Review of “Understanding Institutions. The Science and Philosophy of Living Together”, Francesco Guala, Princeton University Press, 2016

The following is a (long) review of Francesco Guala’s recent book Understanding Institutions. The Science and Philosophy of Living Together (Princeton University Press, 2016).

Twenty years ago, John Searle published his influential account of the nature of institutions and institutional facts (Searle 1995). Searle’s book has been a focal point for philosophers and social scientists interested in social ontology and its claims and arguments continue to be hotly disputed today. Francesco Guala, a professor at the University of Milan and a philosopher with a strong interest in economics, has written a book that in many ways can be considered both as a legitimate successor but also a thoroughly-argued critique of Searle’s pioneering work. Understanding Institutions is a compact articulation of Guala’s thoughts about institutions and social ontology that he has developed in several publications in economic and philosophy journals. It is a legitimate successor to Searle’s book as all the central themes in social ontology that Searle discussed are also discussed by Guala. But it is also a strong critique of Searle’s general approach to social ontology: while the latter relies on an almost complete (and explicit) rejection of social sciences and their methods, Guala instead argues for a naturalistic approach to social ontology combining the insights of philosophers with the theoretical and empirical results of social sciences. Economics, and especially game theory, play a major role in this naturalistic endeavor.

The book is divided into two parts of six chapters each, with an “interlude” of two additional chapters. The first part presents and argues for an original “rules-in-equilibrium” account of institutions that Guala has recently developed in several articles, some of them co-authored with Frank Hindriks. Two classical accounts of institutions have indeed been traditionally endorsed in the literature. On the institutions-as-rules account, “institutions are the rules of the game in a society… the humanly devised constraints that shape human interactions” (North 1990, 3-4). Searle’s own account in terms of constitutive rules is a subspecies of the institutions-as-rules approach where institutional facts are regarded as being the products of the assignment of status function through performative utterances of the kind “this X counts as Y in circumstances C”. The institutions-as-equilibria account has been essentially endorsed by economists and game theorists. It identifies institutions to equilibria in games, especially in coordination games. In this perspective, institutions are best seen as devices solving the classical problem of multiple equilibria as they select one strategy profile over which the players’ beliefs and actions converge. Guala’s major claim in this part is that the relevant way to account for institutions calls for the merging of these two approaches. This is done through the key concept of correlated equilibrium: institutions are figured out as playing the role of “choreographers” coordinating the players’ choices on the basis of public (or semi-public) signals indicating to each player what she should do. Institutions then take the form of lists of indicative conditionals, i.e. statements of the form “if X, then Y”. Formally, institutions materialize as statistically correlated patterns of behavior with the equilibrium property that no one has an interest to unilaterally change her behavior.

The motivation for this new approach follows from the insufficiencies of the institutions-as-rules and institutions-as-equilibria accounts but also to answer fundamental issues regarding the nature of the social world. Regarding the former, it has been widely acknowledged that one the main defect of the institutions-as-rules is that it lacks a convincing account of the reason of why people are motivated in following rules. The institutions-as-equilibria approach for its part is unable to account for the specificity of human beings regarding their ability to reflect over the rules and the corresponding behavioral patterns that are implemented. Playing equilibria is far from being human specific, as evolutionary biologists have recognized long ago. However, being able to explain why one is following some rule or even to communicate through a language about the rules that are followed are capacities that only humans have. There are also strong reasons to think that the mental operations and intentional attitudes that sustain equilibrium play in human populations are far more complex than in any other animal population. Maybe the most striking result of this original account of institutions is that Searle’s well-known distinction between constitutive and regulative rules collapses. Indeed, building on a powerful argument made by Frank Hindriks (2009), Guala shows that Searle’s “this X counts as Y in C” formula reduces to a conjunction of “if X then Y” conditionals corresponding to regulative rules. “Money”, “property” or “marriage” are theoretical terms that are ultimately expressible through regulative rules.

The second part of the book explores the implications of the rules-in-equilibrium account of institutions for a set of related philosophical issues about reflexivity, realism and fallibilism in social ontology. This exploration is done after a useful two-chapter interlude where Guala successively discusses the topics of mindreading and collective intentionality. In these two chapters, Guala contends, following the pioneering work of David Lewis (1969), that the ability of institutions to solve coordination problems depends on the formation of iterated chains of mutual expectations of the kind “I believe that you believe that I believe…” and so on ad infinitum. It is suggested that the formation of such chains is generally the product of a simulation reasoning process where each player forms expectations about the behavior of others by simulating their reasoning, on the assumption that others are reasoning like her. In particular, following the work of Morton (2003), Guala suggests that coordination is often reached through “solution thinking”, i.e. a reasoning process where each player first asks which is the most obvious or natural way to tackle the problem and then assumes that others are reasoning toward the same conclusion than her. The second part provides a broad defense of realism and fallibilism in social ontology. Here, Guala’s target is no longer Searle as the latter also endorses realism (though Searle’s writings on this point are ambiguous and sometimes contradictory as Guala shows) but rather various forms of social constructionism. The latter hold that the social realm and the natural realm are intrinsically different because of a fundamental relation between how the social world works and how humans (and especially social scientists) reflect on how it works. Such a relationship is deemed to be unknown to the natural sciences and the natural world and therefore, the argument goes, “social kinds” considerably differ from natural kinds. The most extreme forms of social constructionism hold the view that we cannot be wrong about social kinds and objects as the latter are fully constituted by our mental attitudes about them.

The general problem tackled by Guala in this part is what he characterizes as the dependence between mental representations of social kinds and social kinds. The dependence can be both causal and constitutive. As Guala shows, the former is indeed a feature of the social world but is unproblematic in the rules-in-equilibrium account. Causal dependency merely reflects the fact that equilibrium selection is belief-dependent, i.e. when there are several equilibria, which one is selected depends on the players’ beliefs about which equilibrium will be selected. Constitutive dependency is a trickier issue. It assumes that an ontological dependence holds between a statement “Necessarily (X is K)” and a statement “We collectively accept that (X is K)”. For instance, on this view, a specific piece of paper (X) is money (K) if and only if it is collectively accepted that this is the case. It is then easy to see why we cannot be wrong about social kinds. Guala claims that constitutive dependence is false on the basis of a strong form of non-cognitivism that makes a radical distinction between folk classifications of social objects and what these objects are really doing in the social world: “Folk classificatory practices are in principle quite irrelevant. What matters is not what type of beliefs people have about a certain class of entities (the conditions they think the entities ought to satisfy to belong to that class) but what they do with them in the course of social interactions” (p. 170). Guala strengthens his point in the penultimate chapter building on semantic externalism, i.e. the view that meaning is not intrinsic but depends on how the world actually is. Externalism implies that the meaning of institutional terms is determined by people’s practices, not by their folk theories. An illustration of the implication of this view is given in the last two chapters through the case of the institution of marriage. Guala argues for a distinction between scientific considerations about what marriage is and normative considerations regarding what marriage should be.

Guala’s book is entertaining, stimulating and thought-provoking. Moreover, as it is targeted to a wide audience of social scientists and philosophers, it is written in plain language and devoid of unnecessary technicalities. Without doubt, it will quickly become a reference work for anyone believing that naturalism is the right way to approach social ontology. Given the span of the book (and is relatively short length – 222 pages in total), there are however many claims that would call for more extensive arguments to be completely convincing. Each chapter contains a useful “further readings” section that helps the interested reader to go further. Still, there are several points where I consider that Guala’s discussion should be qualified. I will briefly mention three of them. The first one concerns the very core of Guala’s “rules-in-equilibrium” account of institutions. As the author notes himself, the idea is not wholly new as it has been suggested several times in the literature. Guala’s contribution however resides in his handling of the conceptual view that institutions are both rules and equilibria with an underlying game-theoretic framework that has been explored and formalized by Herbert Gintis (2009) and even before by Peter Vanderschraaf (1995). Vanderschraaf has been the first to suggest that Lewis’ conventions should be formalized as correlated equilibria and Gintis has expanded this view to social norms. By departing from the institutions-as-equilibria account, Guala endorses a view of institutions that eschews the behaviorism that characterizes most of the game-theoretic literature on institutions, where the latter are simply conceived as behavioral patterns. The concept of correlated equilibrium indeed allows for a “thicker” view of institutions as sets of (regulative) rules having the form of indicative conditionals. I think however that this departure from behaviorism is insufficient as it fails to acknowledge the fact that institutions also rely on subjunctive (and not merely indicative) conditionals. Subjunctive conditionals are of the from “Were X, then Y” or “Had X, then Y” (in the latter case, they correspond to counterfactuals). The use of subjunctive conditionals to characterize institutions is not needed if rules are what Guala calls “observer-rules”, i.e. devices used by social scientists to describe an institutional practice. The reason is that if the institution is working properly, we will never observe behavior off-the-equilibrium path. But this is no longer true if rules are “agent-rules”, i.e. devices used by the players themselves to coordinate. In this case, the players must use (if only tacitly) counterfactual reasoning to form beliefs about what would happen in events that cannot happen at the equilibrium. This point is obscured by the twofold fact that Guala only considers simple normal-form games and does not explicitly formalize the epistemic models that underlie the correlated equilibria in the coordination games he discusses. However, as several game theorists have pointed out, we cannot avoid dealing with counterfactuals when we want to account for the way rational players are reasoning to achieve equilibrium outcomes, especially in dynamic games. Avner Greif’s (2006) discussion of the role of “cultural beliefs” in his influential work about the economic institutions of the Maghribi traders emphasizes the importance of counterfactuals in the working of institutions. Indeed, Greif shows that differences regarding the players’ beliefs at nodes that are off-the-equilibrium path may result in significantly different behavioral patterns.

A second, related point on which I would slightly amend Guala’s discussion concerns his argument about the unnecessity of public (i.e. self-evident) events in the generation of common beliefs (see his chapter 7 about mindreading). Here, Guala follows claims made by game theorists like Ken Binmore (2008) regarding the scarcity of such events and therefore that institutions cannot depend on their existence. Guala indeed argues that neither Morton’s “solution thinking” nor Lewis’ “symmetric reasoning” rely on the existence of this kind of event. I would qualify this claim for three reasons. First, if public events are defined as publicly observable events, then their role in the social world is an empirical issue that is far from being settled. Chwe (2001) has for instance argued for their importance in many societies, including modern ones. Arguably, modern technologies of communication make such events more common, if anything. Second, Guala rightly notes in his discussion of Lewis’ account of the generation of common beliefs (or common reason to believe) that common belief of some state of affairs or event R (where R is for instance any behavioral pattern) depends on a state of affairs or event P and on the fact that people are symmetric reasoners with respect to P. Guala suggests however that in Lewis’ account, P should be a public event. This is not quite right as it is merely sufficient for P to be two-order mutual belief (i.e. everyone believes P and everyone believes that everyone believes P). However, the fact that everyone is a symmetric reasoner with respect to P has to be commonly believed (Sillari 2008). The issue is thus what grounds this common belief. Finally, if knowledge and belief are set-theoretically defined, then for any common knowledge event R there must be a public event P. I would argue in this case that rather than characterizing public events in terms of observability, it is better to characterize them in terms of mutual accessibility, i.e. in a given society, there are events that everyone comes to know or believe even if she cannot directly observe them simply because they are assumed to be self-evident.

My last remark concerns Guala’s defense of realism and fallibilism about social kinds. I think that Guala is fundamentally right regarding the falsehood of constitutive dependence. However, his argument ultimately relies on a functionalist account of institutions: institutions are not what people take them to be but rather are defined by the functions they fulfill in general in human societies. To make sense of this claim, one should be able to distinguish between “type-institutions” and “token-institutions” and claim that the functions associated to the former can be fulfilled in several ways by the latter. Crucially, for any type-institution I, the historical forms taken by the various token-institutions I cannot serve as a basis to characterize what I is or should be. To argue for the contrary would condemn one to some form of traditionalism forbidding the evolution of an institution (think of same-sex marriage). The problem with this argument is that while it may be true that the way people represent a type-institution I at a given time and location through a token-institution I cannot define what I is, it remains to determine how the functions of I are to be established. Another way to state the problem is the following: while one (especially the social scientist) may legitimately identify I with a class of games it solves, thus determining its functions, it is not clear why we could not identify I with another (not necessarily mutually exclusive) class of games. Fallibilism about social kinds supposes that we can identify the functions of an institution but is this very identification not grounded on collective representations and acceptance? If this is the case, then some work remains to be done to fully establish realism and fallibilism about social kinds.

References

Binmore, Ken. 2008. “Do Conventions Need to Be Common Knowledge?” Topoi 27 (1–2): 17.

Chwe, Michael Suk-Young. 2013. Rational Ritual: Culture, Coordination, and Common Knowledge. Princeton University Press.

Gintis, Herbert. 2009. The Bounds of Reason: Game Theory and the Unification of the Behavioral Sciences. Princeton University Press.

Greif, Avner. 2006. Institutions and the Path to the Modern Economy: Lessons from Medieval Trade. Cambridge University Press.

Hindriks, Frank. 2009. “Constitutive Rules, Language, and Ontology.” Erkenntnis 71 (2): 253–75.

Lewis, David. 1969. Convention: A Philosophical Study. John Wiley & Sons.

Morton, Adam. 2003. The Importance of Being Understood: Folk Psychology as Ethics. Routledge.

North, Douglass C. 1990. Institutions, Institutional Change and Economic Performance. Cambridge University Press.

Searle, John R. 1995. The Construction of Social Reality. Simon and Schuster.

Sillari, Giacomo. 2008. “Common Knowledge and Convention.” Topoi 27 (1–2): 29–39.

Vanderschraaf, Peter. 1995. “Convention as Correlated Equilibrium.” Erkenntnis 42 (1): 65–87.

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 Tn starting at node n of T, the ordering of the subset of consequences accessible in Tn is the same in T than in Tn.

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.

Capitalist Economies, Commodification and Cooperation

Branko Milanovic has an interesting post on the topic of commodification and the nature of economic relations in capitalist economies. Milanovic argues that commodification (by which he roughly means the extension of market relations, i.e. price-governed relations, to social activities that were historically outside the realm of markets) works against the development of cooperative behavior based on “repeated games”. Milanovic’s main point is that while non-altruistic cooperative behavior may indeed be rational and optimal when interactions are repeated with a sufficiently high probability, the commodification process makes economic relations more anonymous and ephemeral:

Commodification of what was hitherto a non-commercial resource makes each of us do many jobs and even, as in the renting of apartments, capitalists. But saying that I work many jobs is the same thing as saying that workers do not hold durably individual jobs and that the labor market is fully “flexible” with people getting in and out of jobs at a very high rate. Thus workers indeed become, from the point of view of the employer, fully interchangeable “agents”. Each of then stays in a job a few weeks or months: everyone is equally good or bad as everyone else. We are indeed coming close to the dream world of neoclassical economics where individuals, with their true characteristics, no longer exists because they have been replaced by “agents”.

The problem with this kind of commodification and flexibilization is that it undermines human relations and trust that are needed for the smooth functioning of an economy. When there are repeated games we try to establish relationships of trust with people with whom we interact. But if we move from one place to another with high frequency, change jobs every couple of weeks, and everybody else does the same, then there are no repeated games because we do not interact with the same people. If there are no repeated games, our behavior adjusts to expecting to play just a single game, a single interaction. And this new behavior is very different.

This claim can be seen as a variant of Karl Polanyi’s old “disembeddedness thesis” according to which commodification, through the institutionalization of “fictitious commodities” (land, money, labor), has led to a separation between economic relations and the sociocultural institutions in which they were historically embedded. As it is well-known, Polanyi considered this as the major cause for the rise of totalitarianism in the 20th century. Though less dramatic, Milanovic’s claim similarly points out that by changing the structure of social relations, commodification leads to less cooperative behavior, especially because it creates opportunity costs that previously do not exist and favors anonymity. Is that completely true? There are two separate issues here according to me: the “monetization” of social relations and the “anonymization” of social relations. Regarding the former, it seems now well established that the introduction of (monetary) opportunity costs may change people’s behavior and their underlying preferences. This is the so-called “crowding-out effects” well-documented by behavioral economists and others. Basically, the fact that opportunity costs can be measured in monetary unit favors economic behaviors based on “extrinsic preferences” (i.e. favoring maximization of monetary gains) and weakens “intrinsic preferences” related, for instance, to a sense of civic duty. It is unclear to what extent this crowding-out effect has had a cultural impact in Western societies from a macrosocial perspective but at a more micro level, the effect seems hard to discard.

I am less convinced regarding the “anonymization thesis”. It is indeed quite usual in sociology and in economics to characterize market relations as being anonymous and ephemeral. This is contrasted with family and other kinds of “communitarian” relations that are assumed to be more personal and durable. To some extent, this is probably the case and it would be absurd to deny that there is no difference between giving the kids some money for them to buy some meal to an anonymous employee and cooking the meal myself. Now, the picture of the anonymous and ephemeral market relationship mostly corresponds to the idealistic Walrassian model of the perfectly competitive market. Such market, as famously argued by the philosopher David Gauthier, is a “morally-free zone”. But actually, every economist will recognize that markets are imperfect and that their functioning leads to many kinds of failures: asymmetric information and externalities are especially the cause of many market suboptimal outcomes. This is at this point that the “anonymization thesis” is unsustainable. Basically, because of market failures and imperfections, market relations cannot be fully anonymous and ephemeral to survive. Quite the contrary, mechanisms favoring the stability of these relations and making them more personal are required. The examples of Uber and AirB&B provide a case to this point: the economic model of these companies is precisely based on the possibility (and indeed the necessity) for their users to provide information to the whole community regarding the quality of the service provided by the other party. Reputation (i.e. the information regarding one’s and others’ “good-standing”), segmentation (i.e. the ability for one to choose his partner) and retaliation (i.e. one’s ability to sanction directly or indirectly uncooperative behavior) are all mechanisms that favor cooperation in market relations and they are indeed central in the kind of social relations promoted by companies like Uber. Moreover, new technologies tend to reduce considerably the cost of these mechanisms for economic agents as giving one’s opinion about the quality of the service is almost free of any opportunity cost (though that may lead to a different problem regarding the quality of information).

Now, once again, the point is not to say that there is no difference between providing a service through the market and within the family. But it is important to recognize that market relations have to be cooperative to be efficient. In this perspective, trust and other kinds of social bonds are quite needed in capitalist economies. Complete anonymity is the enemy, not the constitutive characteristic, of market institutions.

Isaac Levi on Rationality, Deliberation and Prediction (3/3)

This is the last of a three-part post on the philosopher Isaac Levi’s account of the relationship between deliberation and prediction in decision theory and which is an essential part of Levi’s more general theory of rationality. Levi’s views potentially have tremendous implications for economists especially regarding the current use of game theory. These views are more particularly developed in several essays collected in his book The Covenant of Reason, especially “Rationality, prediction and autonomous choice”, “Consequentialism and sequential choice” and “Prediction, deliberation and correlated equilibrium”. The first post presented and discussed Levi’s main thesis that “deliberation crowds out prediction”. The second post discussed some implications of this thesis for decision theory and game theory, specifically the equivalence between games in dynamic form and in normal form. On the same basis, this post evaluates the relevance of the correlated equilibrium concept for Bayesianism in the context of strategic interactions. The three posts are collected under a single pdf file here.

 

In his important article “Correlated equilibrium as an Expression of Bayesian Rationality”, Robert Aumann argues that Bayesian rationality in strategic interactions makes correlated equilibrium the natural solution concept for game theory. Aumann’s claim is a direct and explicit answer to a short paper by Kadane and Larkey which argues that the extension of Bayesian decision theory to strategic interactions leads to a fundamental indetermination at the theoretical level regarding how Bayesian rational players will/should play. To these authors, the way a game will be played depends on contextual and empirical features on which the theorist has few things to say. Aumann’s aim is clearly to show that the game theorist endorsing Bayesianism is not committed to such nihilism. Aumann’s paper was one of the first contributions to what is nowadays sometimes called the “epistemic program” in game theory. The epistemic program can be characterized as an attempt to characterize various solution concepts for normal- and extensive-form games (Nash equilibrium, correlated equilibrium, rationalizability, subgame perfection, …) in terms of sufficient epistemic conditions regarding the players’ rationality and their beliefs and knowledge over others’ choices, rationality and beliefs. While classical game theory in the tradition inspired by Nash has followed a “top-down” approach consisting in determining which strategy profiles in a game correspond to a given solution concept, the epistemic approach rather follows a “bottom-up” perspective and asks what are the conditions for a given solution concept to be implemented by the players. While Levi’s essay “Prediction, deliberation and correlated equilibrium” focuses on Aumann’s defense of the correlated equilibrium solution concept, its main points are essentially relevant for the epistemic program as a whole, as I will try to show below.

Before delving into the details of Levi’s argument, it might be useful to first provide a semi-formal definition of the correlated equilibrium solution concept. Denote A = (A1, …, An) the joint action-space corresponding to the Cartesian product of the set of pure strategies of the n players in a game. Assume that each player i = 1, …, n has a cardinal utility function ui(.) representing his preferences over the set of outcomes (i.e. strategy profiles) determined by A. Finally, denote Γ some probability space. A function f: Γ –> A defines a correlated equilibrium if for any signal γ, f(γ) = a is a strategy profile such that each player maximizes his expected utility conditional on the strategy he is playing:

For all i and all strategy ai’ ≠ ai, Eui(ai|ai) ≥ Eui(ai|ai)

Correspondingly, the numbers Prob{f-1(a)} define the correlated distribution over A that is implemented in the correlated equilibrium. The set of correlated equilibria in any given game is always at least as large than the set of Nash equilibria. Indeed, a Nash equilibrium is also a correlated equilibrium while correlated equilibria correspond to the convex hull of Nash equilibria. As an illustration, consider for instance the famous hawk-dove game:

Column

C

D

Row

C

5 ; 5

3 ; 7

D

7 ; 3

2 ; 2

This game has two Nash equilibria in pure strategy (i.e. [D, C] and [C, D]) and one Nash equilibrium in mixed strategy where each player plays C with probability 1/3. There are many more correlated equilibria in this game however. One of them is trivially given for instance by the following correlated distribution:

Column

C

D

Row

C

0

1/2

D

1/2

0

In his paper, Aumann establishes the following important theorem:

Aumann’s theorem – For any game, if

(i)        Each player i has a probability measure pi(.) over the joint-action space A;

(ii)       The probability measure is unique, i.e. p1(.) = … = pn(.);

(iii)      The players are Bayesian rational (i.e. maximizes expected utility) and this is common   knowledge;

then, the players implement a correlated equilibrium corresponding to a function f with the correlated distribution defined by Prob{f-1(a)} = p(a).

The theorem thus shows that Bayesian rational players endowed with common knowledge of their rationality and a common prior belief over the joint-action space must implement a correlated equilibrium. Therefore, it seems that Kadane and Larkey were indeed too pessimistic in claiming that nothing can be said regarding what will happen in a game with Bayesian decision makers.

Levi attacks Aumann’s conclusion by rejecting all of its premises. Once again, this rejection is grounded on the “deliberation crowds out prediction” thesis. Actually, Levi’s makes two distinct and relatively independent critics against Aumann’s assumptions. The first concerns an assumption that I have left implicit while the second targets premises (i)-(iii) together. I will consider them in turn.

Implicit in Aumann’s theorem is an assumption that Levi calls “ratifiability”. To understand what that means, it is useful to recall that a Bayesian decision-maker maximizes expected utility using conditional probabilities over states given acts. In other words, a Bayesian decision maker has to account for the possibility that his choice may reveal and/or influence the likelihood that a given state is the actual state. Evidential decision theorists like Richard Jeffrey claim in particular that it is right to see one’s choice as an evidence for the truth-value of various state-propositions even in cases where no obvious causal relationship seems to hold between one’s choice and states of nature. This point is particularly significant in a game-theoretic context where while the players make choice independently (in a normal-form game), some kind of correlation over choices and beliefs may be seen as plausible. The most extreme case is provided by the prisoner’s dilemma which Levi discusses at length in his essay:

Column

C

D

Row

C

5 ; 5

1 ; 6

D

6 ; 1

2 ; 2

The prisoner’s dilemma has a unique Nash equilibrium: [D, D]. Clearly, given the definition given above, this strategy profile is also the sole correlated equilibrium. However, from a Bayesian perspective, Levi argues that it is perfectly fine for Row to reason along the following lines:

“Given what I know and believe about the situation and the other player, I believe almost for sure that if I play D, Column will also play D. However, I also believe that if I play C, there is a significant chance that Column will play C”.

Suppose that Row’s conditional probabilities are p(Column plays D|I play D) = 1 and p(Column plays C|I play C) = ½. Then, Row’s expected utilities are respectively Eu(D) = 2 and Eu(C) = 3. As a consequence, being Bayesian rational, Row should play C, i.e. should choose to play a dominated strategy. Is there any wrong for Row to reason this way? The definition of the correlated equilibrium solution concept excludes this kind of reasoning because, for any action ai, the computation of expected utilities for each alternative actions ai’ should be made using the conditional probabilities u(.|ai). This corresponds indeed to the standard definition of ratifiability in decision theory as put by Jeffrey: “A ratifiable decision is a decision to perform an act of maximum estimated desirability relative to the probability matrix the agent thinks he would have if he finally decided to perform that act.” In the prisoner’s dilemma, it is easy to see that only D is ratifiable because considering to play C with the conditional probabilities given above, Row would do better by playing D; indeed, Eu(D|Columns plays C with probability ½) > Eu(C|Columns plays C with probability ½).

As Levi recognizes, the addition of ratifiability as a criterion of rational choice leads de facto to exclude the possibility that the players in a game may rationally believe that some form of causal dependence holds between their choices. Indeed, as formally shown by Oliver Board, Aumann’s framework tacitly builds upon an assumption of causal independence but also of common belief in causal independence. For some philosophers and game theorists, this is unproblematic and indeed required since it is constitutive of game-theoretic reasoning (see for instance this paper of Robert Stalnaker). Quite the contrary, Levi regards this exclusion as illegitimate at least on a Bayesian ground.

Levi’s rejection of premises (i)-(iii) are more directly related to his “deliberation crowds out prediction thesis”. Actually, we may even focus on premises (i) and (iii) as premise (ii) depends on (i). Consider the assumption that the players have a probability measure over the joint-action space first. Contrary to a standard Bayesian decision problem where the probability measure is defined over a set of states that is distinct from the set of acts, in a game-theoretic context the domain of the probability measures encompasses each player’s own strategy choice. In other words, this leads the game theorist to assumes that each player ascribes an unconditional probability to his own choice. I have already explained why Levi regards this assumption as unacceptable if one wants to account for the way decision makers reason and deliberate.* The common prior assumption (ii) is of course even less commendable in this perspective, especially if we consider that such an assumption pushes us outside the realm of strict Bayesianism. Regarding assumption (iii), Levi’s complaint is similar: common knowledge of Bayesian rationality implies that each player knows that he is rational. However, if a player knows that he is rational before making his choice, then he already regards as feasible only admissible acts (recall Levi’s claims 1 and 2). Hence, no deliberation has to take place.

Levi’s critique of premises (i)-(iii) seem to extend to the epistemic program as a whole. What is at stake here is the epistemological and methodological status of the theoretical models build by game theorists. The question is the following: what is the modeler trying to establish regarding the behavior of players in strategic interactions? There are two obvious possibilities. A first one is that, as an outside observer, the modeler is trying to make sense (i.e. to describe and to explain) of players’ choices after having observed them. Relatedly, still as an outside observer, he may try to predict players’ choices before they are made. A second possibility is to game-theoretic models as tools to account for the players’ reasoning process prospectively, i.e. how players’ deliberate to make choice. Levi’s “deliberation crowds out prediction” thesis could grant some relevance to the first possibility may not for the second. However, he contends that Aumann’s argument for correlated equilibrium cannot be only retrospective but must also be prospective.** If Levi is right, the epistemic program as a whole is affected by this argument, though fortunately there is room for alternative approaches, as illustrated by Bonanno’s paper mentioned in the preceding post.

Notes

* The joint-action space assumption results from a technical constraint: if we want to exclude the player’s own choice from the action space, we then have to account for the fact that each player has a different action space over which he forms beliefs. In principle, this can be dealt with even though this would lead to more cumbersome formalizations.

** Interestingly, in a recent paper with Jacques Dreze which makes use of the correlated equilibrium solution concept, Aumann indeed argues that the use of Bayesian decision theory in a game-theoretic context has such prospective relevance.

Isaac Levi on Rationality, Deliberation and Prediction (2/3)

This is the second of a three-part post on the philosopher Isaac Levi’s account of the relationship between deliberation and prediction in decision theory and which is an essential part of Levi’s more general theory of rationality. Levi’s views potentially have tremendous implications for economists especially regarding the current use of game theory. These views are more particularly developed in several essays collected in his book The Covenant of Reason, especially “Rationality, prediction and autonomous choice”, “Consequentialism and sequential choice” and “Prediction, deliberation and correlated equilibrium”. The first post presented and discussed Levi’s main thesis that “deliberation crowds out prediction”. This post discusses some implications of this thesis for decision theory and game theory, specifically the equivalence between games in dynamic form and in normal form. On the same basis, the third post will evaluate the relevance of the correlated equilibrium concept for Bayesianism in the context of strategic interactions. The three posts are collected under a single pdf file here.

 

In his article “Consequentialism and sequential choice”, Isaac Levi builds on his “deliberation crowds prediction” thesis to discuss Peter Hammond’s account of consequentialism in decision theory presented in the paper “Consequentialist Foundations for Expected Utility”. Hammonds contends that consequentialism (to be defined below) implies several properties for decision problems, especially (i) the formal equivalence between decision problems in sequential (or extensive) form and strategic (or normal) form and (ii) ordinality of preferences over options (i.e. acts and consequences). Though Levi and Hammonds are essentially concerned with one-person decision problems, the discussion is also relevant from a game-theoretic perspective as both properties are generally assumed in the latter. This post will focus on point (i).

First, what is consequentialism? Levi distinguishes between three forms: weak consequentialism (WC), strong consequentialism (SC) and Hammond’s consequentialism (HC). According to Levi, while only HC entails point (i), both SC and HC entail point (ii). Levi contends however that none of them is defensible once we take into account the “deliberation crowds out prediction” thesis. We may define these various forms of consequentialism on the basis of the notation introduced in the preceding post. Recall that any decision problem D corresponds then to a triple < A, S, C > with A the set of acts (defined as functions from states to consequences), S the set of states of nature and C the set of consequences. A probability distribution over S is defined by the function p(.) and represents the decision-maker DM’s subjective beliefs while a cardinal utility function u(.) defined over C represents DM’s preferences. Now the definitions of WC and SC are the following:

Weakly consequentialist representation – A representation of D is weakly consequentialist if, for each a 󠄉 ∈ A, an unconditional utility value u(c) is ascribed to any element c of the subset Ca  C and where we allow for a  ∈ Ca. If a is not the sole element of Ca, then the representation is nontrivially weakly consequentialist.

(WC)   Any decision problem D has a weakly consequentialist representation.

Strongly consequentialist representation – A representation of D is strongly consequentialist if, (i) it is nontrivially weakly consequentialist and (ii) given the set of consequence-propositions C, if ca and cb are two identical propositions, then the conjuncts aca and bcb are such that u(aca) = u(bcb).

            (SC)     Any decision problem D has a strongly consequentialist representation.

WC thus holds that it is always possible to represent a decision problem as a set of acts to which we can ascribe unconditional utility value to all consequences each act leads to, and where an act itself can be analyzed as a consequence. As Levi notes, WC formulated this way is undisputable.* SC has been endorsed by Savage and most contemporary decision theorists. The difference with WC lies in the fact that SC holds a strict separation between acts and consequences. Specifically, the utility value of any consequence c is independent of the act a that brought it. SC thus seems to exclude various forms of “procedural” account of decision problems. Actually, I am not sure that the contrast between WC and SC is as important as Levi suggests for all is required for SC is to have a sufficiently rich set of consequences C to guarantee the required independence.

According to Levi, HC is stronger than SC. This is due to the fact that while SC does not entail that sequential form and strategic form decision problems are equivalent, HC makes this equivalence its constitutive characteristic. To see this, we have to refine our definition of a decision problem to account for the specificity of the sequential form. A sequential decision problem SD is constituted by a set N of nodes n with a subset N(D) of decision nodes (where DM makes choice), a subset N(C) of chance nodes (representing uncertainty) and a subset N(T) of terminal nodes. All elements of N(T) are consequence-propositions and therefore we may simply assume that N(T) = C. N(D) is itself partitioned into information sets I where two nodes n and n’ in the same I are indistinguishable for DM. For each n ∈ N(D), DM has subjective beliefs measured by the probability function p(.|I) that indicates DM’s belief of being at node n given that he knows I. The conditional probabilities p(.|I) are of course generated on the basis of the unconditional probabilities p(.) that DM holds at each node n ∈ N(C). The triple < N(D), N(C), N(T) > defines a tree T. Following Levi, I will however simplify the discussion by assuming perfect information and thus N(C) = ∅. Now, we define a behavior norm B(T, n) for any tree T and any decision node n in T the set of admissible options (choices) from the set of available options at that node. Denote T(n) the subtree starting from any decision node n. A strategy (or act) specifies at least one admissible option for all decision nodes reachable, i.e. B(T(n), n) must be non-empty for each n ∈ N(D). Given that N(T) = C, we write C(T(n)) the subset of consequences (terminal nodes) that are reachable in the subtree T(n) and B[C(T(n)), n] the set of consequences DM would regard as admissible if all elements in C(T(n)) were directly available at decision node n. Therefore, B[C(T(n)), n] is the set of admissible consequences in the strategic form equivalent of SD as defined by (sub)tree T(n). Finally, write φ(T(n)) the set of admissible consequences in the sequential form decision problem SD. HC is then defined as follows:

(HC)   φ(T(n)) = B[C(T(n)), n]

In words, HC states the kind of representation (sequential or strategic) of a decision problem SD used is irrelevant in the determination of the set of admissible consequences. Moreover, since we have assumed perfect information, its straightforward that this is also true for admissible acts which, in sequential form decision problems, correspond to exhaustive plans of actions.

Levi argues that assuming this equivalence is too strong and cannot be an implication of consequentialism. This objection is of course grounded on the “deliberation crowds out prediction” thesis. Consider a DM faced with a decision problem SD with two decision nodes. At node 1, DM has the choice between consuming drug (a1) or abstaining (b1). If he abstains, the decision problem ends but if the adduces, he then has the choice at node 2 between continuing taking drugs and becoming addict (a2) or stopping and avoiding addiction (c2). Suppose that DM’s preferences are such that u(c2) > u(b1) > u(a2). DM’s available acts (or strategies) are therefore (a1, a2), (a1, c2), (b1, a2) and (b1, c2).** Consider the strategic form representation of this decision problem where DM has to make a choice once for all regarding the whole decision path. Arguably, the only admissible consequence is c2 and therefore the only admissible act is (a1, c2). Assume however that if DM were to choose a1, he would fall prey to temptation at node 2 and would not be able to refrain from continuing consuming drugs. In other words, at node 2, only option a2 would actually be available. Suppose that DM knows this at node 1.*** Now, a sophisticated DM will anticipate his inability to resist temptation and will choose to abstain (b1) at node 1. It follows that a sophisticated DM will choose   (b1, a2) in the extensive form of SD, thus violating HC (but not SC).

What is implicit behind Levi’s claim is that, while it makes perfect sense for DM to ascribe probability (including probability 1 or 0) to his future choices at subsequent decision nodes, this cannot be the case for his choice over acts, i.e. exhaustive plans of actions in the decision path. For if it was the case, then as (a1, c2) is the only admissible act, he would have to ascribe probability 0 to all acts but (a1, c2) (recall Levi’s claim 2 in the previous post). But then, that would also imply that only (a1, c2) is feasible (Levi’s claim 1) while this is actually not the case.**** Levi’s point is thus that, at node 1, the choices at node 1 and at node 2 are qualitatively different: at node 1, DM has to deliberate over the implications of choosing the various options at his disposal given his beliefs over what he would do at node 2. In other words, DM’s choice at node 1 requires him to deliberate on the basis of a prediction about his future behavior. In turn, at node 2, DM’s choice will involve a similar kind of deliberation. The reduction of extensive form into strategic form is only possible if one conflates these two choices and thus ignores the asymmetry between deliberation and prediction.

Levi’s argument is also relevant from a game-theoretic perspective as the current standard view is that a formal equivalence between strategic form and extensive form games holds. This issue is particularly significant for the study of the rationality and epistemic conditions sustaining various solution concepts. A standard assumption in game theory is that the players have knowledge (or full belief) of their strategy choices. The evaluation of the rationality of their choices both in strategic and extensive form games however requires to determine what the players believe (or would have believed) in counterfactual situations arising from different strategy choices. For instance, it is now well established that common belief in rationality does not entail the backward induction solution in perfect information games or rationalizability in strategic form games. Dealing with these issues necessitates a heavy conceptual apparatus. However, as recently argued by economist Giacomo Bonanno, not viewing one’s strategy choices as objects of belief or knowledge allows an easier study of extensive-form games that avoids dealing with counterfactuals. Beyond the technical considerations, if one subscribes to the “deliberation crowds out prediction”, this is an alternative path worth exploring.

Notes

* Note that this has far reaching implications for moral philosophy and ethics as moral decision problems are a strict subset of decision problems. All moral decision problems can be represented along a weakly consequentialist frame.

** Acts (b1, a2) and (b1, c2) are of course equivalent in terms of consequences as DM will never actually have to make a choice at node 2. Still, in some cases it is essential to determine what DM would do in counterfactual scenarios to evaluate his rationality.

*** Alternatively, we may suppose that DM has at node 1 a probabilistic belief over his ability to resist temptation at node 2. This can be simply implemented by adding a chance node before node 1 that determines the utility value of the augmented set of consequences and/or the available options at node 2 and by assuming that DM ignores the result of the chance move.

**** I think that Levi’s example is not fully convincing however. Arguably, one may argue that since action c2 is assumed to be unavailable at node 2, acts (a1, c2) and (b1, c2) should also be regarded as unavailable. The resulting reduced version of the strategic form decision problem would then lead to the same result than the sequential form. This is not different even if we assume that DM is uncertain regarding his ability to resist temptation (see the preceding note). Indeed, the resulting expected utilities of acts would trivially lead to the same result in the strategic and in the sequential forms.  Contrary to what Levi argues, it is not clear that that would violate HC.

Isaac Levi on Rationality, Deliberation and Prediction (1/3)

This is the first of a three-part post on the philosopher Isaac Levi’s account of the relationship between deliberation and prediction in decision theory and which is an essential part of Levi’s more general theory of rationality. Levi’s views potentially have tremendous implications for economists especially regarding the current use of game theory. These views are more particularly developed in several essays collected in his book The Covenant of Reason, especially “Rationality, prediction and autonomous choice”, “Consequentialism and sequential choice” and “Prediction, deliberation and correlated equilibrium”. The first post presents and discusses Levi’s main thesis that “deliberation crowds out prediction”. The next two posts will discuss some implications of this thesis for decision theory and game theory, specifically (i) the equivalence between games in dynamic form and in normal form and (ii) the relevance of the correlated equilibrium concept for Bayesianism in the context of strategic interactions. The three posts are collected under a single pdf file here.

The determination of principles of rational choice is the main subject of decision theory since its early development at the beginning of the 20th century. Since its beginnings, decision theory has pursued two different and somehow conflicting goals: on the one hand, to describe and explain how people actually make choices and, on the other hand, to determine how people should make choices and what choices they should make. While the former goal corresponds to what can be called “positive decision theory”, the latter is constitutive of “normative decision theory”. Most decision theorists, especially the proponents of “Bayesian” decision theory, have agreed that decision theory cannot but be partially normative. Indeed, while today Bayesian decision theory is generally not regarded as an accurate account of how individuals are actually making choices, most decision theorists remain convinced that it is still relevant as a normative theory of rational decision-making. This is in this context that Isaac Levi’s claim that “deliberation crowds out prediction” should be discussed.

In this post, I will confine the discussion to the restrictive framework of Bayesian decision theory though Levi’s account more generally applies to any form of decision theory that adheres to consequentialism. Consequentialism will be more fully discussed in the second post of this series. Consider any decision problem D in which an agent DM has to make a choice over a set of options whose consequences are not necessarily fully known for sure. Bayesians will generally model D as a triple < A, S, C > where A is the set of acts a, S the set of states of nature s and C the set of consequences c. In the most general form of Bayesian decision theory, any a, s and c may be regarded as a proposition to which truth-values might be assigned. In Savage’s specific version of Bayesian decision theory, acts are conceived as functions from states to consequences, i.e. a: S à C or c = a(s). In this framework, it is useful to see acts as DM’s objects of choice, i.e. the elements over which he has a direct control, while states may be interpreted as every features in D over which DM has no direct control. Consequences are simply the result of the combination of an act (chosen by DM) and a state (not chosen by DM). Still following Savage, it is standard to assume that DM has (subjective) beliefs over which state s actually holds. These beliefs are captured by a probability function p(.) with ∑sp(s) = 1 for a finite state space. Moreover, each consequence c is assigned a utility value u representing DM’s preferences over the consequences. A Bayesian DM will then choose the act that maximizes his expected utility given his subjective beliefs and his preferences, i.e.

Maxa Eu(a) = ∑sp(s|a)u(a(s)) =  ∑sp(s|a)u(c).

Two things are worth noting. First, note that the probabilities that enter into the expected utility computation are conditional probabilities of states given acts. We should indeed account for the possibility that the probabilities of states depend on the act performed. The nature of the relationship between states and acts represented by these conditional probabilities is the main subject of conflict between causal and evidential decision theorists. Second, as it is well-known, in Savage’s version of Bayesian decision theory, we start with a full ordering representing DM’s preferences over acts and given a set of axioms, it is shown that we can derive a unique probability function p(.) and a cardinal utility function u(.) unique up to any positive affine transformation. It is indeed important to recognize that Savage’s account is essentially behaviorist because it merely shows that given the fact that DM’s preferences and beliefs satisfy some properties, then his choice can be represented as the maximization of some function with some uniqueness property. Not all Bayesian decision theorists necessarily share Savage’s behaviorist commitment.

I have just stated that in Savage’s account, DM ascribes probabilities to states, utilities to consequences and hence expected utilities to acts. However, if acts, states and consequences are all understood as propositions (as argued by Richard Jeffrey and Levi among others), then there is nothing in principle prohibiting to ascribe utilities to states and probabilities to both consequences and acts. This is this last possibility (ascribing probabilities to acts) that is the focus of Levi’s claim that deliberation crowds out prediction. In particular, does it make sense for DM to have unconditional probabilities over the set A? How having such probabilities could be interpreted from the perspective of DM’s deliberation in D? If we take a third person perspective, ascribing probabilities to DM’s objects of choice seems not particularly contentious. It makes perfect sense for me to say for instance “I believe that you will start again to smoke before the end of the month with probability p”. Ascribing probabilities to others’ choices is an essential part of our daily activity consisting in predicting others’ choices. Moreover, probability ascription may be a way to explain and rationalize others’ behavior. The point of course is that these are my probabilities, not yours. The issue here is whether a deliberating agent has to, or even can ascribe such probabilities to his own actions, acknowledging that such probabilities are in any case not relevant in the expected utility computation.

Levi has been (with Wolfgang Spohn) the most forceful opponent to such a possibility. He basically claims that the principles of rationality that underlie any theory of decision-making (including Bayesian ones) cannot at the same time serve as explanatory and predictive tools and as normative principles guiding rational behavior. In other words, as far as the deliberating agent is using rationality principles to make the best choice, he cannot at the same time use these principles to predict his own behavior at the very moment he is making his choice.* This is the essence of the “deliberation crowds out prediction” slogan. To understand Levi’s position, it is necessary to delve into some technical details underlying the general argument. A paper of philosopher Wlodek Rabinowicz makes a great job in reconstructing this argument (see also this paper by James Joyce). A crucial premise is that, following De Finetti, Levi considers belief ascription as fully constituted by the elicitation of betting rates, i.e. DM’s belief over some event E is determined and corresponds to what DM would consider as the fair price of a gamble where event E pays x$ and event non-E pays y$.** Consider this example: I propose you to pay y$ (the cost or the price of the bet) to participate to the following bet: if Spain win the Olympic gold medal of basketball at Rio this month, I will pay you x$, otherwise I pay you nothing. Therefore, x is the net gain of the bet and x+y is called the stake of the bet. Now, the fair price y*$ of the bet corresponds to the amount for which you are indifferent between taking and not taking the bet. Suppose that x = 100 and that y* = 5. Your betting rate for this gamble is then y*/(x+y*) = 5/105 = 0,048, i.e. you believe that Spain will win with probability less than 0,05. This is the traditional way beliefs are determined in Bayesian decision theory. Now, Levi’s argument is that such a procedure cannot be applied in the case of beliefs over acts on pain of inconsistency. The argument relies on two claims:

(1)       If DM is certain that he will not perform some action a, then a is not regarded as part of the feasible acts by DM.

(2)       If DM assigns probabilities to acts, then he must assign probability 0 to acts he regards as inadmissible, i.e. which do not maximize expected utility.

Clearly, (1) and (2) entail together that only feasible acts (figuring in the set A) are admissible (maximize expected utility), in which case deliberation is unnecessary for DM. If it is the case however, that means that principles of rationality cannot be used as normative principles in the deliberation process. While claim (1) is relatively transparent (even if it is disputable), claim (2) is less straightforward. Consider therefore the following illustration.

DM has a choice between two feasible acts a and b with Eu(a) > Eu(b), i.e. only a is admissible. Suppose that DM assigns probabilities p(a) and p(b) according to the procedure presented above. We present DM with a fair bet B on a where the price is y* and the stake is x+y*. As the bet is fair, y* is the fair price and y*/(x+y*) = p(a) is the betting rate measuring DM’s belief. Now, DM has four feasible options:

Take the bet and choose a (B&a)

Do not take the bet and choose a (notB&a)

Take the bet and choose b (B&b)

Do not take the bet and choose b (notB&b)

As taking the bet and choosing a guarantee a sure gain of x to DM, it is easy to see that B&a strictly dominates notB&a. Similarly, as taking the bet and choosing b guarantee a sure loss of y*, notB&b strictly dominates B&b. The choice is therefore between B&a and notB&b and clearly Eu(a) + x > Eu(b). It follows that the fair price for B is  y* = x + y* and hence p(a) = 1 and p(b) = 1 – p(a) = 0. The inadmissible option b has probability 0 and is thus regarded as unfeasible by DM (claim 1). No deliberation is needed for DM if he predicts his choice since only a is regarded as feasible.

Levi’s argument is by no means undisputable and the papers of Rabinowicz and Joyce referred above make a great job at showing its weaknesses. In the next two posts, I will however take it as granted and discuss some of its implications for decision theory and game theory.

 Notes

* As I will discuss in the second post, Levi considers that there is nothing contradictory or problematic in the assumption that one may be able to predict his future choices.

** A gamble’s fair price is the price at which DM is indifferent accepting to buy the bet and accepting to sell the bet.

Effective Altruism and the Unavoidability of Ethical Trade-Offs

The so-called “effective altruism” (EA) movement has recently received a significant attention in the press. Many articles have been critical of EA for various reasons that significantly overlap over the general theme that too much quantification and calculus implies the risk of losing the “big picture” of the issues related to charity and poverty. The last example is an article published on the website “The Conversation”. The author’s main argument is that as a reason-based approach to charity and poverty, EA proponents ignore the fact that ethics and morality cannot be reduced to some “cold” utilitarian calculus:

“[EA proponents] have PhDs in the disciplines requiring the highest level of analytical intelligence, but are they clever enough to understand the limits of reason? Do they have an inner alarm bell that goes off when the chain of logical deductions produces a result that in most people causes revulsion?”

According to the author, a society full of “effectively altruist” people would be a society where any ethical issues would be dealt with through cold-minded computations actually eliminating any role for emotions and gut instincts.

“To be an effective altruist one must override the urge to give when one’s heart is opened up and instead engage in a process of data gathering and computation to decide whether the planned donation could be better spent elsewhere.

If effective altruists adopt this kind of utilitarian calculus as the basis for daily life (for it would be irrational to confine it to acts of charity) then good luck to them. The problem is that they believe everyone should behave in the same hyper-rational way; in other words, they believe society should be remade in their own image.”

The author then makes a link with free-market economists like Gary Becker, suspecting “that, for most people, following the rules of effective altruism would be like being married to Gary Becker, a highly efficient arrangement between contracting parties, but one deprived of all human warmth and compassion.”

There are surely many aspects of EA that can be argued against but I think that this kind of critique is pretty weak. Moreover, it is grounded on a deep misunderstanding of the contribution that social sciences (and especially economics) can make to dealing with ethical issues. As a starting point, I think that any discussion on the virtues and dangers of EA should start on a basic premise that I propose to call the “Hard Fact of Ethical Reasoning”:

Hard Fact of Ethical Reasoning (HFER) – Any ethical issue involves a decision problem with trade-offs to be made.

Giving to a charity to alleviate the sufferings due to poverty is a decision problem with a strong ethical component. What the HFER claims is that when considering how to alleviate those sufferings, you have to make a choice regarding how to use scarce resources in such a way your objective is reached. This a classical means-ends relationship the study of which has been at the core of modern economics for the last hundred years. If one accepts the HFER (and it is hard to see how one could deny it), then I would argue that EA has the general merit of leading us to reflect on and to make explicit the values and the axiological/deontic criteria that underlie our ethical judgments regarding what is considered to be good or right. As I interpret it, a key message of EA is that these ethical judgments should/cannot exclusively depend on our gut feelings and emotions but should also be the subject of rational scrutiny. Now, some of us may be indeed uncomfortable with the substantive claims made by EA proponents, such as Peter Singer’s remark that  “if you do the sums” then “you can provide one guide dog for one blind American or you could cure between 400 and 2,000 people of blindness [in developing countries]”. Here, I think the point is to distinguish between two kinds of EA that I would call formal EA and substantive EA respectively.

Formal EA provides a general framework to think of ethical issues related to charity and poverty. It can be characterized by the following two principles:

Formal EA P1: Giving to different charities leads to different states of affairs that can be compared and ranked according to their goodness following some axiological principles, possibly given deontic constraints.

Formal EA P2: The overall goodness of states of affairs is a (increasing) function of their goodness for the individuals concerned.

Principles P1 and P2 are very general ones. P2 corresponds to what is sometime called the Pareto principle and seems, in this context, to be hardly disputable. It basically states that if you have the choice between giving to two charities and that everyone is equally well-off in the two resulting states of affairs except for at least one person that is better in one of them, then the latter state of affairs is the best. P1 states that it is possible to compare and rank states of affairs, which of course still allow for indifference. Note that we allow the possibility for the ranking to be constrained by any deontological principle that is considered as relevant. Under these two principles, formal EA essentially consists in a methodological roadmap: compute individual goodness in the different possible states of affairs that may result from charity donation, aggregate individual goodness according to some principles (captured by an Arrowian social welfare function in social choice theory) and finally rank the states of affairs according to their resulting overall goodness. This version of EA is thus essentially formal because it is silent regarding i) the content of individual goodness and ii) which social welfare function should be used. However, we may plausibly think of two additional principles that that make substantive claims regarding these two features:

Formal EA P3: Individual goodness is cardinally measurable and comparable.

Formal EA P4: Number counts: for any state of affairs with n persons whose individual goodness is increased by u by charity giving, there is in principle a better state of affairs with m > n persons whose individual goodness is increased by v < u by charity giving.

I will not comment on P3 as it is basically required to conduct any sensible ethical discussion. P4 is essential and I will return on it below. Before, compare formal EA with substantive EA. By substantive EA, I mean any combination of P1-P4 that adds at least one substantive assumption regarding a) the nature of individual goodness and/or b) the constraints the social welfare function must satisfy. Clearly, substantive EA is underdetermined by formal EA. There are many ways to pass from the latter to the former. For instance, one possibility is to use standard cost-benefit analysis to define and measure individual goodness. A utilitarian version of substantive EA which more or less captures Singer’s claims is obtained by assuming that the social welfare function must satisfy a strong independence principle such that overall goodness is additively separable. The possibilities are indeed almost infinite. This is the main virtue of formal EA as a theoretical and practical tool: it forces us to reflect on and to make explicit the principles that sustain our ethical judgments, acknowledging the fact that such judgments are required due to the HFER. Note moreover that in spite of its name, on this reading EA needs not be exclusively concerned with efficiency: fairness may be also taken into account by adding the appropriate principles when passing from formal to substantive EA. What remains true is that a proponent of EA will always claim that one should give to the charity that leads to the best state of affairs in terms of the relevant ordering. There is thus still a notion of “efficiency” but more loosely defined.

My discussion parallels an important discussion in moral philosophy between formal aggregation and substantive aggregation which has been thoroughly discussed in a recent book of Iwao Hirose. Hirose provides a convincing defense of formal aggregation as a general framework in moral philosophy. It is also similar to the distinction made by Marc Fleurbaey between formal welfarism and substantive welfarism. A key feature of formal aggregation is the substantive assumption that numbers count (principle P4 above). Consider the following example due to Thomas Scanlon and extensively discussed by Irose:

“Suppose that Jones has suffered an accident in the transmitter room of a television station. Electrical equipment has fallen on his arm, and we cannot rescue him without turning off the transmitter for fifteen minutes. A World Cup match is in progress, watched by many people, and it will not be over for an hour. Jones’s injury will not get any worse if we wait, but his hand has been mashed and he is receiving extremely painful electrical shocks. Should we rescue him now or wait until the match is over?”

According to formal aggregation, there exists some number n* of persons watching the match such that for any n > n* it is better to wait the end of the match to rescue Jones. Scanlon and many others have argued against this conclusion and claimed that we cannot aggregate individual goodness this way. Hirose thoroughly discusses the various objection against formal aggregation but in the end concludes that none of them are fully convincing. The point here is that if someone wants to argue against EA as I have characterized it, then one must make a more general point against formal aggregation. This is a possibility of course, but that has nothing to do with rejecting the role of reason and of “cold calculus” in the realm of ethics.