Aug 22, 2017 - assumes that man has free will, in the sense that he is free to think and act independently. ..... Thinking, Fast and Slow. Doubleday Canada.
A Mathematics of Morality For Utopian Economics Steven D. Moffitt, Ph.D. 2017-08-22
Abstract Concepts of morality are absent from modern “rational” economic theory. Incorporating morality into economics requires the recognition that economic actors have a wider range of choices than those allowed by narrow self-interest. It also requires that intentions be distinguished from actions. By creating a mathematical framework that reflects these distinctions, it is shown that (1) a coherent economic theory can include strategies other than self-serving ones, (2) two polar choices and mixtures thereof are available to economic actors, those that are individual-centric and those that are groupcentric, (3) “moral” strategies can be expressed mathematically, allowing an assessment of a strategy’s degree of morality, and (4) exclusive use of selfserving strategies leads to actions that in a conventional sense, are immoral.
“After you, Alphonse.”, “No, you first, my dear Gaston!” Byword of Alphonse &Gaston in the American Comic strip, by Federick Burr Opper
“And what is the greatest number? Number one. David Hume
Introduction From the Renaissance to the eighteenth century, economics was a branch of moral philosophy. In that period, chivalry was the dominant moral code among gentlemen — defending one’s honor, defending the honor of friends and allies, courage in battle and courtesy toward other gentlemen. But during the eighteenth century, English moral philosophers began arguing that society would benefit substantially if “the passions” (chivalry) were abandoned in favor of “the interests” (enlightened self-interest) (Hirschman et al. (2013)). Of course, acting solely in one’s “interests” was antithetical to practically all prevailing religious, moral and political doctrine. Nonetheless it was championed by Mandeville and Kaye (1714) in a scandalous poem “The Fable of the Bees: or, Private Vices, Publick Benefits.” Mandeville described a society of industrious bees whose “private vices,” however heinous, are transformed into “publick benefits.” A polemic (or perhaps satire) of devastating effect, the Fable thrust into the public consciousness the view that avarice is not sinful or ignoble. To the contrary, its salutary effects for society greatly outweigh moral remonstrations: exitus acta probat. While Mandeville’s work advanced no grand theory, it set the stage for the better-reasoned treatise “An Inquiry into the Wealth of Nations,” Smith (1776a,b). Smith argued that a society animated by self-interest would be a wealthier, therefore better society. Smith lived and wrote in the early industrial era, a time of great poverty and hardship for the English lower classes, so his advocacy of a system that provided material improvements was quite understandable. Yet while Smith is known today as the father of 1
economics, in his own day his reputation owed to the treatise “The Theory of Moral Sentiments,” published 17 years earlier (Smith (1759)). And contrary to revisionist beliefs, Smith was no champion of unrestrained self-interest as a basis of capitalism. In the nineteenth century, moral philosophy regained some of the ground lost to this beneficient view of self-interest in the works of John Stuart Mill and Karl Marx. Mill argued that the hardships visited upon adult and child workers in the early industrial revolution was a stage of capitalism that in time would be replaced by a benign socialism. In that wealthy society of the future, he thought, self-interest would play a minor role. Mill imagined that the transition to that society would be gradual and peaceful. Like Mill, Marx argued that capitalism would continue to improve material well-being, but unlike Mill, he believed that capitalism would breed a class of employers with the incentive to pay workers as little as possible, a system whose instability would generate perpetual social conflict and financial crises. Marx believed that a capitalist system would climax in violent class confrontation between capitalists and workers, after which victorious workers would install a system of enlightened socialism. Dispite their vastly different visions of the future, both Mill and Marx believed that eventually, society’s animus of individual self-interest would be supplanted replaced by universal, public-minded spirit of cooperation (Heilbroner (1999)). From the last quarter of the nineteenth century through the end of the twentieth, economics completed its divorce from moral philosophy. In this period, economics became increasingly mathematical and “scientific,” in the sense that idealized models of the economy were constructed without moral considerations — thus they were considered “objective.” Two notable effects of the shift to a scientific perspective were: (1) abstract models became more sophisticated, and at the same time increasingly distant from an economy having real humans, real markets and real governments, and (2) economics of this type assumed that nearly all economic actors are entirely self-interested, and the focus is upon efficiency, not morality. Names associated with the divorce, albeit to different degrees, are Alfred Marshall, John Maynard Keynes, Paul Samuelson, Milton Friedman and their descendants, a list which includes many of the economic giants of the period (Heilbroner (1999)). Thus, mainstream economics of the early 21st century rests on a fundamental assumption about the nature of man — that in thought and action he is entirely self-serving. Rational choice theory (RCT) embodies the most 2
extreme version of this assumption by treating economic actors as maximizers of their perceived personal interests, those interests being represented by ordinal or cardinal utility. In this model, individuals choose by maximizing expected utility, irrespective of those decisions’ effects on other persons; RCT therefore ignores moral considerations. Microeconomic theory under RCT then becomes the study of the joint behavior many RCT actors performing utility maximization. An underemphasized aspect of RCT is that all economic actors act as if they are maximizing their utility functions. This simplifying assumption sidesteps thorny issues of motivation and morality, and leads to a seldom spoken belief about RCT — that it is morally neutral. The usual argument is that a maximizer is free to choose an entirely self-serving utility function, an altruistic utility function or indeed, any utility whatsoever. Since in a lenient interpretation of RCT, players are free to choose their utility functions, this argument has some validity. But under the assumption that utilities are increasing functions of wealth alone, and that RCT actors act independently (the usual assumption in finance), the argument fails because utility maximizers are then playing a non-cooperative game for money, and as we will demonstrate, a bunch of RCT utility maximizers playing a game for money in no conventional sense behave “morally.” This work has three main purposes: (1) to place RCT into a larger framework that incorporates a concept of morality, (2) to show that conventional morality is afforded a mathematical expression in this framework, and (3) to show that within this framework, RCT leads to actions that in a conventional sense, are immoral.
Overview The proposed framework will be called moral choice theory (MOCT). Unlike RCT, MOCT does not assert normative behavior, but rather recognizes that individuals can freely select their intentions as well as their actions. MOCT assumes that man has free will, in the sense that he is free to think and act independently. It does not require that each individual maximize a personal utility function, or that he serve the general welfare or that he take any action at all. Instead, it leaves the choices to the individual and examines their consequences. Second, a crucial distinction is made between intention and action. Once 3
this distinction is accepted, RCT fails to hold if there are individuals with different skill levels, that is, individuals whose intentions are self-serving, but whose skill in realizing them differs widely. And of course, it completely ignores players whose intentions are less than completely self-serving. The closest that standard financial theory comes to modeling this distinction is the inclusion of “noise traders” in efficient market theory and Simon’s bounded rationality model. Noise traders are obviously incompetent if their intentions are self-serving and foolish if they are not and their very existence acknowledges that not all players are rational. In the case of bounded rationality, players are assumed to be self-serving, but decide imperfectly due to limited data and facility at computing. Players try to be rational but fall short due to their humanness, and I will argue, due also to their humanity. This is all quite convenient because issues of fairness and morality in either theory are implicitly ignored. Shall a player be allowed to “die” because of lack of skill? Apparently so. Third, the proposed framework avoids RCT’s mistake of assuming without evidence that all players entirely self-serving. MOCT instead allows players to select their intentions through free will. In order to emphasize the implications of freely chosen intentions, two polar cases are treated first: (1) pure self-service, and (2) pure group-service. Following this, mixtures of the polar types are analyzed. A surprising by-product of the analysis is a game-theoretic way to measure “moral” or “ethical” behavior. In effect, there are two distinct versions of morality depending on one’s polar intentionality. From the viewpoint of the self-serving, those who are group-serving pursue inferior strategies. And in many evolutionary models, inferior players die out; thus morality from this viewpoint is “survival of the (economically) fittest.” But from the viewpoint of the group-serving, the self-serving act “unethically,” a view that captures the usual sense of ethical action. Given a particular game and a strategy for playing it, one can associate that strategy with a number between -1 and 1, where a value of 0 is associated with a self-serving strategy and 1 is associated with a group-serving strategy. A strategy’s score near 0 indicates an enlightened strategy from the self-serving viewpoint and an unethical strategy from the group-serving viewpoint. A strategy’s score near 1 indicates an inferior, “exploitable” strategy from the self-serving viewpoint and an ethical one from the group-serving viewpoint. Strategies may have values less than 0; these are associated with retaliation and revenge. From the self-serving viewpoint, they are also ex4
ploitable but not so much as group-serving ones; from the group-serving viewpoint, they are more misguided than unethical. The new framework can be extended to metagames that model a struggle to select the types of games to play. For the self-serving, the preference is for games that penalize n¨aive self-serving and group-serving strategies. For the group-serving, the preference is for positive sum games; zero sum games are strictly avoided. There is an almost laughable irony iimplicit in this new framework. As the conclusion argues, there can be no real communication between polar opposite types of players, since the very terms by which they represent their “utilities” are incomparable. Brief suggestions are given for ways to deal with this problem.
1.1
Background and Previous Work
The use of game-like reasoning in moral philosophy and economics has a long and storied history to which this short introduction can scarcely do justice. Although political and moral philosophy before the mid-twentieth century contains much that today is recognized as game-theoretic, the formal theory of games was not initiated until 1944 when John von Neumann and Oskar Morgenstern published “Theory of Games and Economic Behavior” (von Neumann et al. (2007)). This abstract mathematical theory of games diffused over the years through the social sciences, but for present purposes, especially into philosophy, psychology, sociology and economics. This section is a light and selective review of developments since the mid-twentieth century in the aforementioned disciplines proposing that group behavior is not reducible to individual behavior, and that the modes of thought and strategies pursued need a wider basis than the methodological individualism available in noncoperative and so-called cooperative game theory. Since game theory studies interactions among agents in the play of idealized games, it seems inevitable that it would find a place in moral and political philosophy. In 1944, Braithwaite (1955) suggested that game theory offered a new and promising tool for moral philosophy. That suggestion was pursued by Barry (2010) and Lewis (2013) to make moral arguments, but no complete theory was proposed until the work of Gauthier (1986) used a consequentialist argument — that an outcome is good because of ends, not means — to justify morality as a decision-theoretic constraint which produces 5
superior individual and societal outcomes. Other philosophers and game theorists have developed theories of morality in societies; these are called welfarist theories. There are two competing approaches to welfarism: (1) the egalitarianism of John Rawls, and (2) the utilitarianism of John Harsanyi (Moulin (1991)). Rawls (2009) in “A Theory of Justice” argues using concepts from game theory that producing the best outcome for the worst-off should be the main goal of a compassionate society. Rawls’ approach is usually called minimax or Rawlsian welfarism, i.e. maximizing the welare of the least well-off. Harsanyi, on the other hand, aligns with classical utilitiarians Bentham and John Stuart Mill in promoting the best outcome as the greatest predominance of pleasure over pain, this being measured by the modern theory of utility. Harsanyi (1955) produced two theorems of social aggregation welfarism, both involving Bentham-like summing of individual utilities. In Harsanyi (1955), he assumes that interpersonal comparison of utilities among individuals is possible (so that a sum makes sense) and using certain other assumptions, shows that a weighted average of individual utilities is the essentially the unique social welfare function. In Harsanyi (1978), he does not assume that interpersonal comparison of utilities is possible, but again produces axioms that justify some weighted average of utlities as an essentially unique social welfare function. But this latter approach requires an “objective observer” to assign the weights, in what is tantamount to a subjective assignment of ethical values for the society. We remark that the approaches of Rawls and Harsanyi require different assumptions and lead to different outcomes (Moulin (1991)), i.e. egalitarianism is not equivalent to utilitarianism. In particular the egalitarian approach is directly concerned with distribution of society’s bounty, whereas utilitarianism is not so concerned. In effect, one can say that egalitarianism solves a decision problem and an allocational problem, whereas utilitarianism only solves a decision problem. It is also worth remarking that both Rawls and Harsanyi produced normative theories, not descriptive theories. In particular, the Harsanyi work relies heavily on von Neumann-Morgenstern utility (von Neumann et al. (2007)), which has been thoroughly discredited as a descriptive theory (Kahneman (2011)). Some investigators have contributed to moral theory without directly addressing it. One such group were those attempting to explain and justify social coordination and cooperation, including concepts of justice, fairness and equity. 6
The Finnish philosopher Tuomela (2007) has developed a theory of social action in which two modes, the “I-mode” and the “We-Mode,” are invoked to explain group actions. The I-mode is assumed by individualistic theories of “rational” action that in economics are considered sufficient to explain social behavior; the theories of rational choice and non-cooperative games are the main vehicles of I-mode expression. The We-mode differs in asserting that there are group actions that are not reducible to I-mode explanations, e.g. collective intentionality in which individuals act in perceived interests of a group. Hakli, Miller and Tuomela in discussing the relationship of such connections to game-theoretic analysis Hakli et al. (2010) write: . . . philosophical theories of collective intentionality study such phenomena as collective intentional behavior (e.g. joint action), collective attitudes (e.g. group beliefs) and collective reasoning (e.g. collective decision making). A major question in the literature concerns whether the analysis of these phenomena requires conceptually or ontologically irreducible collectively intentional mental states or actions – for instance, collective attitudes that are not mere aggregates of individual attitudes – or whether the phenomena can be reduced to individual intentional states and actions. According to standard rational choice theory, cooperation and collective intentionality phenomena can be adequately explained without reference to irreducible group attitudes. A contrary approach is taken by philosophers Gilbert (1992), Tuomela (1995, 2000, 2007) and Searle (1995, 2010) who argue that irreducible group attitudes are required for understanding cooperative behavior. In economics, a related ’team thinking’ approach has been advocated by Sugden (1993, 2003) and Bacharach (1999); Bacharach et al. (2006). The economist Michael Bacharach developed an epistemic approach to the question of cooperation, trying to identify valid modes of reasoning in game theory, especially “team reasoning” as opposed to “individualistic reasoning.” Essentially, Bacharach had to argue that it is “rational,” that is, logical, for individuals to act even in part according to group interests. Bacharach’s major work, “Beyond Individual Choice: Teams and Frames in Game Theory,” was only partially completed at the time of his death, and was later reconstructed and completed by Natalie Gold and Robert Sugden (Bacharach 7
et al. (2006)). It is indeed a testament to the entrenched belief in methodological individualism, that Bacharach had to go to such lengths to show that cooperative behavior in economics is even possible. Other investigators have attempted to explain prosocial behavior as an evolutionary development. Three such attempts that we discuss are by Robert Axelrod, Brian Skyrms and Ken Binmore. In “The Evolution of Cooperation,” Axelrod (2009) investigated the question of how cooperation could evolve among selfish individuals using the prisoner’s dilemma as a vehicle. The prisoner’s dilemma has a cooperative choice, the best available for either player. But if one player makes that choice and the other does not, the cooperative player loses and the “double-crosser” wins even more. Yet it can be shown under certain conditions of repeated play, that it is selfishly correct to cooperate. Thus Axelrod suggests that long-term considerations can outweigh short-term ones, even if all players are selfish. Axelrod’s work does not discuss moral theory. In “Evolution of the Social Contract” Skyrms (1996), Brian Skyrms argues that evolutionary game theory can show how the “social contract” came to be. Yet he produces only fragments of a fuller theory, and in particular, does not discuss a crucial issue — coalition formation. This work does not directly discuss moral theory. Ken Binmore has spent years developing a theory of the social contract. His book “Natural Justice” (Binmore (2005)) is a nontechnical introduction to those theories that attempts to reconcile John Rawl’s egalitarian theory with John Harsanyi’s utilitarianism. Binmore argues that morality is the result of biological and social evolution that has improved human fitness. Many, many others have contributed to theories about morality, social welfare and social evolution. This brief introduction serves only to erect signposts that point the way to salient research. However, none of these developments presage the content of the current essay, as we will now see.
1.2
Utopian Economics Involving Purely Self-Serving Actors
The theory of games with self-serving players is the cornerstone of modern economics. Broadly speaking, game theory makes two distinctions between games with self-serving players. There is non-cooperative game theory, which
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