Is it Rational to be Bayesian Rational?

Most economists and many decision theorists equate the notion of rationality with Bayesian rationality. While the assumption that individuals actually are Bayesian rational has been largely disputed and is now virtually rejected, the conviction that Bayesianism defines the normative standard of rational behavior remains fairly entrenched among economists. However, even the normative relevance of Bayesianism has been questioned. In this post, I briefly survey one particular and interesting kind of argument that has been particularly developed by the decision theorist Itzhak Gilboa with different co-authors in several papers.

First, it is useful to start with a definition of Bayesianism in the context of economic theory: the doctrine according to which it is always rational to behave according to the axioms of Bayesian decision theory. Bayesianism is a broad church with many competing views (e.g. radical subjectivism, objective Bayesianism, imprecise Bayesianism…) but it will be sufficient to retain a generic characterization through the two following principles:

Probabilism: Bayesian rational agents have beliefs that can be characterized through a probability function whose domain is some state space.

Expected Utility Maximization: The choices of Bayesian rational agents can be represented by the maximization of the expectation of a utility function according to some probability function.

Gilboa’s critique of Bayesianism is uniquely concerned with probabilism though some of its aspects could be easily extended to the expected utility maximization principle. Probabilism can itself be characterized as the conjunction of three tenets:

(i) Grand State Space: each atom (“state of nature”) in the state space is assumed to resolve all uncertainty, i.e. everything that is relevant for the modeler is specified, included all causal relationships. Though in Savage’s version of Bayesian decision theory, states of nature where understood as “small worlds” corresponding to some coarse partition of the state space, in practice most economists implicitly interpret states of nature as “large worlds”, i.e. as resulting from the finest partition of the state space.

(ii) Prior Probability: Rational agents have probabilistic beliefs over the state space which are captured by a single probability measure.

(iii) Bayesian updating: In light of new information, rational agents update their prior to a posterior belief according to Bayes’s rule.

While the third tenet may be disputed, included within the realm of Bayesianism (see for instance Jeffrey’s probability kinematics or views entertained by some objective Bayesians), it is the first two that are targeted by Gilboa. More exactly, while each tenet taken separately seems pretty reasonable normatively speaking, problems arise as soon as one decides to combine them.

Consider an arbitrary decision problem where it is assumed (as economists routinely do) that all uncertainty is captured through a Grand State Space. Say, you have to decide between choosing to bet on what is presented to you as a fair coin falling on heads and betting on the fact that the next winner of the US presidential will be a Republican. There seem to be only four obvious states of nature: [Heads, Republican], [Heads, Democrat], [Tail, Republican], [Tail, Democrat]. Depending on your prior beliefs that the coin toss will fall on Heads (maybe a 1:1 odd) and that the next US president will be a Republican (and assuming monotonic preferences in money), your choice will reveal your preference for one of the two bets. Even if ascribing probabilities to some of the events may be difficult, it seems that the requirements of Bayesian rationality cannot be said to be unreasonable here. But matters are actually more complicated because there are many things that may causally affect the likelihood of each event. For instance, while you have been said that the coin is fair, maybe you have reason to doubt this affirmation. This will depend for instance on who has made the statement. Obviously, the result of the next US presidential elections will depend on the many factual and counterfactual events that may happen. To form a belief about the result of the US elections not only you have to form a belief over these events but also over the nature of the causal relationships between them and the result of the US election. Computationally, the task quickly becomes tremendous as the number of states of nature to consider is quite huge. Assuming that a rational agent should be able to assign a prior over all of them is normatively unreasonable.

An obvious answer (at least for economists and behaviorists-minded philosophers) is to remark that prior beliefs need not be “in the mind” of the decision-maker. What matters is that the betting behavior of the decision-maker reveals preferences over prospects that can be represented by a unique probability measure over as larger a state space as needed to make sense of it. There are many things to be said against this standard defense but for the sake of the argument we may momentarily accept it. What happens however of the behavior of the agents fail to reveal the adequate preferences? Must we conclude then that the decision-maker is irrational? A well-known case leading to such questions is Ellsberg’s paradox. Under a plausible interpretation, the latter indicates that most actual agents reveal through their choices an aversion for probabilistic ambiguity which directly led to the violation of the independence axiom of Bayesian decision theory. In this case, the choice behavior of agents cannot be consistently represented by a unique probability measure. Rather than arguing that such a choice behavior is irrational, a solution (which I have already discussed here) is to adopt the Grand State Space approach. It is then possible to show that with an augmented state space there is nothing “paradoxical” in Ellsber’s paradox. The problem however with this strategy is twofold. On the one hand, many choices are “unobservable” by definition, which fits uneasily in the behaviorist interpretation of Bayesian axioms. On the other hand,  it downplays the reasons that explain the choices that actual agents are actually making.

To understand this last point, it must be acknowledged that Bayesianism defines rationality merely in terms of consistency with respect to a set of axioms. As a result, such an approach completely disregards the way agents form their beliefs (as well as their preferences) and – more importantly – abstains from making any normative statement regarding the content of beliefs. “Irrational” beliefs are merely beliefs that fail to qualify for a representation through a unique probability measure. Now, consider whether it is irrational to fail or to refuse to have such beliefs in cases where some alternatives but not others suffer from probabilistic ambiguity. Also, consider whether it is irrational to firmly believe (eventually to degree 1) that smoking presents no risk for health. Standard Bayesianism will answer positively in the first case but negatively in the second. Not only this is unintuitive but it also seems to be pretty unreasonable. Consider the following alternative definition of rationality proposed by Gilboa:

A mode of behavior is irrational for a decision maker, if, when the latter is exposed to the analysis of her choices, she would have liked to change her decision, or to make different choices in similar future circumstances.

This definition of rationality appeals to the reflexive abilities of human agents and, crucially, to our capacity to motivate our choices through reasons. This suggests first that the axioms of Bayesian decision theory can be submitted both as reasons to make specific choices but also has the subject of the normative evaluation. This also indicates that whatever may be thought of these axioms, Bayesianism lacks an adequate account of beliefs formation. In other words, Bayesianism cannot pretend to constitute a normative theory of rationality because it does not offer any justification neither for the way an agent should partition the state space nor for deciding which prior to adopt. The larger the state space is made to capture all the relevant features explaining an agent’s prior, the lesser it seems reasonable to expect rational agents to be able or to be willing to entertain such a prior.

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Behavioral Welfare Economics and the ‘View from Nowhere’

As Richard Thaler has just received a well-deserved ‘Nobel prize’ for his pioneering contribution in behavioral economics and behavioral finance, many commentators are reflecting over the scientific and ethical significance of Thaler’s work and more generally of behavioral economics regarding policy matters. Thaler is of course well-known for having developed with legal scholar Cass Sunstein the whole nudge idea as well as the seemingly oxymoronic “libertarian paternalism” notion. In a somehow challenging review of Thaler’s contribution, Kevin Bryan expresses some worries regarding the ethical implications relating to the nudging practice:

“Let’s discuss ethics first. Simply arguing that organizations “must” make a choice (as Thaler and Sunstein do) is insufficient; we would not say a firm that defaults consumers into an autorenewal for a product they rarely renew when making an active choice is acting “neutrally”. Nudges can be used for “good” or “evil”. Worse, whether a nudge is good or evil depends on the planner’s evaluation of the agent’s “inner rational self”, as Infante and Sugden, among others, have noted many times. That is, claiming paternalism is “only a nudge” does not excuse the paternalist from the usual moral philosophic critiques! Indeed, as Chetty and friends have argued, the more you believe behavioral biases exist and are “nudgeable”, the more careful you need to be as a policymaker about inadvertently reducing welfare. There is, I think, less controversy when we use nudges rather than coercion to reach some policy goal. For instance, if a policymaker wants to reduce energy usage, and is worried about distortionary taxation, nudges may (depending on how you think about social welfare with non-rational preferences!) be a better way to achieve the desired outcomes. But this goal is very different that common justification that nudges somehow are pushing people toward policies they actually like in their heart of hearts. Carroll et al have a very nice theoretical paper trying to untangle exactly what “better” means for behavioral agents, and exactly when the imprecision of nudges or defaults given our imperfect knowledge of individual’s heterogeneous preferences makes attempts at libertarian paternalism worse than laissez faire.”

As Noah Smith however rightly notes, that is not a problem that is peculiar to the nudge approach nor more generally to behavioral welfare economics:

“There are, indeed, very real problems with behavioral welfare economics. But the same is true of standard welfare economics. Should we treat utilities as cardinal, and sum them to get our welfare function, when analyzing a typical non-behavioral model? Should we sum the utilities nonlinearly? Should we consider only the worst-off individual in society, as John Rawls might have us do?
Those are nontrivial questions. And they apply to pretty much every economic policy question in existence. But for some reason, Kevin chooses to raise ethical concerns only for behavioral econ. Do we see Kevin worrying about whether efficient contracts will lead to inequality that’s unacceptable from a welfare perspective? No. Kevin seems to be very very very worried about paternalism, and generally pretty cavalier about inequality.”

According to Robert Sugden, what standard and behavioral welfare economics have in common is that they endorse – if implicitly – the ‘view from nowhere’ in ethics. The latter – whose name has been coined by Thomas Nagel – is the view that goodness or rightness is to be judged according to criteria set by some exogenous impartial or benevolent dictator. In welfare economics, the criteria imposed by the benevolent dictator are instantiated through a (Arrowian or Bergsonian) social welfare function (SWF). An SWF is itself traditionally obtained through the definition of the relevant informational basis (which kind of information should be taken into account in the normative analysis) and aggregation rule (how to use this information to make social evaluations and comparisons).

In this perspective, it is right that standard and behavioral welfare economics share a feature that some may regard as problematic: the very definition of the relevant SWF is left to a putatively impartial and benevolent being who is thought to lay outside the group of persons to whom the normative evaluation is addressed. The problem with the view from nowhere is that it creates a divide between the one making the impartial ethical judgments and evaluations and the persons whose welfare, rights and so on, are the objects of these judgments and evaluations. That means that welfare economics as a whole is somehow paternalistic in its very foundations.  Arguably there is a difference between standard and behavioral welfare economics: the latter is more restrictive regarding the relevant informational basis. In the classical preference-satisfaction account of welfare that most welfare economists endorse (including most but not all behavioral economists), preferences whatever their content are considered as relevant from a welfare point of view. Behavioral welfare economists argue however that it is legitimate to ignore preferences that are revealed by choices resulting from cognitive biases, lack of awareness, errors and so on. This only contributes to strengthen the paternalistic tendencies of welfare economics. In other words, the difference between standard and behavioral welfare economics is not one of nature but rather “merely” of degree.

Ultimately, it is important to acknowledge that welfare economics as a whole is not fitted to discuss most issues related to (libertarian) paternalism, especially the problems of manipulation and autonomy. Welfare economics is nowadays essentially a theoretical framework to make social evaluations given exogenous welfare criteria but cannot be a substitute for moral and ethical reasoning (though the related social choice approach can be a way to reflect on ethical problems).

Parfit on How to Avoid the Repugnant Conclusion (And Some Additional Personal Considerations)

Derek Parfit, one of the most influential contemporary philosophers, died last January. The day before his death, he submitted what seems to be his last paper to the philosophy journal Philosophy and Public Affairs. In this paper, Parfit tackles the famous “non-identity problem” that he has himself settled in Reasons and Persons almost 35 years ago. Though unachieved, the paper is quite interesting because it appears to offer a way to avoid the not less famous “repugnant conclusion”. I describe below Parfit’s tentative solution and also add some comments on the role played by moral intuitions in Parfit’s (and other moral philosophers’) argumentation.

Parfit is concerned with cases where we have to compare the goodness of two or more outcomes where different people exist across these outcomes. Start first with Same Number cases, i.e. cases where at least one person exists in one outcome but no in the other but where the total number of people is the same. Example 1 is an instance of such a case (numbers denote quality of life according to some cardinal and interpersonally comparable measure):

Example 1

Outcome A Ann 80 Bob 60 ——–
Outcome B ——— Bob 70 Chris 20
Outcome C Ann 20 ——— Chris 30

 

How should we compare these three outcomes? Many moral philosophers entertain one kind or another of “person-affecting principles” according to which betterness or worseness necessarily depend on some persons being better (worse) in an outcome than in another one. Consider in particular the Weak Narrow Principle:

Weak Narrow Principle: One of two outcomes would be in one way worse if this outcome would be worse for people.

 

Since it is generally accepted that we cannot make someone worse by not making her exist, outcome A should be regarded as worse (in one way) than outcome B by the Weak Narrow Principle. Indeed, Bob is worse in A than in B while the fact that Ann does not exist in B cannot make her worse than in A (even though Ann would have a pretty good life if A were to happen). By the same reasoning, C should be considered as worse than A and B worse than C. Thus the ‘worse than’ relation is not transitive. Lack of transitivity may be seen as dubious but is not in itself sufficient to reject the Weak Narrow Principle. Note though that if we have to compare the goodness of the three outcomes together, we are left without any determinate answer. Consider however:

Example 2

Outcome D Dani 70 Matt 50 ——– ——–
Outcome E ——— Matt 60 Luke 30 ——–
Outcome F ——— ——— Luke 35 Jessica 10

 

According to the Weak Narrow Principle, D is worse than E and E is worse than F. If we impose transitivity on the ‘worse than’ relation, then D is worse than F. Parfit regards this kind of conclusion as implausible. Even if we deny transitivity, the conclusion than E is worse than F is also hard to accept.

Given that the Weak Narrow Principle leads to implausible conclusion in Same Number cases, it is desirable to find alternative principles. In Reasons and Persons, Parfit suggested adopting impersonal principles that do not appeal to facts about what would affect particular people. For instance,

Impersonal Principle: In Same Number cases, it would be worse if the people who existed would be people whose quality of life would be lower.

 

According to this principle, we can claim that F is worse than E which is worse than D. Obviously, ‘worse than’ is transitive. What about Different Number cases (i.e. when the number of people who exist in one outcome is higher or lower than in another one)? In Reasons and Persons, Parfit originally explored an extension of the Impersonal Principle:

The Impersonal Total Principle: It would always be better if there was a greater sum of well-being.

 

Parfit ultimately rejected this last principle because it leads to the Repugnant Conclusion:

The Repugnant Conclusion: Compared with the existence of many people hose quality of life would be very high, there is some much larger number of people whose existence would be better, even though these people’s lives would be barely worth living.

 

In his book Rethinking the Good, the philosopher Larry Temkin suggests avoiding the repugnant conclusion by arguing that the ‘all things considered better than relation’ is essentially comparative. In other words, the goodness of a given outcome depends on the set of outcomes with which it is compared. But this has the obvious consequence that the ‘better than’ relation is not necessarily transitive (Temkin claims that transitivity applies only to a limited part of our normative realm). Parfits instead sticks to the view that goodness is intrinsic and suggests an alternative approach through another principle:

Wide Dual Person-Affecting Principle: One of two outcomes would be in one way better if this outcome would together benefit people more, and in another way better if this outcome would benefit each person more.

 

Compare outcomes G and H on the basis of this principle:

Outcome G: N persons will exist and each will live a life whose quality is at 80.

Outcome H: 2N persons will exist and each will live a life whose quality is at 50.

 

According to the Wide Dual Person-Affecting Principle, G is better than H in at least one way because it benefits each person more, assuming that you cannot be made worse by not existing. H may be argued to be better than G on another way, by benefiting people more, at least on the basis of some additive rule. Which outcome is all things considered better remains debatable. But consider

Outcome I: N persons will exist and each will live a life whose quality is at 100.

Outcome J: 1000N persons will exist and each will live a life whose quality is at 1.

 

Here, although each outcome is better than the other on one respect, it may be plausibly claimed that I is better all things considered because the lives in J are barely worth living. This may be regarded as sufficient to more than compensate for the fact that the sum of well-being is far superior in J than in I. This leads to the following conclusion:

Analogous Conclusion: Compared with the existence of many people whose lives would be barely worth living, there is some much higher quality of life whose being had by everyone would be better, even though the numbers of people who exist would be much small.

This conclusion is consistent with the view that goodness is intrinsic and obviously avoids the repugnant conclusion.

 

I would like to end this post with some remarks with the role played by moral intuitions in Parfit’s reasoning. This issue had already came to my mind when reading Partit’s Reasons and Persons as well as Temkin’s Rethinking the Good. Basically, both Parfit and Temkin (and many other moral philosophers) ground their moral reasoning on intuitions about what is good/bad or right/wrong. For instance, Parfit’s initial rejection of impersonality principles in Reasons and Persons was entirely grounded on the fact that they seem to lead to the repugnant conclusion which Parfit regarded as morally unacceptable. The same is true for Temkin’s arguments against the transitivity of the ‘all things considered better than’ relation. Moral philosophers seem mostly to use a form of backward reasoning about moral matters: take some conclusions as intuitively acceptable/unacceptable or plausible/implausible and then try to find principles that may rationalize our intuitions about these conclusions.

As a scholar in economics & philosophy with the background of an economist, this way of reasoning is somehow surprising me. Economists who are thinking about moral matters are generally doing so from a social choice perspective. The latter almost completely turns the philosopher’s reasoning on its head. Basically, a social choice theorists will start from a small set of axioms that encapsulate basic principles that may be plausibly regarding as constraints that should bind any acceptable moral view. For instance, Pareto principles are generally imposed because we take as a basic moral constraint the fact that everyone is better (in some sense) in a given outcome than in another one make the former better than the latter. The social choice approach then consists in determining which social choice functions (i.e. moral views) are compatible with these constraints. In most of the case, this approach will not be able to tell which moral view is obligatory; but it will tell which moral views are and are not permissible given our accepted set of constraints. The repugnant conclusion provides a good illustration: in one of the best social choice treatment of issues related to population ethics, John Broome (a philosopher but a former economist) rightly notes that if the “repugnant” conclusion follows from acceptable premises, then we should not reject it on the ground that we regarded as counterintuitive. The same is true for transitivity: the fact that it entails counterintuitive conclusion is not sufficient to reject it (at least, independent argument for rejection are needed).

There are two ways to justify the social choice approach to moral matters. The first is the fact that we generally have a better understanding of “basic principles” than of more complex conclusions that depend on a (not always well-identified) set of premises. It is far easier to discuss the plausibility of transitivity or of Pareto principles in general than to assess moral views and their more or less counterintuitive implications. Of course, we may also have a poor understanding of basic principles but the attractiveness of the social choice approach is precisely that it helps to focus the discussion on axioms (think of the literature on Arrow’s impossibility theorem). The second reason to endorse the social choice approach on moral issues is that we now start to understand where our moral intuitions and judgments are coming from. Moral psychology and experimental philosophy tend to indicate that our moral views are deeply rooted in our evolutionary history. Far from vindicating them, this should quite the contrary encourage us to be skeptical about their truth-value. Modern forms of moral skepticism point out that whatever the ontological status of morality, the naturalistic origins of moral judgments do not guarantee and actually make highly doubtful that whatever we believe about morality is epistemically well-grounded.

 

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.

Recent Working Papers

You will find below several working papers I have written recently on different (but somewhat related) topics. Comments are welcome!

A Bayesian Conundrum: From Pragmatism to Mentalism in Bayesian Decision and Game Theory

Abstract: This paper discusses the implications for Bayesian game theory of the behaviorism-versus-mentalism debate regarding the understanding of foundational notions of decision theory. I argue that actually the dominant view among decision theorists and economists is neither mentalism nor behaviorism, but rather pragmatism. Pragmatism takes preferences as primitives and builds on three claims: i) preferences and choices are analytically distinguishable, ii) qualitative attitudes have priority over quantitative attitudes and iii) practical reason has priority over theoretical reason. Crucially, the plausibility of pragmatism depends on the availability of the representation theorems of Bayesian decision theory. As an extension of decision-theoretic principles to the study of strategic interactions, Bayesian game theory also essentially endorses the pragmatist view. However, I claim that the fact that representation theorems are not available in games makes this view implausible. Moreover, I argue that pragmatism cannot properly account for the the generation of belief hierarchies in games. If the epistemic program in game theory is to be pursued, this should probably be along mentalistic lines.

Keywords: Bayesian synthesis – Bayesian game theory – Pragmatism – Mentalism – Preferences

 

Neo-Samuelsonian Welfare Economics: From Economic to Normative Agency

Abstract: This paper explores possible foundations and directions for “Neo-Samuelsonian Welfare Economics” (NSWE). I argue that neo-Samuelsonian economics entails a reconciliation problem between positive and normative economics due to the fact that it cuts the relationship between economic agency (i.e. what and who the economic agent is) and normative agency (i.e. what should be the locus of welfare analysis). Developing a NSWE thus implies to find a way to articulate economic and normative agency. I explore two possibilities and argue that both are attractive but have radically different implications for the status of normative economics. The first possibility consists in fully endorsing a normative approach in terms of “formal welfarism” which is completely neutral regarding both the locus and the unit measure of welfare analysis. The main implication is then to make welfare economics a branch of positive economics. The second possibility is to consider that human persons should be regarded as axiologically relevant because while they are not prototypical economic agents, they have the ability to represent them both to themselves and to others as reasonable and reliable beings through narrative construction processes. This gives a justification for viewing well-being as being constituted by the persons’ preferences, but only because these preferences are grounded on reasons and values defining the identity of the persons. This view is somehow compatible with recent accounts of well-being in terms of value-based life satisfaction and implies a sensible reconsideration of the foundations of welfare economics.

Keywords: Neo-Samuelsonian economics – Welfare Economics – Revealed preference theory – Preference-satisfaction view of welfare – Economic agency

 

History, Analytic Narratives and the Rules-in-Equilibrium View of Institutions

Abstract: Analytic narratives are case studies of historical events and/or institutions that are formed by the combination of the narrative method characteristic of historical and historiographical works with analytic tools, especially game theory, traditionally used in economics and political science. The purpose of this paper is to give a philosophy-of-science view of the relevance of analytical narratives for institutional analysis. The main claim is that the AN methodology is especially appealing in the context of a non-behaviorist and non-individualist account of institutions. Such an account is fully compatible with the “rules-in-equilibrium” view of institutions. On this basis, two supporting claims are made: first, I argue that within analytical narrative game-theoretic models play a key role in the identification of institutional mechanisms as the explanans for economic phenomena, the latter being irreducible to so-called “micro-foundations”. Second, I claim that the “rules-in-equilibrium” view of institutions provides justification for the importance given to non-observables in the institutional analysis. Hence, institutional analysis building on analytical narrative typically emphasizes the role of derived (i.e. non-directly observed) intentional states (preferences, intentions, beliefs).

Keywords: Analytic narratives – Rules-in-equilibrium view of institutions – Institutional analysis – Game theory

Accounting for Choices in Economics

Economics is sometimes characterized as the “science of rational choices over the allocation of scarce resources” or even more straightforwardly as the “science of choices”. In a recent blog, Chris Dillow makes some interesting remarks about people’s economic behavior. He notes that our behavior is often partially unconscious and/or habit-based. Moreover, the set of available options is quite frequently severely restricted such that there is few room to make voluntary choices. Finally, many decisions are actually more or less random and grounded on social norms, conventions and other factors on which we barely reflect. The conclusion is then that

“when we ask “why did he do that?” we must look beyond “max U” stories about mythical individuals abstracted from society and look at the role of habit, cultural persistence and constraints.”

These are interesting and important remarks because they directly concern the scope of economics as well as the meaning of the key concept of choice. It seems that Dillow is using the choice concept according to its folk meaning. According to the latter, to properly say “she chooses x” requires at least that (a) one has several available options at her disposal to choose between and (b) she opts for one of the available option consciously and voluntarily. However, I would argue that this is not how economists generally use and understand the choice concept. They rather use a concept of choice* in a technical sense. To put it using some jargon, in economics choices* are basically behavioral patterns that correlate with changes in opportunity costs. In other words, when we say that economics is the science of choices*, what is actually meant is that it studies how some particular variable reflecting for instance the consumption level of a given good, changes as the good’s relative price or consumers’ information change. This definition of choice* has at least two noteworthy implications:

1) Economists are not interested in individual choices per se. Economists almost always work at some aggregated level and they do not aim at explaining the choices made by specific individuals or firms. They are rather interested in the properties of aggregate demand and supply.

2) Economists are agnostic regarding the specific mechanisms through which economic agents are making choices. In particular, there is no presumption that these choices are conscious and not habit-based. The U-Max framework only assumes that individual choices are responsive to change in opportunity costs, not how and why they are responsive.

These two implications work in conjunctions. Choices* need not be conscious nor based on any form of complex calculus but they are however intentional: choices (in both the folk and technical meanings) are about something and they are the product of the agents’ intentional states (desires, beliefs, wants…). As philosophers of mind have emphasized, there is nothing paradoxical in the combination of unconsciousness and intentionality. The U-Max framework, as well as decision and game theory as a whole are tools that are particularly well-fitted to study intentional behavior, whether conscious or not. These tools indeed assume that individual choices are responsive to changes in opportunity costs which, in special cases (e.g. addictive behavior), may not be true. However, this is mostly irrelevant as long as responsiveness is preserved at some market level. Gary Becker’s paper “Irrational Behavior and Economic Theory” provides an extreme example of this point. It shows how we can derive “well-behaved” demand and supply functions with individual agents (households and firms) using “irrational” decision rules. This result is by no way a necessity: there are cases where irrational behavior will lead to unconventional demand and supply functions and because of income effects even rational behavior at the individual level can generate upward-slopping demand curves. Generally speaking, institutions matter: the way exchanges are organized will determine the aggregate outcome for a given profile of preferences and production costs.

All of this depends on the claim that economists are not interested in explaining individual choices. Economists with the strongest revealed-preference stance are likely to agree with this claim. But there are many economists who are likely to disagree, considering that accounting for individual choices is necessary to understand aggregate outcomes such as a financial crisis. More generally, I would argue that attempting to explain individual choices can hardly be avoided in the numerous cases where multiple equilibria exist. The point is that to explain why a given equilibrium has been selected, it will most of the time be required to understand how individuals make choices. Here, whether choices are habit- or calculus-based, conscious or automatic, and so on, may matter. For instance, Thomas Schelling famously pointed out in The Strategy of Conflict the important of focal points to account for the way people are able to coordinate without communicating. As Schelling made it clear, focal points are not determined by the mathematical properties of the game nor by purely instrumental considerations. They depend on cultural, social and aesthetic features.

A slightly more complex example but which is even more relevant, especially in industrial organization, is the existence of multiple (Bayesian perfect) equilibria in incomplete information games. In incomplete information games, one player (the “principal”) ignores the other players’ (the “agent”) type. The agent’s choice may sometimes convey an information to the principal and helps him to identify the agent’s type. Such games typically have multiple equilibria with some of them separating and other pooling ones. Which equilibrium is implemented is partially determined by the way the principal interprets the agent’s choice. Under a separating equilibrium, the principal interprets the agent’s choice in such a way that it provides him with an information about the agent’s type. This is not the case under a pooling equilibrium. Of course, since under a pooling equilibrium all agents behave the same way whatever their type, observed behavior cannot serve as a basis to infer agents’ type. But the fact that all agents behave the same is itself a rational response to their own understanding of the way the principal will interpret their choice at the equilibrium.

My point is thus that in strategic interactions where players have to think about how other players are thinking, it is less clear that economists can safely ignore how people make choices. Given the same set of “fundamentals” (preferences, technology, information distribution), different behavioral patterns may arise and these differences are likely to be due to the way individual agents are choosing.

Bayesian Rationality and Utilitarianism

In a recent blog, Bryan Caplan gives his critical views about the “rationality community”, i.e. a group of people and organizations who are actively developing ideas related to cognitive bias, signaling and rationality. Basically, members of the rationality community are applying the rationality norms of Bayesianism to a large range of issues related to individual and social choices. Among Caplan’s complaints figures the alleged propensity of the community’s members to endorse consequentialist ethics and more specifically utilitarianism, essentially for “aesthetic” reasons. In a related Twitter exchange, Caplan states that by utilitarianism he refers to the doctrine that one’s duty is to act as to maximize the sum of happiness in the society. This corresponds to what his generally called hedonic utilitarianism.

Hedonic utilitarianism faces many problems well-known to moral philosophers. I do not know if the members of the rationality community are hedonic utilitarians, but there is another route for Bayesians to be utilitarians. This route is logical rather than aesthetic and is grounded on a theorem exposed by the economist John Harsanyi in the 1950s and since largely discussed by philosophically-minded economists and mathematically-minded philosophers. Harsanyi’s initial demonstration was grounded on the von Neumann and Morgenstern’s axioms (actually Marshak’s version of them) of decision under risk but has since been extended to other versions of decision theory, especially Savage’s axioms for decision under uncertainty. The theorem can be briefly stated in the following way. Denote S the set of states of nature, i.e. morally-relevant features that are outside the control of the decision-makers and O the set of outcomes. Intuitively, an outcome is a possible world specifying everything that is morally relevant for the individuals: their wealth, their health, their history, and so on. Finally, denote X the set of “prospects”, i.e. social alternatives or public policies mapping any state s onto an outcome o. We assume that the n members of the population have preferences over the set of prospects and that these preferences satisfy Savage’s axioms. Therefore, the preferences of any individual i can be represented by an expectational utility function: each prospect x is ascribed a utility number ui(x) that cardinally represent i’s preferences. ui(x) corresponds to the probability weighted-sum of utility of all possible outcomes (which correspond to “sure” prospects). Hence, each individual also has beliefs regarding the likelihood of the states of nature that are captured by a probability function pi(.).

Given the individuals’ preferences, each prospect x is assigned a vector of utility numbers (u1(x), …, un(x)). Now, we assume that there is a “benevolent dictator” k (possibly one of the member of the population) whose preferences over X also satisfy Savage’s axioms. It follows that the dictator’s preferences can also be represented by an expectational utility function with each prospect x mapped into a number uk(x). Last assumption: the individuals’ and dictator’s preferences over X are related by a Pareto principle: if every individual prefers (resp. is indifferent) prospect x to prospect y, then the dictator prefers (resp. is indifferent) x to y. Harsanyi’s theorem states that the dictator’s preferences can then be represented by a utility function corresponding to the weighted-sum of the individuals’ utilities for any prospect x. Suppose moreover than utilities are interpersonally comparable and that the dictator’s preferences are impartial (they do not arbitrarily weight more a person’s utility than another’s one), then for any x

uk(x) = u1(x) + … + un(x).

Of course, this is the utilitarian formulae but stated in utility rather than hedonic terms. Note that here utility does not correspond to happiness or pleasure but rather to preference-satisfaction. Harsanyi’s utilitarianism is preference-based. The point of the theorem is to show that consistent Bayesians should be utilitarians in this sense.

It should be acknowledged that what the theorem demonstrates is actually far weaker. A first reason (discussed by Sen among others) is that the cardinal representation of the individuals’ preferences is not imposed by Savage’s theorem. Obviously, the use of other representations of individuals’ preferences will have the effect of making the additive structure unable to represent the dictator’s preferences. Some authors like John Broome have argued however that the expectational representational is the most natural one and fits well with some notion of goodness. There is another, different kind of difficulty related to the Pareto principle. It can be shown that the assumption that the dictator’s preferences are transitive (which is imposed by Savage’s axioms) combined with the Pareto principle imply “probabilistic agreement”, i.e. that all individuals agree regarding their probabilistic assessment over the likelihood of the states of nature. Otherwise, probabilistic disagreement and the Pareto principle would lead to cases where the dictator’s preferences are inconsistent and thus unamenable to a utility representation. Probabilistic agreement is of course a very strong assumption, an assumption that Harsanyi would have been ready to defend without doubt (see the “Harsanyi doctrine” in game theory). Objective Bayesians may indeed argue that rationality entails a unique correct probabilistic assessment. But subjective Bayesians will of course disagree.

What happen if we give up the Pareto principle for prospects (not for outcomes however)? Then, the dictator’s preferences are amenable to being represented by an ex post prioritarian social welfare function such that

uk(x) = ∑spk(s)∑iv(ui(x(s)=o))

where v(.) is a strictly increasing and concave function. This corresponds to what Derek Parfit called the “priority view” and leads to giving priority to the satisfaction of preferences of the less well-off in the population.