the appropriate reform of the idea of rationality within economics’ (Hamlin, 1997: 1593). There is indeed a need, as Alan Hamlin has pointed out, ‘for the reintegration of a richer and more philosophically attractive notion of rationality into economic theory’ (Hamlin, 1997: 1592).

Nicholas Baigent has drawn attention to the importance of asking, when considering an account of rational choice, what are the purposes for which it was constructed? He observes that ‘many neoclassical economists will argue that, for their purposes their narrow characterization is appropriate while they may well agree … that for other purposes, their characterizations are too narrow’ (Baigent, 1997: 550). Baigent suggests that, for Arrow and Debreu, ‘their main purpose was to address the issue of whether prices could be determined only by preferences, technology and endowments and, if so, whether the corresponding allocations would have desirable properties from a collective point of view’ (ibid.). Well, if they had stopped with the determination of prices, then many would feel that the sparse treatment of rationality was appropriate, for their narrow purposes. But they tried to combine this with that inconsistent tangle of utilitarianism and logical positivism known as Pareto optimality, whereupon their treatment of rationality is not too sparse “it is incoherent. The moral discourse of ‘desirable properties’ and ‘optimality’ and so on reveals a utilitarian subtext quite inconsistent with their prior axiomatic characterization of ‘utility functions’ as simply real-valued representations of orderings, with supposedly no welfarist presumptions. Their supposedly ‘value-free’ discourse has a subtext that is a full-blown welfarist, consequentialist, ordinal act of utilitarianism — a highly contentious moral stance (see Walsh, 1996: 174–202).

Why rationality was not more discussed in 20th-century classical circles

It has been observed by S. Abu Turab Rizvi that ‘the concept of rationality has not received much discussion in recent elaborations of ideas from classical economics’ (Rizvi, 1998: 256). He adds that ‘there are several good reasons for this, but some good reasons to further the discussion as well’ (ibid.). He is surely right on both counts. An important point is that the intellectual historians of the neoclassical period did not see rationality claims, even when the classics were making them. For the eighteenth-century classics, Nature and Reason walk hand in hand. Both the Physiocrats and Adam Smith are describing and advocating systems that they believed to be in accord with nature and thus reasonable, beneficent, and what a person of sense (a rational, or responsible person) would be wise to choose. It is easier to see this now that a present-day classical model of a natural system has been modelled for us by Luigi Pasinetti (1981, 1993), with its normative aspect explicitly on display.

The intellectual historians of the neoclassical period saw rationality ‘as being identical with utility (or preference) maximization’ (Rizvi, 1998: 256). This, of course, reduces rationality to preference act utilitarianism, or ‘preference function utilitarianism’, as Hilary Putnam calls it (Putnam, 1987: 58–62). It should be observed that, even as versions of utilitarianism go, this is a narrow and contentious moral position. It was slipped over the counter by neoclassics as just a simple, real-valued function, with no harmful ingredients” just a bit of ‘value-free’ science. In any case, as Rizvi notes, ‘classical theory makes no use of utility maximization and can even be seen as proposing arguments against its use’ (ibid.). Thus, neoclassics, identifying rationality with utility maximization, looked for this in the classics and did not find it.

Of course, someone reading the Smith texts as a whole would find it a little hard to ignore the fact that, as a moral philosopher who regarded political economy as a moral science, Smith was concerned with rational choice. But, from the early nineteenth century, attention came to be concentrated on the Wealth of nations, and on only a small part of that work, and David Ricardo’s (very understandable) concentration on only certain topics in Smith’s work may have had the (unintended) consequence of advancing this process of narrowing (Walsh, 1998a: 189–90, 2000: 5–6).

This habit of concentration on a few absolutely key analytical questions of classical theory would pass from Ricardo to a number of those who played major roles in the revival of classical economics from the turn of the century into the 1960s, notably in the case of Piero Sraffa (1960). Thus, this minimalist treatment was also characteristic of John von Neumann (see Kurz and Salvadori, 1995) and in some respects of Wassily Leontief. In fact, such a minimalism reflected the most critical need for the successful revival of classical theory: the most precise possible mathematical development of the structure of the theory (compare Walsh, 2000: 6). However, clearly a concentration on such a minimal complexity would tend to eliminate precisely the complexities of structure that draw attention to the significance of rational choice in classical contexts. Add to this the fact that those reviving classical theory were confronted on all sides by a dominant opponent whose theorists put a narrow concept of rationality at the centre of their theory and gave it especial prominence through the role played by demand in that theory. If this was what made theories of rational choice important, the revivers of classicism could conclude, then, as demand does not play this role in classical models, ‘rationality seems irrelevant’ (Rizvi, 1998: 256; Walsh, 1996: 231–56). The association of the ideas of rational choice, utility, and demand functions, in the mind of a twentieth-century classic, with all that was deeply wrong with neoclassical theory could well make the elimination of all such ideas seem a positive virtue.

It is, therefore, quite remarkable that one or two of the pioneers of the earlier classical revival did include some investigations that bear on rationality in their work. Vladimir Karpovich Dmitriev ([1898–1902] 1974) has been seen as an unhappy blend of classical and marginal utility theory, although it has been pointed out by Christian Gehrke that he ‘nevertheless retained the fundamental asymmetry in the treatment of the distributive variables which characterizes the classical approach to economic analysis’ (Gehrke, 1998: 226). Of more relevance here, however, is the work of that tragic figure Robert Remak, who ‘died in the concentration camp at Auschwitz’ (Kurz and Salvadori, 1995: 397). As Kurz and Salvadori note, ‘the idea of some kind of ideal prices, that is, prices fulfilling certain requirements or norms, kept fascinating intellectuals throughout the centuries … it surfaced again … in Robert Remak’s concept of “superposed prices”’ (Kurz and Salvadori, 1995: 36). They add that, more recently, such ‘concepts of ideal prices are encountered in Luigi Pasinetti’s “natural prices” … and in Francis Seton’s “eigenprices” (Seton, 1992)’ (ibid.). The case of Remak is all the more remarkable because he would appear to have adopted a severely narrow view of what counts as an exact science “a view that ‘bears a close resemblance to Leontief’s “naturalistic” point of view: an exact science regards as “exactly correct” only what can be ascertained by physical observation, counting on calculation’ (Kurz and Salvadori, 1995: 397). This attitude, as is well known, enters classical theory right at the beginning, with Sir William Petty. But it was present in twentieth-century dress in the work of some of the theorists who played major roles in the revival of classical ideas.

This is the moment to introduce a final reason for the absence of discussion of rational choice “especially philosophically rich discussion” in the works of these leading proponents of a classical revival: it would not have suited the philosophical climate of the age, and would have forced the twentieth-century classics to fight on an extra front. It has been noted by Lord Eatwell and Carlo Panico that a ‘compelling empiricism’ and ‘the rejection of the use of subjective concepts, are themes running throughout Sraffa’s economics. Economics should be constructed from variables and relationships which are, at least in principle, observable and measurable’ (Eatwell and Panico, 1987: Vol. IV, 445).

It has already been observed here that classical theory, from Petty on, has favoured a certain common-sense realism, an inclination towards number, weight, and measure hardly surprising in a theory some of whose key concepts are viability, total product, surplus, and the like. It was natural that, when classical theory revived, it would again manifest this down-to-earth point of view” as it notably does early on with Remak, and again later with Leontief and Sraffa. To reveal the anatomy of classical theory, this was just what was fitting.

It happened, however, that, from the beginning of the 1930s, a set of views emerged in Vienna and spread from continental Europe to Britain and America that can be seen now, with hindsight, to have been no friend to common-sense realism “despite an initial appearance of offering strong support (See Putnam, 1987: 3–40; Walsh, 2000: 6–10). Neoclassical theory rapidly absorbed these views in their original, most extreme form” the form roughly identified with the term ‘logical positivism’. A number of positions highly valuable to neoclassics depend on this original form of the epistemology and were no longer available when the erstwhile logical positivists retreated under deadly fire to their last stand in so-called logical empiricism. However, most neoclassical economists did not stay around in philosophical circles to discover that positions dear to their hearts, which they only believed in because of certain philosophers, had now been rejected by the philosophical community. (I have discussed the bearing of the failure of the logical positivist fact-value dichotomy for economics elsewhere: Walsh, 1996, 1998a, 1998b, and the equal failure of a ‘new dichotomy’, 2000. See, further, Putnam, 2002; Walsh, 2002).

Briefly, twin pillars that had together supported the logical positivist position were their sharp analytic-synthetic dichotomy and their equally sharp fact–value dichotomy. The first of these supported especially the neoclassical belief that the core of their theory was an axiomatically formulated, uninterpreted system,³ as is claimed by Gerard Debreu (1959). The second pillar supported especially the neoclassical claim that a true science must be totally ‘value-free’. Both pillars had fallen by the end of the 1950s, but the Arrow-Debreu class of model was entering the gilded age of its imperial sway. Economics has always lagged somewhat behind philosophy, mathematics (especially metamathematics), and logic.

Classical political economy, on the other hand, required a discourse that intricately combined facts, analysis, and evaluation. The original classics observed the fact that the economies in which they lived yielded a net product, or surplus. Their analysis showed them that this surplus was extracted from one economic class and absorbed by another, and led them to the conclusion, arrived at through a blend of factual observation, analysis, and moral judgement, that the responsible use of the surplus in their period was for the accumulation of capital (Walsh, 1998: 188–94). The fact must be faced, however, that, when classical theory revived, it became infected to some degree by the philosophical atmosphere of the 1930s, 1940s, and 1950s. For brevity, only one case of this will be noted here (see Walsh, 1996: 256–62). It concerns demand functions and Sraffa’s attitude towards these. Now, of course, given Sraffa’s objectives in his major work (Sraffa, 1960) and the nature of the stark classical drama that he wished to depict, it was natural for demand to be off-stage: ‘the observer can only grasp some elements of [the drama]’ (Salvadori, 1995: 163). Sraffa had performed the feat, perfectly reasonable for a classic but startling to marginalists, of explaining the relationship between prices, productions, and distributions ‘without considering any change “factual or counterfactual” and without, thus, invoking any “marginal” concepts at all’ (Sen, 1989: 305).

Now, it has sometimes been suggested that Sraffa’s whole object was to avoid counterfactuals, and perhaps Sraffa’s letter to A. Asimakopulos of 11 July 1971, cited by Salvadori (1995: 154), lends some support to such a claim. However, surely Sraffa’s main object was to present key components of classical theory, free from complications that were likely to confuse readers whose heads were stuffed with Marshallian fog “as Joan Robinson used to call it. And Sraffa, a major scholar of the original classics,⁴ knew that the works of every classic from Petty to Marx are full of counterfactuals and none the worse for it.

What is true is that a distrust of counterfactuals was in the air that economists still breathed when Sraffa wrote. Philosophers had moved on “and Sraffa, as will appear, had had a major influence on this. For the logical positivists, however, truly scientific statements had often been seen ‘as those that could be translated satisfactorily into Russellian symbolic logic. It was then discovered that counter-factual claims did not translate nicely. This caused great heart searchings during the heyday of logical positivism’ (Walsh, 1996: 257). Therefore, the fuss over counterfactuals was incidental to the logical positivists’ quest for an ideally rational language, in which only what was truly part of a unified science would appear. This quest was

linked to their belief in the unity of science, and thus to their acceptance of reductionism in regard to the languages of special sciences. It also underlay their belief in the desirability of translating things said in natural languages (seen as full of confusions and of primitive ‘metaphysical’ notions) into the supposedly pellucid logical clarity of the constructed language whose chaste perfections were their goal.

(Walsh, 1996: 92)

This project of Titanic hubris collapsed under its own weight, of course. But one of the most important influences, which changed the whole direction of philosophy, was that of Ludwig Wittgenstein’s Philosophical investigations (1972). There, Wittgenstein writes of the criticism that Sraffa ‘for many years increasingly practiced on my thoughts. I am indebted to this stimulus for the most consequential ideas of this book’ (Wittgenstein, 1972: viii; emphasis in original). And, of course, this work of Wittgenstein’s ‘was the fountainhead of much of that subtle analysis of ordinary language which was one of the acids which ate away at the crude logical positivist analysis of the meaningful uses of language’ (Walsh, 1996: 258). Hence, Sraffa played a major role in the downfall of the philosophical tradition that was a principle support for neoclassical economics, and the epistemological basis for its formalism and for its supposed ‘value-free’ status. The main barrier to philosophically richer rationality claims by a reviving classical school had thus been removed, to a considerable extent through Sraffa’s influence. It has taken some time, however, for this to sink in.

An enriched classical theory

The time is thus ripe for the development of such an enriched classical theory, and I have argued elsewhere that one can see strong signs that the classical revival, its analytical core established, is moving into a second stage (Walsh, 2000). This can be seen by an examination of the body of work by Amartya Sen during a number of years, and in strikingly related work by Luigi Pasinetti (1981, 1993) and by Bertram Schefold (1990) among others (for a short discussion of Pasinetti and Schefold, see Walsh, 2000: 16–22).

The work of Sen on human capabilities, functionings, and flourishings, and on the bearing of these on poverty, inequality, and exploitation, is unmistakably classical, and equally unmistakably a revival of the richly descriptive classicism of Smith and Marx. It triumphantly violates every canon of the old logical positivist discourse. Schefold, taking a classical point of view, insists that, ‘there are certain hierarchies of needs, from basic needs up to higher needs such as the need for self-fulfillment’ (Schefold, 1990: 187). For classical theory this is true and appropriate, but it must be noted that, for formal neoclassical theory, the verb ‘to need’ and what are referred to in ordinary language as ‘basic needs’ or ‘higher needs’ cannot appear with their usual family of legitimate uses. These words all belong to a logical family whose role in natural language is three-fold: to describe facts, to convey analytical distinctions, and to make moral claims. Such discourse violates the epistemological principles underlying the formalism of Arrow-Debreu (specifically the analytic-synthetic dichotomy and the fact-value dichotomy). The formal language of Arrow-Debreu theory can make no distinction between a poor mother who denies herself necessities to buy food for her child and a commodities speculator who buys himself a seven-million-dollar house: both appear as simply ‘agents’ who ‘reveal preferences’.

It is important to observe that nineteenth-century and early twentieth-century neoclassicism was not in this situation. Economists such as Francis Ysidro Edgeworth and Arthur Cecil Pigou were believing utilitarians, and utilitarianism when honestly embraced in one of its richer forms could be a serious moral philosophy “even if a narrow and flawed one. Surveying the obvious facts of the Britain he lived in, and applying his economic analysis and his utilitarian moral judgement, Pigou could claim that the desperate needs of the poor had more importance than the whims of the rich. Logical positivism saved neoclassical theory from having to face such issues “just when the great depression was making them awkwardly pressing. How could the neoclassics not cherish such a consoling philosophy?

The original classics, of course, always felt able to distinguish between needs and wants of various levels of seriousness. For them, it was a part of the role of the moral science of political economy. For Adam Smith, in particular, there was a distinction between ‘necessaries, conveniencies and luxuries’ (Gram, 1998: 162). Such concepts, Harvey Gram argues, are ‘central to the classical theory of value and distribution … No account of the general reproduction problem can proceed for long without taking into account the wide range of issues considered by Smith’ (Gram, 1998: 165–6). As Gram notes, there is a very large web of interdependent components of a comfortable human life. These are ‘conveniencies’, and should by no means be dismissed as luxurious waste of the surplus. Luigi Pasinetti chooses ‘to remain on the objective ground, previously trod by classical economists, of the variations of the physical quantities of the various goods and services demanded as income changes’ (Pasinetti, 1993: 37). He insists, however, that ‘a dynamic analysis requires a decisive enrichment of the reference framework’ (Pasinetti, 1993: 38; emphasis added). He expects various needs to be satisfied in ‘a certain hierarchical order’ (ibid.) and that changes in consumption will also result independently of income, or price changes, as newly invented goods appear. He does not explicitly discuss the role of lexical orderings in this context, though the possibility of their arising is clearly present.

By confining himself to goods and services and to needs, Pasinetti lags some -what behind Sen’s more flexible and comprehensive account in terms of capabilities. Nevertheless, Pasinetti’s ‘natural system’ is described by him as possessing ‘strong normative properties’ (1993: 117), and his whole approach implies a rejection of logical positivist dichotomies every bit as deeply seated as that of Sen. Furthermore, as I have noted elsewhere, Pasinetti ‘explicitly compares his uses of the word “natural” with the ways in which that word appears in the discourse of the original classics’ (Walsh, 2000: 18). He stresses the sharp differences between his natural system and the market outcomes we can expect in today’s world of unrestrained transnationals and ‘hot’ finance, remarking that ‘the truth is that labor could be traded as any other commodity only in a slave society’ (Pasinetti, 1993: 127–8). His argument highlights the vulnerability of labour in the world today. What coalitions can a working class form in order to resist the oppressive forces ranged against it?

Towards classical concepts of choice among strategies

As rapid technical change takes place, and new commodities appear, some of which are benign conveniencies while others are profoundly damaging, what coalitions can be formed to resist the dehumanization of labour, the destruction of the earth, and the unchecked growth of irresponsible power? Game theory now comes centre stage.

There can surely be no doubt that, once classical theory ventures into Pasinetti’s world of structural dynamics (if not before!), rational choice must include some form of strategic choice. Younger theorists, trained on Arrow-Debreu of course (but who assure one that they have rejected some of the axioms of the old church), delicately press the claims of game theory. And there are some unimpeachably progressive people who have been converted to what is called ‘rational choice Marxism’, and who write with elegance and wit, but also with the passion of recent converts.

The problem for a classic about game theory as it has evolved is in its genes. Many of these genes are pure neoclassic, of the axiomatic, formalist period. The concept of the ‘core’ was, as is well known, informally treated by Francis Ysidro Edgeworth, but (more importantly) when it was rescued from neglect, this was done by scholars living and working in the Arrow-Debreu establishment (Walsh, 1996: 151–62; for an advanced treatment, see Mas-Colell, 1982, 1985). One of the most famous axiomatizations of expected utility theory was that of John von Neumann and Oskar Morgenstern (1944), and this influenced the axiomatic treatment of rationality in the work of Arrow and Debreu on general equilibrium theory, ably summarized in Debreu (1959). The history and personalities of canonical Arrow-Debreu theory, game theory, and what Maurice Allais calls the ‘American School’ of decision theory are closely intertwined.⁵ Their ideas intermingle at the deepest levels. Consider one technical point: it has been remarked that ‘the major advance in relevant mathematical methods during this period [1940–50] was Kakutani’s fixed point theorem (1941). An abstract expression of the existence of equilibrium, it is the vital active ingredient of countless proofs in economics and game theory’ (Aumann, 1987: 467; emphasis in original). Robert Aumann, by the way, was one of the most important contributors to the investigation of the cores of Edgeworth economies and the cores of games.

A situation seems to be developing within game theory circles that has some similarities to that which developed in decision theory (Walsh, 1996: 48–67). For a long time, Allais was almost the only voice challenging the ‘American School’. Now, a number of younger theorists have challenged its axioms (some of which, incidentally, are also to be found in game theory). Only a brief sketch of what may be signs of a similar critical wave can be given here.

It has been argued that ‘the most important analytical tool in non-cooperative game theory is the concept of the Nash equilibrium’ (Jacobsen, 1996: 67). Hans Jørgen Jacobsen then comments: ‘that justification of the Nash equilibrium is needed, is evidenced by the recent growing literature seeking foundations for game theoretical solution concepts’ (ibid.). The reader will find references to a fairly extensive selection of recent papers raising questions as to one or other of a number of points concerning Nash equilibria in S. Abu Turab Rizvi (1994: 1–28). A Nash equilibrium is a choice of strategies such that it is impossible for any individual player to gain by playing differently, given that the other players abide by their prescribed strategies. This aspect of Nash equilibria, Rizvi notes, ‘is intuitively compelling to many’ (Rizvi, 1994: 10). ‘Once the players are in a Nash equilibrium there is, by construction, no incentive for any one of them to deviate from it’ (ibid.). He cites Aumann’s rather revealing comment that ‘Nash equilibrium is the embodiment of the idea that economic agents are rational. They simultaneously act to maximize their utility’ (Aumann, 1987: 43).

However, if players can communicate at all, then, as Rizvi observes ‘cooperative coalition formation is possible [Fudenberg and Tirole, 1989: 275]. Thus a group of individuals may want to deviate from the Nash strategy even if no individual does’ (Rizvi, 1994: 10–11). There have, of course, been efforts to model group deviations. But ‘this is not generally an equilibrium phenomenon. Thus the Nash equilibrium concept, the tool always put forward for analyzing strategic behavior, does not really address truly strategic interactions such as those involving group deviations from its prescriptions’ (ibid.). He adds a point that suddenly brings into prominence the neoclassical flavour of existing game theory: ‘the only setting in which group deviations cannot profitably be made is the continuum characterization of perfect competition … but this is precisely one reason why perfect competitors and Nash equilibrium go so well together’ (ibid.; emphasis added). The Nash concept, it will be recalled, was used to prove existence for perfectly competitive equilibrium. It was all very cosy.

John von Neumann and Oskar Morgenstern had hoped to find ‘the mathematically complete principles that define “rational behavior” for the participants in a social economy, and to derive from them the general characteristics of the behavior’ (Neumann and Morgenstern, 1947 [1944]: 32). Rizvi comments on this by citing work in support of his claim that ‘recently it has become clear that such a goal is not attainable’ (Rizvi, 1994: 12). From his discussion, a conclusion that stands out from the point of view of the present paper is the result (of widespread debate) ‘that game-theoretical rationality, as defined by a variety of criteria … is inconsistent with the intuition based or common sense way to play a game’ (Rizvi, 1994: 13). Researchers describe well-informed players disobeying game-theory recommendations.

One might compare these reports with the experimental evidence that people do not conform to the axioms of (American School) expected utility theory. As has been noted,

persistent failure of the theory [of expected utility] as an account of actual choice or action can impinge on its status as an account of rationality. Philosophically, this failure forces the theorist to adopt a radically revisionist concept of rationality. The theorist must say in effect ‘if you don’t act in conformity with my axioms then you simply are not rational’.

(Walsh, 1996: 52)

Rizvi’s argument continues, treating a number of game-theoretical issues that cannot be dealt with here but that the reader is strongly encouraged to sample for herself.

One point of arguably considerable interest to classics concerns the possible reason why neoclassical theorists turned as a mass to game theory in the 1980s. The Balkanization of the empire of the original Arrow-Debreu models after about 1975 has already been noted, but certain results in the same period were in fact even more fatal. As Rizvi notes:

In the 1970s, Hugo Sonnenschein, Rolf Mantel, and Gerard Debreu established a series of results regarding the properties of aggregate excess demands arising in Walrasian general equilibrium models of the Arrow-Debreu” McKenzie type. They showed that, despite the usual assumptions made on preferences, endowments, and technology, the aggregate excess demands were arbitrary, save that they satisfied Walras’s Law and continuity (Sonnenschein, 1972, 1973a, b; Mantel 1974, 1976, 1977; Debreu, 1974)

(Rizvi, 1997: 269)

Other characterizations followed, but Rizvi refers to this development as SMD theory, after its three originators. Now he notes that one of the consequences of the SMD results has been ‘an abandonment of strict microfoundations’ (Rizvi, 1997: 270). At first there was scepticism, but ‘by now, however, even such erstwhile stalwarts of general equilibrium theory as Christopher Bliss compare that theory to theology (1993, 227)’ (Rizvi, 1997: 271). He cites Bliss: ‘The near emptiness of general equilibrium theory is a theorem of the theory’ (Bliss, 1993: 227).

Rizvi notes that ‘an important feature of these new approaches is that they are no longer based on strict microfoundations. Societal characteristics are used to underpin the analysis of the macroeconomic regularities’ (Rizvi, 1997: 275; emphasis in original). He cites Jean-Michel Grandmont:

The present analysis raises again some (old) questions about the actual status of the postulates of individual ‘rationality’ in the Walrasian paradigm … An alternative research strategy would be indeed to actually reverse the traditional Neoclassical research programme, and to try to obtain some form of aggregate rationality.

(Grandmont, 1992: 33; emphasis in original)

Rizvi is hardly exaggerating when he observes that these changes will have methodological and philosophical repercussions on neoclassical theory, nor is he unreasonable in suggesting that ‘game theory methods were adopted because the general equilibrium project, under the influence of the arbitrariness results, was left with nowhere to go’ (Rizvi, 1994: 25).

The reasons why neoclassics embraced game theory need not persuade a classic to follow suit. This is especially so if these reasons had to do with the weaknesses rather than the strengths of the neoclassical position. However, these reasons do set the stage for the remaining topic of this paper, which concerns how classics should regard ‘rational choice’ Marxian analyses and their methods.

‘Analytical’ Marxian theory: rationality concepts for the surplus approach?

Much of the literature critical of ‘rational choice’ or ‘analytic’ Marxian theory is concerned with the question of whether or not this theory is faithful to Marx. This literature is well represented by, for example W.H. Anderson and Frank W. Thompson (1988) and by Michael Lebowitz (1988). This question, however, will be left to specialist Marxian scholars. A quite different (and hopefully simpler) question will be glanced at here, namely, ‘the bearing of Roemer’s work for any present-day model of surplus and class’ (Walsh, 1996: 263). It should be noted, however, that even some of Roemer’s fairly severe critics, such as James Devine and Gary Dymski, ‘do not propose a blanket rejection’ of Roemer’s ‘game-theoretical approaches’ (Devine and Dymski, 1991: 161). It has been observed, on the other hand, that Roemer is committed to a particularly strong form of methodological individualism, as the Walrasian general equilibrium system, whose assumptions he adopts, ‘is even stronger than methodological individualism per se in that it in addition precludes coercion’ (Devine and Dymski, 1991: 238; emphasis in original).

Now, it can be shown that methodological individualism involves reductionism of at least two types, both long since discredited; indeed the serious supporter of the doctrine is committed to maintaining a veritable museum of abandoned early twentieth-century philosophical projects (Walsh, 1996: 12–28). However, there is now a more worldly reason why a classical theorist should have second thoughts before offering to take up and carry the methodological baggage of ‘analytic’ Marxian theory. It is this: arguably, one of the charms of this theory was that it enabled a theorist (who wanted to analyse surplus, class, and exploitation) nevertheless to appear dressed correctly in the axioms and doctrines of that supposed paragon of ‘rigor’, the canonical Arrow-Debreu model. However, as the literature surveyed by Rizvi shows, the canonical Arrow-Debreu model is a mansion deserted by its owners, the party is over, and the rigour has become rigor mortis. One could almost define Roemer’s project as the provision of solidly neoclassical microfoundations for the erstwhile (to neoclassics) impermissible concepts of classes and their exploitation. The one school of thought that demanded microfoundations as the price of admission, however, has abandoned this project, which rather leaves ‘analytical’ Marxian theory hanging.

A lively debate about the merits of the ‘analytical’ approach in general, and game theory in particular, will be found in the exchanges between Thomas F. Mayer (1993–4: 446–53) and Yanis Varoufakis (1993–4: 453–60; see also 1991 and 1992–3: 440–66). Mayer accepts the neoclassical methodology wholeheartedly, but for startlingly new, non-neoclassical reasons. He defends the concept of instrumental rationality (which even neoclassics fail to be faithful to) as ‘the most lucid and precise concept’ and therefore one ‘victims of exploitation require’ (Mayer, 1993–4: 447). Varoufakis attacks on the front opened up by the problems concerning Nash equilibria. Mayer concedes that ‘many games have multiple Nash equilibria, and game-theory does not yet provide a satisfactory explanation of how players arrived at a particular one’ (Mayer, 1993–4: 450–1). But he believes that the Nash strategy has a better chance than others. Varoufakis argues that a very strong assumption is needed to support game theory:

In simple words, agents (e.g. workers) must always assume that they cannot outwit their opponents; that their conceptualization of the social interaction is always shared with their foes (who know this to be true). Granted that in utterly simplistic games this may be so … there is no evidence that this uniqueness exists in larger struggles.

(Varoufakis, 1993–4: 456)

Mayer’s position would appear to imply that it is never rational for an organized class to attempt to outwit its opponents.

Mayer and Varoufakis appear both to have written without awareness of the consequences of SMD theory. The implications of this would surely have notably strengthened Varoufakis’s hand. Commenting on the deeply neoclassical tendencies of a game theoretical discourse, he remarks ‘we can ignore them, but they are bound to haunt any emancipatory narrative which accepts its philosophical foundations’ (Varoufakis, 1993–4: 455). What one feels most strongly in reading Mayer and Varoufakis, however, is the acute need for a great deal of work, freed from the albatross of neoclassical assumptions, on the nature and possibilities of an account of strategic choices consistent with classical theory.

Notes

1 I am indebted to Steve Pressman and Gary Mongiovi for many helpful conversations on this and other works of mine, and to Lisa Bendall-Walsh for editorial assistance. The usual disclaimers apply.

2 In this paper, the term ‘demand’ will normally be used to refer to Smith’s ‘effectual demand’, defined as ‘the quantity demanded at the natural or normal price’ (Garegnani, 1990: 133). The relationships between demand and income, commonly represented by Engel curves, will also underlie some of the discussion, especially of the work of Luigi Pasinetti (1981, 1993). On some questions concerning the role of demand in Sraffa (1960), which will not be treated here, the reader should consult Neri Salvadori (1995) and the sources cited there.

3 Perhaps is should be mentioned that plenty of present-day classical theorists use an axiomatic style of presentation in their proofs, without even suggesting endorsement of the extreme metamathematical and epistemological claims for ‘uninterpreted systems’ of the formalist period. A little axiom set is a good and gentle creature and it be well used” and as useful as a shopping list to aid human memory!

4 Gary Mongiovi has remarked in conversation how much Sraffa’s papers confirm his deep interest in the richer versions of classical and Marxian theory.

5 For added complexity, note that, although Neumann was always regarded as a neoclassic by the mainstream, he and Morgenstern were in fact an important part of the twentieth-century revival of classical theory. This is a theme of Kurz and Salvadori (1995); see also Kurz and Salvadori 1988b, 25–6; and Walsh, 2003). Perhaps one might say that the neoclassics were influenced by Neumann’s mathematics rather than by his economics.

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