Hard Obscurantism and Unrealistic Models in Economics

The philosopher and social scientist Jon Elster is well-known for his critical and insightful views about the (ir)relevance of rational choice theory (RCT) in the social sciences. Among his recent writings on the subject, Elster has published last year a paper in the philosophy journal Synthese concerning what he calls “hard obscurantism” in economic modeling (gated version here). By hard obscurantism, Elster essentially refers to a practice where “ends and procedures become ends in themselves, dissociated form their explanatory functions” (p. 2163). This includes many rational choice models, but also a part of agent-based modeling, behavioral economics and statistical analysis in economics.

Elster’s paper focuses on the case of rational choice models and builds on several “case studies” that are thought to illustrate the practice of hard obscurantism. These case studies include Akerlof & Dickens’s and Rabin’s use of cognitive dissonance theory, Becker and Mulligan’s accounts of altruism as well as Acemoglu & Robinson’s theory of political transitions. Beyond these examples, Elster underlines two general problems with rational choice models and more generally with RAT: first, theory is indeterminate, second it ignores the irrationality of the agents. Indetermination is indeed a well-known problem that is partly (though not equivalent) related to the existence of multiple equilibria in many rational choice models. According to Elster, it has three sources: (i) the fact that the determination of the optimal amount of information leads to an infinite regress (i.e. to compute the marginal utility of information requires to collect the information but whether or not to collect the information necessitates to know its marginal utility), (ii) brute and strategic uncertainty (the latter is of course closely related to the existence of multiple equilibria) and (iii) the agents’ cognitive limitations. The latter is regarded by Elster as the most important source and is somewhat related to the irrationality problem. In Elster’s words,

“How can we impute to real-life agents the capacity to make in real time the calculations that occupy many pages of mathematical appendixes in the leading journals and that can be acquired only through years of professional training?” (p. 2166)

Elster’s objection is hardly new and many different responses have been developed. It is not my intention to survey them. I shall rather on one issue that follows from Elster’s critique: can we learn anything with unrealistic models and how? There is an empirical disagreement among economists regarding the degree at which individual agents are truly irrational. Against the behavioral economists’ claim that individuals’ behavior and reasoning exhibit a long list of biases, other economists claim that this depends on the institutional setting in which individuals’ choices take place (for instance, it is probably not true that hyperbolic discounting is dominant in many market and many biases seem to diminish in importance if agents have the opportunity to learn). It is a fact however that individuals’ behaviors do not have the consistency properties that most rational choice models assume they have. Moreover, most rational choice models are unrealistic beyond their “behavioral” assumptions about agents’ reasoning abilities. They also make rather unrealistic “structural” assumptions such as for instance the number of players, the homogeneity of their preferences, the fact that features of the game are common knowledge, and so on. A good example among the case discussed by Elster is Acemoglu & Robinson’s theory of political transitions. The latter builds on a game-theoretic model with only two players which are thought to be representative of two groups of actors, the elites and the citizens. The preferences of the members of each group are assumed to be homogenous and, for the citizens group, to correspond to the median voter’s preferences. The model also makes several strong assumptions regarding what the players are knowing.

So, can we learn anything about real world mechanisms from such unrealistic models? The philosopher of social science Harold Kincaid has recently made an interesting suggestion for a (partially) positive answer. Kincaid rightly starts by indicating that it is vain to search for a general defense of unrealistic models in the social sciences and that each evaluation must be made on a case-by-case basis. Regarding perfect competition and game-theoretic models, Kincaid argues that may offer relevant explanations in spite of the fact that they build on highly unrealistic assumptions:

“The insight is that assumptions of the perfect competition and game theory models may just be assumptions the analyst – the economist or political scientist – uses to identify equilibria. However, in certain empirical applications, the explanations are equilibrium explanations that make no commitment to what process leads individuals to find equilibrium”

In my view, this account of the relevance of unrealistic models particularly works well in the case of mechanism design which is at the same time a highly theoretical but also applied branch of microeconomics. A typical approach in mechanism design is to consider that the right institutional design will entail equilibrium play from the players, even if the designer ignores the players’ actual preferences. The modeler does not make any commitment regarding how the players will find their way to the equilibrium. The model simply indicates that if the institutional set up has such or such characteristics (e.g. a continuous double bid auction), then the outcome will have such or such characteristics (e.g. allocative efficiency). It is then possible to check for this conjecture through experiments.

On this account, the model is thus merely a device to identify the equilibrium but has no use for explaining the mechanism through which the equilibrium is reached. It is not sure however that this account applies to rational choice models used in other settings, especially if experiments are impossible. For instance, Acemoglu & Robinson’s model highlight the importance of commitment to explain political transitions. Indeed, their theory aims at accounting for the change from a dictatorial equilibrium toward a democratic equilibrium. The elites’ ability to commit not to raise taxes in the future is the key feature that determines whether or not the political transition will occur. The model thus suggests that a highly general mechanism is at play but it is unsure which level of confidence we can have in this explanation given the highly unrealistic assumptions on which it builds. An alternative defense would be that the model’s value comes from the fact that it highlights a mechanism that may possibly partially explain political transitions. Thanks to the model, we perfectly understand how this mechanism works, even though we cannot be sure that this mechanism is actually responsible for the relevant phenomenon to be explained. In other words, the relevance of the model comes from the fact that it depicts a possible world which we are able to fully explore and that this world bears some (even remote) resemblance with the actual world. As I have argued elsewhere, many models in economics seem to be valued for this reason.

The problem with this last account is that, while it may explain why economists give credence to rational choice models, it is highly unlikely to convince skeptics like Elster that they are explanatory relevant. Indeed, as Elster has argued elsewhere, the academic value given to these models may itself result from the fact that the economic profession is trapped in a bad equilibrium.

Consequentialism and Formalism in Rational and Social Choice Theory

Rational and social choice theory (RCT and SCT respectively) in economics are broadly consequentialists. Consequentialism can be characterized as the view that all choice alternatives should be evaluated in terms of their consequences and that the best alternatives are those which have the best consequences. This is a very general view which allows for many different approaches and frameworks. In SCT, welfarism is for example a particular form of consequentialism largely dominant in economics and utilitarianism is a specific instance of welfarism. In RCT, expected utility theory and revealed preference theory are two accounts of rational decision-making that assume that choices are made on the basis of their consequences.

Consequentialism is also characterized by a variety of principles or axioms that take different and more or less strong forms depending on the specific domain of application. The most important are the following:

Complete ordering (CO): The element of any set A of alternatives can be completely ordered on the basis of a reflexive and transitive binary relation ≥.

Independence (I): The ranking of any pair of alternatives is unaffected by a change in the likelihood of consequences which are identical across the two alternatives.

Normal/sequential form equivalence (NSE): The ordering of alternatives is the same whether the decision problem is represented in normal form (the alternative is directly associated to a consequence or a probability distribution of consequences) or in sequential form (the alternative is a sequence of actions leading to a terminal node associated to a consequence or a probability distribution of consequences).

Sequential separability (SS): For any decision tree T and any subtree T_n starting at node n of T, the ordering of the subset of consequences accessible in T_n is the same in T than in T_n.

Pareto (P): If two alternatives have the same or equivalent consequences across some set of locations (events, persons), then there must be indifference between the two alternatives.

Independence of irrelevant alternatives (IIA): The ordering of any pair of alternatives is independent of the set of available alternatives.

All these axioms are used either in RCT or in SCT, sometimes in both. CO, I, NSE, SS and IIA are almost always imposed on individual choice as criteria of rationality. CO and IIA, together with P, are generally regarded as conditions that Arrowian social welfare functions must satisfy. I is also sometimes considered as a requirement for social welfare functionals, especially in the context of discussions over utilitarianism and prioritarianism.

It should be noted that they are not completely independent: for instance, CO will generally require the satisfaction of IIA or of NSE. Regarding the former for instance, define a choice function C(.) such that, for any set S of alternatives, C(S) = {x|x ≥ y for all y  S}, i.e. the alternatives that can be chosen are those and only those which are not ranked below any other alternative in terms of their consequences. Consider a set of three alternatives x, y, z and suppose that C(x, y) = {x} but C(x, y, z) = {y, z}. This is a violation of IIA since while x ≥ y and (not y ≥ x) when S = (x, y), we have y ≥ x and (not x ≥ y) when S = (x, y, z). Now suppose that C(x, z) = {z}. We have a violation of the transitivity of the negation of binary relation ≥ since while we have (not z ≥ y) and (not y ≥ x), we nevertheless have z ≥ x. However, this is not possible if CO is satisfied.

All these axioms have traditionally been given a normative interpretation. By this, I mean that they are seen as normative criteria of individual and collective rationality: a rational agent should or must have completely ordered preferences over the set of all available alternatives, he cannot on pain of inconsistency violate I or NSE, and so on. Similarly, collective rationality entails that any aggregation of the individuals’ evaluations of the available alternatives generates a complete ordering satisfying P and IIA and possibly I. Understood this way, these axioms characterize consequentialism as a normative doctrine setting constraints on rational and social choices. For instance, in the moral realm, consequentialism rules out various forms of egalitarian accounts which violate I and sometimes P. In the domain of individual choice, it will regard criteria such as minimization of maximum regret or maximin as irrational. Consequentialists have to face however several problems. The first and most evident one is that reasonable individuals regularly fail to meet the criteria of rationality imposed by consequentialism. This has been well-documented in economics, starting with axiom I in Allais’ paradox and Ellsberg’s paradox. A second problem is that the axioms of consequentialism sometimes lead to counterintuitive and disturbing moral implications. It has been suggested that criterion of individual rationality should not apply to collective rationality, especially CO and I (but also P and IIA).

These difficulties have led consequentialists to develop defensive strategies to preserve most of the axioms. Most of these strategies refer to what I will call formalism: in a nutshell, they consist as regarding the axioms as structural or formal constraints for representing, rather than assessing, individual and collective choices. In other words, rather than a normative doctrine, consequentialism is instead best viewed as a methodological and theoretical framework to account for the underlying values that ground individual and collective choices. As this may sound quite abstract, I will discuss two examples, one related to individual rational choice the other to social choice, both concerned with axiom I. The first example is simply the well-known Ellsberg’s paradox. Assume you are presented with two consecutive decision-problems, each time between a pair of alternatives. In the first one, we suppose that an urn contains 30 red balls and 60 other balls which can be either black or yellow. You are presented with two alternatives: alternative A gives you 100$ in case a red ball is drawn and alternative B gives you 100$ in case a black ball is drawn. In the second decision-problem, the content of the urn is assumed to be the same, but this time alternative C gives you 100$ in case you draw either a red or yellow ball and alternative D gives you 100$ in case you draw either a black or yellow ball.

Alternative/event	E1: Red ball is drawn	E2: Black ball is drawn	E3: Yellow ball is drawn
A	100$	0$	0$
B	0$	100$	0$

Alternative/event	E1: Red ball is drawn	E2: Black ball is drawn	E3: Yellow ball is drawn
C	100$	0$	100$
D	0$	100$	100$

Axiom I entails that if the decision-maker prefers A to B, then he should prefer C to D. The intuition is that if one prefers A to B, that must mean that the decision-maker ascribes a higher probability to event E1 than to event E2. Since the content of the urn is assumed to be the same in both decision-problems, this should imply that the expected gain of C (measured either in money or in utility) should be higher than D’s. The decision-maker’s ranking of alternatives should be independent of what happen in case event E3 holds, since in each decision-problem the alternatives have the same outcome. However, as Ellsberg’s experiment shows, while most persons prefer A to B, they prefer D to C which is sometimes interpreted as the result of some ambiguity-aversion.

The second example has been suggested by Peter Diamond in a discussion of John Harsanyi’s utilitarian aggregation theorem. Suppose a doctor has two patients waiting for kidney transplantation. Unfortunately, only one kidney is available and it is not expected that another one will be before quite some time. We assume that the doctor, endorsing the social preference of the society, is indifferent between giving the kidney to one or the other patient. The doctor is considering choosing between three allocation mechanisms: mechanism S1 gives the kidney to patient 1 for sure, mechanism S2 gives the kidney to patient 2 for sure, while in mechanism R he tosses a fair coin and gives the kidney to patient 1 if tails but to patient 2 if heads.

Alternative/event	E1: Coin toss falls Tails	E2: Coin toss falls Heads
S1	Kidney is given to patient 1	Kidney is given to patient 1
S2	Kidney is given to patient 2	Kidney is given to patient 2
R	Kidney is given to patient 1	Kidney is given to patient 2

Given that it is assumed that the society (and the doctor) is indifferent between giving the kidney to patient 1 or 2, axiom I implies that the three alternatives should be ranked as indifferent. Most people have the strong intuition however that allocation mechanism R is better because it is fairer.

Instead of giving up axiom I, several consequentialists have suggested instead to reconcile our intuitions with consequentialism through a refinement of the description of outcomes. The basic idea is that, following consequentialism, everything in the individual or collective choice should be featured in the description of outcomes. Consider Ellsberg’s paradox first. If we assume that the violation of I is due to the decision-makers’ aversion to probabilistic ambiguity, then we modify the tables in the following way:

Alternative/event	E1: Red ball is drawn	E2: Black ball is drawn	E3: Yellow ball is drawn
A	100$ + sure to have a 1/3 probability of winning	0$ + sure to have a 1/3 probability of winning	0$ + sure to have a 1/3 probability of winning
B	0$ + unsure of the probability of winning	100$ + unsure of the probability of winning	0$ + unsure of the probability of winning

Alternative/event	E1: Red ball is drawn	E2: Black ball is drawn	E3: Yellow ball is drawn
C	100$ + unsure of the probability of winning	0$ + unsure of the probability of winning	100$ + unsure of the probability of winning
D	0$ + sure to have a 2/3 probability of winning	100$ + sure to have a 2/3 probability of winning	100$ + sure to have a 2/3 probability of winning

The point is simple. If we consider that being unsure of one’s probability of winning the 100$ is something that makes an alternative less desirable everything else equals, then this has to be reflected in the description and valuation of outcomes. It is then easy to see that ranking A over B but D over C no longer entails a violation of I because the outcomes associated to event E3 are no longer the same in each pair of alternatives. A similar logic can be applied to the second example. If it is collectively considered that the fairness of the allocation mechanism is something valuable, then this must be reflected in the description of outcomes. Then, we have

Alternative/event	E1: Coin toss falls Tails	E2: Coin toss falls Heads
S1	Kidney is given to patient 1	Kidney is given to patient 1
S2	Kidney is given to patient 2	Kidney is given to patient 2
R	Kidney is given to patient 1 + both patients are fairly treated	Kidney is given to patient 2 + both patients are fairly treated

Once again, this new description allows to rank R strictly above S1 and S2 without violating I. Hence, the consequentialist’s motto in all the cases where one axiom seems to be problematic is simply “get the outcome descriptions right!”.

A natural objection to this strategy is of course that it seems to make things too easy for the consequentialist. On the one hand, it makes the axioms virtually unfalsifiable as any choice behavior can be trivially accounted for by a sufficiently fine grain partition of the outcome space. On the other hand, all moral intuitions and principles can be made compatible with a consequentialist perspective, once again provided that we have the right partition of the outcome space. However, one can argue that this is precisely the point of the formalist strategy. The consequentialist will argue that this is unproblematic as long as consequentialism is not seen as a normative doctrine about rationality and morality, but rather as a methodological and theoretical framework to account for the implications of various values and principles on rational and social choices. More precisely, what can be called formal consequentialism can be seen as a framework to uncover the principles and values underlying our moral and rational behavior and judgments.

Of course, this defense is not completely satisfactory. Indeed, most consequentialists will not be comfortable with the removal of all the normative content from their approach. As a consequentialist, one wants to be able to argue what it is rational to do and to say what morality commends in specific circumstances. If one wants to preserve some normative content, then the only solution is to impose normative constraints on the permissible partitions of the outcome space. This is indeed what John Broome has suggested in several of his writings with the notion of “individuation of outcomes by justifiers”: the partition of the outcome space should distinguish outcomes if and only if they differ in a way that makes it rational to not be indifferent between them. It follows then that theories of rational choice and social choice are in need of a substantive account of rational preferences and goodness. Such an account is notoriously difficult to conceive. A second difficulty is that the formalist strategy will sometimes be implausible or may even lead to some form of inconsistency. For instance, in the context of expected utility theory, Broome’s individuation of outcomes depends on the crucial and implausible assumption that all “constant acts” are available. This leads to a “richness” axiom (made by Savage for instance) according to which all probabilistic distribution of outcomes should figure in the set of available alternatives, including logically or materially impossible alternatives (e.g. being dead and in a good health). In sequential decision-problems, the formalist strategy is bounded to fail as soon as the path taken to reach a given outcome is relevant for the decision-maker. In this case, to include the path taken in the description of outcomes will not be always possible without leading to inconsistent descriptions of what is supposed to be the same outcome.

These difficulties indicate that formalism cannot fully vindicate consequentialism. Still, it remains an interesting perspective both in rational and social choice theory.

Economics, Rational Choice Theory and Utility Maximization

Economist Geoff Hodgson has a short article at Evonomics on the issue of the theoretical and methodological status of the rationality principle in economics. Hodgson sketches an argument that he has more fully developed in his book From Pleasure Machines to Moral Communities. In a nutshell, Hodgson argues that the rationality principle, according to which individuals act such as to maximize their utility, is (i) not a tautology but (ii) is unfalsifiable. Let me take these two points in order.

First, Hodgson argues that the rationality principle is not a tautology because utility maximization “is potentially false”. That is, there may be cases where people’s choices fail to maximize their utility. We may suppose that the non-maximizing behavior may be intentional or not: there are cases where we intend to maximize our utility but we fail, for instance because of weakness of will (a phenomenon known as Akrasia in ancient Greece); there are other cases where reason provides us with good reason to make choices that do not maximize our utility. This latter possibility is at the core of Amartya Sen’s criticism of rational choice theory developed in the 1970’s. Second, Hodgon points out that in spite of the fact that the U-max assumption may be false, we can never know when or at least we can never establish that is false in any specific case. This is due to the fact that it is at least always possible to change the description of some decision problem such as to make the observed behavior compatible with any consistency assumption and thus utility maximization. This is indeed true in all versions of rational choice theory, either under the form of revealed preference theory or of expected utility theory. The basic strategy consists in changing the description of the outcome space of the decision problem such as to make the choice behavior consistent. Unless a behavior is completely random, there should always be in principle a way to rationalize it according to some consistency criterion. U-max only requires transitivity of the underlying preference ordering (plus some reflexivity and continuity conditions). According to Hodgson, these two points make rational choice theory useless as a theory of human behavior. In particular, he rightly note that rational choice theory applies equally well to machines, insects and animals and that as a consequence it cannot tell us anything specific about humans.

I partially agree with Hodgson but his argument requires some qualifications. More specifically, I would argue that (i) actually rational choice theory is a tautology and that (ii) the fact that is unfalsifiable is not necessarily problematic depending on its purpose. Consider the former point first. The only reason Hodgson can validly claim that utility maximization is not a tautology is because he takes utility to be something to be independently measurable. This is of course the way the utility concept was understood by Bentham and by the first marginalists. There is also a bunch of behavioral economists defending a “back to Bentham” paradigmatic move who speak in terms of “experienced utility”, where the latter refers to something akin to happiness or pleasure. Finally, we may also admit that some economists of the Chicago school may have entertained an interpretation of utility as something independently measurable. But all of this is unorthodox. Since the days of Pareto and Samuelson, economic theory (and especially consumer theory) has given up the interpretation of utility as an independently measurable quantity. The ordinalist revolution and Samuelson’s pioneering contribution to revealed preference theory have shown how consumer theory can be formulated without any reference to the utility concept. More exactly, they have established that utility maximization is nothing but a mathematically convenient statement equivalent to the assumption that people make consistent choices and/or have well-ordered preferences. The same is true for expected utility theory, especially Savage’s version which is explicitly behaviorist. Absolutely nothing is assumed regarding what happens “in the head” of the person making some choice. U-max is not an assumption; it is only a descriptive statement of what one is doing. It is a tautology as long as there is always a possibility to rationalize one’s choices in terms of some consistency condition.

Consider now the second point. The fact that the U-max principle is actually a tautology only strengthens Hodgson’s claim that it is unfalsifiable. You cannot falsify a tautology as it is true by definition. Does it make it useless from a scientific perspective? The short answer is clearly “no”. Science is full of useful tautologies, also in economics. Consider only one example coming from biology, one on which Hodgson extensively relies in his work: the Price equation. The Price equation is a highly general mathematical statement of a process of differential replication, i.e. natural selection. The mathematical beauty of the Price equation is that whatever the specificities of the actual process of selection (whether organisms are haploid, haplodiploid, diploid, whether it is cultural or genetic, …), it captures them in a straightforward formula according to which, to simplify matters, the growth rate of some trait in a population can be expressed as the covariance between the trait frequency and the fitness of its bearer. Under the classical meaning of fitness (a measure of reproductive success), Price equation is of course both unfalsifiable and a tautology. But no biologists or behavioral scientists would reject it for this reason. The usefulness of the Price equation comes from its value as a problem-solving device. It gives the scientist a methodological strategy to solve empirical or theoretical problems. As an instance of the latter case, consider for instance how Price equation is useful to derive Hamilton’s rule and to make explicit the assumptions on which the latter rely regarding the property of selection and inclusive fitness.

I would argue that the same is true for rational choice theory in economics. From a Weberian point of view, rational choice theory provides us with a methodological strategy to uncover people’s motivations and reasons for action. Similarly, Don Ross argues it is part of the “intentional stance strategy” through which we are able to understand and predict agents’ behavior. Hodgson is right that rational choice theory is rather weak as an explanatory theory of individual behavior, simply because the theory suffers from an obvious problem of under-determination. But individual behavior is not the right level at which the theory should be applied. It is way more useful for instance to understand how the change in the institutional framework, by modifying people’s incentives and beliefs, may affect their behavior. This strategy is at the core of the applied branch of microeconomics, known as mechanism design. A branch which has enjoyed some empirical successes recently. Of course, there are other reasons to reject the imperialistic claims of the proponents of rational choice theory. I explore some of them in this (version of a) forthcoming paper in the Journal of Economic Methodology.