Home > Uncategorized > Revealed preference theory — much ado about almost nothing

Revealed preference theory — much ado about almost nothing

from Lars Syll

samTwenty-seven years ago yours truly wrote an article on revealed preference theory that got published in History of Political Economy (no. 25, 1993).

Paul Samuelson wrote a kind letter and informed me that he was the one who had recommended it for publication. But although he liked a lot in it, he also wrote a comment — published in the same volume of HOPE — saying:

Between 1938 and 1947, and since then as Pålsson Syll points out, I have been scrupulously careful not to claim for revealed preference theory novelties and advantages it does not merit. But Pålsson Syll’s readers must not believe that it was all redundant fuss about not very much.

Notwithstanding Samuelson’s comment, I do still think it basically was much fuss about ‘not very much.’

In 1938 Paul Samuelson offered a replacement for the then accepted theory of utility. The cardinal utility theory was discarded with the following words: “The discrediting of utility as a psychological concept robbed it of its possible virtue as an explanation of human behaviour in other than a circular sense, revealing its emptiness as even a construction” (1938, 61). According to Samuelson, the ordinalist revision of utility theory was, however, not drastic enough. The introduction of the concept of a marginal rate of substitution was considered “an artificial convention in the explanation of price behaviour” (1938, 62). One ought to analyze the consumer’s behaviour without having recourse to the concept of utility at all, since this did not correspond to directly observable phenomena. The old theory was criticized mainly from a methodological point of view, in that it used non-observable concepts and propositions.

awongThe new theory should avoid this and thereby shed “the last vestiges of utility analysis” (1938, 62). Its main feature was a consistency postulate which said: “if an individual selects batch one over batch two, he does not at the same time select two over one” (1938, 65). From this “perfectly clear” postulate and the assumptions of given demand functions and that all income is spent, Samuelson in (1938) and (1938a), could derive all the main results of ordinal utility theory (single-valuedness and homogeneity of degree zero of demand functions, and negative semi-definiteness of the substitution matrix).

In 1948 Samuelson no longer considered his “revealed preference” approach a new theory. It was then seen as a means of revealing consistent preferences and enhancing the acceptability of the ordinary ordinal utility theory by showing how one could construct an individual’s indifference map by purely observing his market behaviour. Samuelson concluded his article by saying that “[t]he whole theory of consumer’s behavior can thus be based upon operationally meaningful foundations in terms of revealed preference” (1948, 251). As has been shown lately, this is true only if we inter alia assume the consumer to be rational and to have unchanging preferences that are complete, asymmetrical, non-satiated, strictly convex, and transitive (or continuous). The theory, originally intended as a substitute for the utility theory, has, as Houthakker clearly notes, “tended to become complementary to the latter” (1950, 159).

Only a couple of years later, Samuelson held the view that he was in a position “to complete the programme begun a dozen years ago of arriving at the full empirical implications for demand behaviour of the most general ordinal utility analysis” (1950, 369). The introduction of Houthakker’s amendment assured integrability, and by that, the theory had according to Samuelson been “brought to a close” (1950, 355). Starting “from a few logical axioms of demand consistency … [one] could derive the whole of the valid utility analysis as corollaries” (1950, 370). Since Samuelson had shown the “complete logical equivalence” of revealed preference theory with the regular “ordinal preference approach,” it follows that “in principle there is nothing to choose between the formulations” (1953, 1). According to Houthakker (1961, 709), the aim of the revealed preference approach is “to formulate equivalent systems of axioms on preferences and on demand functions.”

But if this is all, what has revealed preference theory then achieved? As it turns out, ordinal utility theory and revealed preference theory are – as Wong puts it – “not two different theories; at best, they are two different ways of expressing the same set of ideas” (2006, 118). And with regard to the theoretically solvable problem, we may still concur with Hicks that “there is in practice no direct test of the preference hypothesis” (1956, 58).

Sippel’s experiments showed “a considerable number of violations of the revealed preference axioms” (1997, 1442) and that from a descriptive point of view – as a theory of consumer behaviour – the revealed preference theory was of a very limited value.

Today it seems as though the proponents of revealed preference theory have given up the original 1938-attempt at building a theory on nothing else but observable facts, and settled instead on the 1950-version of establishing “logical equivalences.”

Mas-Collel et al. concludes their presentation of the theory by noting that “for the special case in which choice is defined for all subsets of X [the set of alternatives], a theory based on choice satisfying the weak axiom is completely equivalent to a theory of decision making based on rational preferences” (1995, 14).

When talking of determining people’s preferences through observation, Varian, for example, has “to assume that the preferences will remain unchanged” and adopts “the convention that … the underlying preferences … are known to be strictly convex.” He further postulates that the “consumer is an optimizing consumer.” If we are “willing to add more assumptions about consumer preferences, we get more precise estimates about the shape of indifference curves” (2006, 119-123, author’s italics). Given these assumptions, and that the observed choices satisfy the consistency postulate as amended by Houthakker, one can always construct preferences that “could have generated the observed choices.” This does not, however, prove that the constructed preferences really generated the observed choices, “we can only show that observed behavior is not inconsistent with the statement. We can’t prove that the economic model is correct.”

Kreps holds a similar view, pointing to the fact that revealed preference theory is “consistent with the standard preference-based theory of consumer behavior” (1990, 30).

The theory of consumer behavior has been developed in great part as an attempt to justify the idea of a downward-sloping demand curve. What forerunners like e.g. Cournot (1838) and Cassel (1899) did was merely to assert this law of demand. The utility theorists tried to deduce it from axioms and postulates on individuals’ economic behaviour. Revealed preference theory tried to build a new theory and to put it in operational terms, but ended up with just giving a theory logically equivalent to the old one. As such it also shares its shortcomings of being empirically unfalsifiable and of being based on unrestricted universal statements.

As Kornai (1971, 133) remarked, “the theory is empty, tautological. The theory reduces to the statement that in period t the decision-maker chooses what he prefers … The task is to explain why he chose precisely this alternative rather than another one.” Further, pondering Amartya Sen’s verdict of the revealed preference theory as essentially underestimating “the fact that man is a social animal and his choices are not rigidly bound to his own preferences only” (1982, 66) and Georgescu-Roegen’s (1966, 192-3) apt description, a harsh assessment of what the theory accomplished should come as no surprise:

georgescu1Lack of precise definition should not … disturb us in moral sciences, but improper concepts constructed by attributing to man faculties which he actually does not possess, should. And utility is such an improper concept … [P]erhaps, because of this impasse … some economists consider the approach offered by the theory of choice as a great progress … This is simply an illusion, because even though the postulates of the theory of choice do not use the terms ‘utility’ or ‘satisfaction’, their discussion and acceptance require that they should be translated into the other vocabulary … A good illustration of the above point is offered by the ingenious theory of the consumer constructed by Samuelson.

Nothing lost, nothing gained.

Cassel, Gustav 1899. ”Grundriss einer elementaren Preislehre.” Zeitschrift für die gesamte Staatswissenschaft 55.3:395-458.

Cournot, Augustin 1838. Recherches sur les principes mathématiques de la théorie des richesses. Paris. Translated by N. T. Bacon 1897 as Researches into the Mathematical Principles of the Theory of Wealth. New York: The Macmillan Company.

Georgescu-Roegen, Nicholas 1966. “Choice, Expectations, and Measurability.” In Analytical Economics: Issues and Problems. Cambridge, Massachusetts: Harvard University Press.

Hicks, John 1956. A Revision of Demand Theory. Oxford: Clarendon Press.

Houthakker, Hendrik 1950. “Revealed Preference and the Utility Function.” Economica 17 (May):159-74.
–1961. “The Present State of Consumption Theory.” Econometrica 29 (October):704-40.

Kornai, Janos 1971. Anti-equilibrium. London: North-Holland.

Kreps, David 1990. A Course in Microeconomic Theory. New York: Harvester Wheatsheaf.

Mas-Collel, Andreu et al. 1995. Microeconomic Theory. New York: Oxford University Press.

Samuelson, Paul 1938. “A Note on the Pure Theory of Consumer’s Behaviour.” Economica 5 (February):61-71.
–1938a. “A Note on the Pure Theory of Consumer’s Behaviour: An Addendum.” Economica 5 (August):353-4.
–1947. Foundations of Economic Analysis. Cambridge, Massachusetts: Harvard University Press.
–1948. “Consumption Theory in Terms of Revealed Preference.” Economica 15 (November):243-53.
–1950. “The Problem of Integrability in Utility Theory.” Economica 17 (November):355-85.
–1953. “Consumption Theorems in Terms of Overcompensation rather than Indifference Comparisons.” Economica 20 (February):1-9.

Sen, Amartya (1982). Choice, Welfare and Measurement. London: Basil Blackwell.

Sippel, Reinhard 1997. “An experiment on the pure theory of consumer’s behaviour.” Economic Journal 107:1431-44.

Varian, Hal 2006. Intermediate Microeconomics: A Modern Approach. (7th ed.) New York: W. W. Norton & Company.

Wong, Stanley 2006. The Foundations of Paul Samuelson’s Revealed Preference Theory. (Revised ed.) London: Routledge & Kegan Paul.

  1. October 7, 2020 at 2:18 am

    I find it mindbogglingly that, in a world dominated and shaped by hierarchical power, economic experts still debate ‘utility theory’ and the ‘rational choices’ of ‘autonomous agents’. In some sense, the very fact they seriously debate this myth serves to invalidate it.

    • October 7, 2020 at 9:13 am

      Whose Utilitiarianism are you talking about, Jonathan? Mill’s macro version or Jevon’s’ micro?

      • October 7, 2020 at 7:09 pm

        I’m not talking about the philosophical contemplation of early political economists. I’m talking about modern-day neoclassicists who believe — and condition others to believe — that the capitalist world we live in consists of autonomous/atomistic calculators of pleasure and pain, and that modelling the interactions of these imaginary automatons can tell us anything at all about the capitalist mode of power we live in.

  2. Ikonoclast
    October 7, 2020 at 11:05 am

    Economist Ernestine Gross, on John Quiggin’s blog, has written;

    “As I have pointed out on numerous occasions, the theoretical models of private ownership economies (from Arrow-Debreu onwards), contain a strong assumption on the wealth distribution (to make the promised freedom of choice more than an empty phrase).”

    Ernestine G. has previously used the phrase “minimum wealth condition” in the context of private ownership economies from Arrow-Debreu theoretical models onward. Ernestine is essentially saying that a minimum wealth condition “inferring a strong assumption on the wealth distribution” is necessary “to make the promised freedom of choice (in the market) more than an empty phrase”. That is, there is no freedom of choice in a market economy for a person with no wealth and no income.

    Ernestine G. concludes “… the results by Quiggin and Gross show that neither price taking, nor profit maximization, nor private ownership are sufficient to rely on (for) ‘micro-economic reform’.” Note, these are separate results in quite separate papers but clearly in the same analytical paradigm.

    I am happy enough to take this theoretical result which shows that we need a minimum wealth condition (for each and every individual) to ensure (some) freedom of choice in a pure market economy. My provisional acceptance here is cognizant of the issues and limits of analytical modelling meaning using axiom or postulate based models to derive theorems. My provisional acceptance can be expressed as follows. The results suggest that IF we provisionally accept that a pure market economy could be ideal (pareto optimum), even then it can be shown rigorously that a minimum wealth condition is required to enable it to deliver operable and survivable choices to all. Either the private ownership / market system must somehow guarantee a minimum wealth condition or a government welfare system must do so.

    I then take a position based on Ulf Martin’s paper “The Autocatalytic Sprawl of Pseudorational Mastery”.

    Martin talka about the relatively greater power of a person in our system who has greater Kapitalvermögen or ‘capital might’ to affect (and even effect) a new condition of the world. or of a part thereof, at a future time, compared to a person with less (usually much less) Kapitalvermögen or ‘capital might’.

    Colloquially we this in English by saying “Money is power”. Since money is power it can be used to create a new order at time t2 such that the ability of money “to make more money” is enhanced. One standard method in a democracy (so-called) is to donate to politicians’ campaigns to get desired legislation passed (legislative capture). Gilens and Page in ” Testing Theories of American Politics:Elites, Interest Groups, and Average Citizens” found that:

    “Each of four theoretical traditions in the study of American politics—which can be characterized as theories of Majoritarian Electoral Democracy, Economic-Elite Domination, and two types of interest-group pluralism, Majoritarian Pluralism and Biased Pluralism—offers different predictions about which sets of actors have how much influence over public policy: average citizens;economic elites; and organized interest groups, mass-based or business-oriented.A great deal of empirical research speaks to the policy influence of one or another set of actors, but until recently it has not been possible to test these contrasting theoretical predictions against each other within a single statistical model. We report on an effort to do so, using a unique data set that includes measures of the key variables for 1,779 policy issues.Multivariate analysis indicates that economic elites and organized groups representing business interests have substantial independent impacts on U.S. government policy, while average citizens and mass-based interest groups have little or no independent influence. The results provide substantial support for theories of Economic-Elite Domination and for theories of Biased Pluralism, but not for theories of Majoritarian Electoral Democracy or Majoritarian Pluralism.”

    Given the power of the elites to push through neoliberalism politically from 1980 to 2020, and the consequent economic, social and environmental problems, we have to conclude that already excessive concentrations of wealth were the proximal initiating reason for the further and continued shift to the greater monopolization of wealth and power in a reinforced feed-back loop. This suggests a need also for a maximum wealth condition in the model.

    Presuming we run a private property / market economy system, then minimally we need to place a minimum wealth condition and a maximum wealth condition for each person on or in the system, by legislative fiat if necessary. Without external controls on the market (viewing legislative and regulatory controls as external to a “pure” market), then both theoretical and empirical outcomes show that market-powerless people are produced (homeless, incomeless and asset-less) and market over-powered people (and firms) are produced (billionaires and oligopolies).

    This suggests that a significant step to the reform of unfettered markets would be the imposition of minimum wealth limit AND maximum wealth limit on persons. Why would we assume that persons should be able to survive on nothing at one end of the spectrum and that some few other persons should be able expand wealth indefinitely in a finite world and that this model would produce (eventually?) pareto optimum outcomes? Such an assumption is patently absurd.

  3. Bernard Guerrien
    October 7, 2020 at 3:17 pm

    Last but not least : Sonnenschein proved its “theorem” about the slope of demand curve using revealed preference axioms.

  4. Yoshinori Shiozawa
    October 7, 2020 at 5:03 pm

    Bernard, what do you want to say by your comment? If you are not intending to defend the preference concept, it is all right. Sonnenschein-Mantel-Debrue theorem is a case that neoclassical theory (of Arrow-Debreu type) revealed its internal weakness. Implication of the theorem is the necessity to build a system of understanding of how market economy works. It must be totally different from Arrow and Debreu’s.

  5. John deChadenedes
    October 7, 2020 at 5:04 pm

    I don’t understand why economists resolutely ignore non-transitive preferences. My first microeconomics prof said they don’t exist! But it is very easy to show that under conditions with three or more options and three or more criteria non-transitive preferences easily arise. This means that depending on which options are considered A is preffered to B, B is preferred to C, but also C is preferred to A.

    • Yoshinori Shiozawa
      October 7, 2020 at 6:53 pm

      John, you have just experienced a typical reaction from those professors who work or think in neoclassical tradition. But you must know that there are lot of economists (including me) who think transitive preference is totally absurd. You observations is one of reasons why heterodox economists reject neoclassical economics. They are trying to construct another economics that does not depends on transitive preference. The transitivity of preference is only necessary for the utility maximization formulation of an equilibrium. Many economists simply throw away the holy trinity of neoclassical economics: individuality, optimization and equilibrium.

      As an example, please read our book on Microfoundations of Evolutionary Economics (2019). You can read Marc Lavoie’s book review on it..

  6. Ikonoclast
    October 8, 2020 at 12:15 am

    One can “prove” anything in theory by assuming the right postulates. For example, “God” as a postulate can be used to prove any desired theorem. This process, being one of speculative metaphysics, depends on the revealed preferences and revealed nature of “God” as adduced by a theorizing individual via recourse to a received dogma or recourse to an explicit or implicit alternative exegesis of the authoritative texts. Conventional economics can be viewed in a similar light as attempting to predict system behaviors from human revealed preferences. However, the case is not quite as bad as that, although it is still rather bad.

    If I use pure reason to develop axioms about a natural system whose fundamental laws are outside of my powers, my axioms can never change the fundamental laws of the system. They cannot reveal the fundamental laws of the system except by serendipity or chance. If I use reason to develop a rules-based system (one with rules rather than fundamental laws) then I can reveal the axioms of the system by communicating the rule set to others. Conventional economics in praxis is set up as a system with formal rules or axioms. There is the rule of private property which confers rights in our system to hold, rent, sell, derive use or income and to raise capital by borrowing and capitalization.

    A complex rule set gives rise to complex behaviors and easy-to-prove through to difficult-to-prove theorems. It is not invalid to model the theorems of a rule set from its axioms. Theoretical models of private ownership economies (from Arrow-Debreu onward) can produce valid results in their operative sphere. Such models say essentially, “if you set up private property and market(s) in such and such a simple, formal model manner then certain theorems can be proven”. Such models do not prove anything about the real world. Rather they are saying that IF the rules are simple and inflexible (as in the theoretical model) and IF all agents are constrained to perfectly obey the rules then such and such theorems can be proven.

    It is in this spirit, I believe, that Ernestine Gross says essentially that a minimum wealth condition “inferring a strong assumption on the wealth distribution” is necessary “to make the promised freedom of choice (in the market) more than an empty phrase”. That is, there is no freedom of choice in a theoretical pure market economy for a person with no wealth and no income.

    This is a more nuanced position than bowdlerized conventional economics, economics 101 and heterodox straw man attacks upon same. At the same time, do not take this as me defending conventional economics as it is currently implemented in the real world. Do take this as me reappraising at least certain strands of academic conventional economics. Ernestine Gross says “… the results by Quiggin and Gross show that neither price taking, nor profit maximization, nor private ownership are sufficient to rely on (for) ‘micro-economic reform’.” This is a statement against the market fundamentalism of neoliberal economics. The market fundamentalists sold the notion that price taking, profit maximization and private ownership were sufficient to rely on (for) ‘micro-economic reform. There is clearly an academic strand in “orthodox” economic theory which stands against market fundamentalist propositions. I would suggest working with this strand rather than alienating it with straw man attacks and ad hominens.

    There are areas where I agree with economists like Gross and Quiggin. There are areas where I disagree with them. The useful zones of debate will be found, I believe, in exploring the overall idea that the economy is a hybrid system with both formal system and real system components and what that means for generating very complex dynamics and also where the economy is, of course, a political economy and not just an economy. I’ve not found any thinkers yet who are properly and fully exploring this space, though Marx, Veblen and Bichler and Nitzan come closest with their varying methods which show considerable complementarity.

    • Ikonoclast
      October 8, 2020 at 1:22 am

      I need to add an amendment to my above post. The more sophisticated formal axiom system modelling of Arrow-Debreu on does tell us something about the less sophisticated claims of axiomatic market fundamentalism. They tell us that the less sophisticated models of market fundamentalism do not work in theory in their own terms. From that, a reasonable prediction, or at least serious caution, could be issued to the effect that the market fundamentalist mode (unfettered capitalism recycled) will have the bad effects of generating poverty and inequality. That was the historical result of early stage, unfettered capitalism and it has been the empirical outcome of the recycling of unfettered capitalism. History, the sophisticated models and the contemporary empirical outcomes all give the same answer. Market fundamentalism doesn’t work. Three strikes and you are out! But of course, the rules of POLITICAL economy mean that “three strikes and you are out” rule only applies to poor people, not to rich people. Often, indeed, “one strike and you are out” is the rule applied to poor people.

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