On the foundations of mean-variance analyses

Let (, ) and (, ) be mean-standard deviation pairs of two probability distributions on the real line. Mean-variance analyses presume that the preferred distribution depends solely on these pairs, with primary preference given to larger mean and smaller variance. This presumption, in conjunction with the assumption that one distribution is better than a second distribution if the mass of the first is completely to the right of the mass of the second, implies that (, ) is preferred to (, ) if and only if either > or ( = and < ), provided that the set of distributions is sufficiently rich. The latter provision fails if the outcomes of all distributions lie in a finite interval, but then it is still possible to arrive at more liberal dominance conclusions between (, ) and (, ).This research was supported by the Office of Naval Research.     

Science as a rational enterprise

Scientists often disagree about whether a new theory is better than the current theory. From this some (e.g., Thomas Kuhn) have inferred that the values of science are changing and subjective, and hence that science is an irrational enterprise. As an alternative, this paper develops a rational model of the scientific enterprise according to which the scope and elegance of theories are important elements in the scientist's utility function. The varied speed of acceptance of new theories by scientists can be explained in terms of the optimal allocation of time among different scientific activities. The model thus accounts for the rationality of science in a way that is broadly consistent with the empirical evidence on the history and practice of science.     

Far-sighted equilibria in 2 × 2, non-cooperative,repeated games

Consider a two-person simultaneous-move game in strategic form. Suppose this game is played over and over at discrete points in time. Suppose, furthermore, that communication is not possible, but nevertheless we observe some regularity in the sequence of outcomes. The aim of this paper is to provide an explanation for the question why such regularity might persist for many (i.e., infinite) periods.Each player, when contemplating a deviation, considers a sequential-move game, roughly speaking of the following form: if I change my strategy this period, then in the next my opponent will take his strategy b and afterwards I can switch to my strategy a, but then I am worse off since at that outcome my opponent has no incentive to change anymore, whatever I do. Theoretically, however, there is no end to such reaction chains. In case that deviating by some player gives him less utility in the long run than before deviation, we say that the original regular sequence of outcomes is far-sighted stable for that player. It is a far-sighted equilibrium if it is far-sighted stable for both players.     

Decision-making under ignorance with implications for social choice

A new investigation is launched into the problem of decision-making in the face of complete ignorance, and linked to the problem of social choice. In the first section the author introduces a set of properties which might characterize a criterion for decision-making under complete ignorance. Two of these properties are novel: independence of non-discriminating states, and weak pessimism. The second section provides a new characterization of the so-called principle of insufficient reason. In the third part, lexicographic maximin and maximax criteria are characterized. Finally, the author's results are linked to the problem of social choice.     

Inductive-nomological explanations and psychological laws

This paper explores some major conceptions of non-deductive explanations, with special reference to the ability of these conceptions to account for some important types of psychological explanations. The central focus is on a kind of tendency generalization and the nature of the explanations that are made possible by generalizations of this sort. It is argued that although these generalizations cannot plausibly be cast in the Hempelian form P(G, F) = r, they are lawlike, and the explanations they ground can have a degree of explanatory power commensurate with exhibiting the phenomenon to be explained as nomically expectable.     

The general relevance of the impossibility teorem in smooth social choice

A complete classification theorem for voting processes on a smooth choice spaceW of dimensionw is presented. Any voting process is classified by two integersv ^* () andw(), in terms of the existence or otherwise of the optima set, IO(), and the cycle set IC().In dimension belowv ^* () the cycle set is always empty, and in dimension abovew() the optima set is nearly always empty while the cycle set is open dense and path con nected. In the latter case agenda manipulation results in any outcome.For admissible (compact, convex) choice spaces, the two sets are related by the general equilibrium result that IO() union IC() is non-empty. This in turn implies existence of optima in low dimensions. The equilibrium theorem is used to examine voting games with an infinite electorate, and the nature ofstructure induced equilibria, induced by jurisdictional restrictions.This material is based on work supported by a Nuffield Foundation grant.     

A systems concept of society: Beyond individualism and holism

Three rival views of the nature of society are sketched: individualism, holism, and systemism. The ontological and methodological components of these doctrines are formulated and analyzed. Individualism is found wanting for making no room for social relations or emergent properties; holism, for refusing to analyze both of them and for losing sight of the individual.A systems view is then sketched, and it is essentially this: A society is a system of interrelated individuals sharing an environment. This commonsensical idea is formalized as follows: A society is representable as an ordered triple Composition of , Environment of , Structure of , where the structure of is the collection of relations (in particular connections) among components of . Included in the structure of any are the relations of work and of managing which are regarded as typical of human society in contrast to animal societies.Other concepts formalized in the paper are those of subsystem (in particular social subsystem), resultant property, and emergent or gestalt property. The notion of subsystem is used to build the notion of an F-sector of a society, defined as the set of all social subsystems performing a certain function F (e.g. the set of all schools). In turn, an F-institution is defined as the family of all F-sectors. Being abstractions, institutions should not be attributed a life and a mind of their own. But, since an institution is analyzable in terms of concrete totalities (namely social subsystems), it does not comply with the individualist requirement either.It is also shown that the systems view is inherent in any mathematical model in social science, since any such schema is essentially a set of individuals endowed with a certain structure. And it is stressed that the systems view combines the desirable features of both individualism and holism.     

Separating marginal utility and probabilistic risk aversion

This paper is motivated by the search for one cardinal utility for decisions under risk, welfare evaluations, and other contexts. This cardinal utility should have meaningprior to risk, with risk depending on cardinal utility, not the other way around. The rank-dependent utility model can reconcile such a view on utility with the position that risk attitude consists of more than marginal utility, by providing a separate risk component: a probabilistic risk attitude towards probability mixtures of lotteries, modeled through a transformation for cumulative probabilities. While this separation of risk attitude into two independent components is the characteristic feature of rank-dependent utility, it had not yet been axiomatized. Doing that is the purpose of this paper. Therefore, in the second part, the paper extends Yaari's axiomatization to nonlinear utility, and provides separate axiomatizations for increasing/decreasing marginal utility and for optimistic/pessimistic probability transformations. This is generalized to interpersonal comparability. It is also shown that two elementary and often-discussed properties — quasi-convexity (aversion) of preferences with respect to probability mixtures, and convexity (pessimism) of the probability transformation — are equivalent.     

Cultural evolution

In this paper I consider the problem of man's evolution - in particular the evolutionary problems raised when we consider man as a cultural animal as well as a biological one. I argue that any adequate cultural evolutionary theory must have the notion of adaptation as a central concept, where this must be construed in a fairly literal (biological) sense, that is as something which aids its possessors (i.e. men) to survive and reproduce. I argue against theories which treat adaptation in a metaphorical sense, particularly those speaking of the adaptation of cultures without reference to men. Iron tools per se are not better adapted than bronze tools - it is the men with iron tools who are better adapted than men with bronze tools. I show that by taking the approach that I do, one can apply at once in a fruitful manner some conclusions of biological evolutionary theory directly to men and their cultures. I conclude with a brief discussion of methodological issues raised by cultural evolutionary theories, particularly those of confirmation and falsification.     

Implications of behavioral consistency in dynamic choice under uncertainty

This paper considers two fundamental aspects of the analysis of dynamic choices under risk: the issue of the dynamic consistency of the strategies of a non EU maximizer, and the issue that an individual whose preferences are nonlinear in probabilities may choose a strategy which is in some appropriate sense dominated by other strategies. A proposed way of dealing with these problems, due to Karni and Safra and called behavioral consistency, is described. The implications of this notion of behavioral consistency are explored, and it is shown that while the Karni and Safra approach obtains dynamically consistent behavior under nonlinear preferences, it may imply the choice of dominated strategies even in very simple decision trees.     

Disparate goods and Rawls' difference principle: A social choice theoretic treatment

Rawls' Difference Principle asserts that a basic economic structure is just if it makes the worst off people as well off as is feasible. How well off someone is is to be measured by an index of primary social goods. It is this index that gives content to the principle, and Rawls gives no adequate directions for constructing it. In this essay a version of the difference principle is proposed that fits much of what Rawls says, but that makes use of no index. Instead of invoking an index of primary social goods, the principle formulated here invokes a partial ordering of prospects for opportunities.     

A strategic foundation for the cooperator's advantage

Orbell and Dawes develop a non-game theoretic heuristic that yields a cooperator's advantage by allowing players to project their own cooperate-defect choices onto potential partners (1991, p. 515). With appropriate parameter values their heuristic yields a cooperative environment, but the cooperation depends, simply, on optimism about others' behavior (1991, p. 526). In earlier work, Dawes (1989) established a statistical foundation for such optimism. In this paper, I adapt some of the concerns of Dawes (1989) and develop a game theoretic model based on a modification of the Harsanyi structure of games with incomplete information (1967–1968). I show that the commonly made conjecture that strategic play is incompatible with cooperation and the cooperator's advantage is false.     

Rational choice and economic behavior

This paper discusses several concepts that can be used to provide a foundation for a unified, theory of rational, economic behavior. First, decision-making is defined to be a process that takes place with reference to both subjective and objective time, that distinguishes between plans and actions, between information and states and that explicitly incorporates the collection and processing of information. This conception of decision making is then related to several important aspects of behavioral economics, the dependence of values on experience, the use of behavioral rules, the occurrence of multiple goals and environmental feedback.Our conclusions are (1) the non-transitivity of observed or revealed preferences is a characteristic of learning and hence is to be expected of rational decision-makers; (2) the learning of values through experience suggests the sensibleness of short time horizons and the making of choices according to flexible utility; (3) certain rules of thumb used to allow for risk are closely related to principles of Safety-First and can also be based directly on the hypothesis that the feeling of risk (the probability of disaster) is identified with extreme departures from recently executed decisions. (4) The maximization of a hierarchy of goals, or of a lexicographical utility function, is closely related to the search for feasibility and the practice of satisficing. (5) When the dim perception of environmental feedback and the effect of learning on values are acknowledged the intertemporal optimality of planned decision trajectories is seen to be a characteristic of subjective not objective time. This explains why decision making is so often best characterized by rolling plans. In short, we find that economic man - like any other - is an existential being whose plans are based on hopes and fears and whose every act involves a leap of faith.This paper is based on a talk presented at the Conference, New Beginnings in Economics, Akron, Ohio, March 15, 1969. Work on this paper was supported by a grant from the National Science Foundation.     

Experiments with cooperative 2 × 2 games

Nash's solution of a two-person cooperative game prescribes a coordinated mixed strategy solution involving Pareto-optimal outcomes of the game. Testing this normative solution experimentally presents problems in as much as rather detailed explanations must be given to the subjects of the meaning of threat strategy, strategy mixture, expected payoff, etc. To the extent that it is desired to test the solution using naive subjects, the problem arises of imparting to them a minimal level of understanding about the issue involved in the game without actually suggesting the solution.Experiments were performed to test the properties of the solution of a cooperative two-person game as these are embodied in three of Nash's four axioms: Symmetry, Pareto-optimality, and Invariance with respect to positive linear transformations. Of these, the last was definitely discorroborated, suggesting that interpersonal comparison of utilities plays an important part in the negotiations.Some evidence was also found for a conjecture generated by previous experiments, namely that an externally imposed threat (penalty for non-cooperation) tends to bring the players closer together than the threats generated by the subjects themselves in the process of negotiation.     

Testing Descriptive Utility Theories: Violations of Stochastic Dominance and Cumulative Independence

Choices between gambles show systematic violations of stochastic dominance. For example, most people choose ($6, .05; $91, .03; $99, .92) over ($6, .02; $8, .03; $99, .95), violating dominance. Choices also violate two cumulative independence conditions: (1) If S = (z, r; x, p; y, q) R = (z, r; x, p; y, q) then S = (x, r; y, p + q) R = (x, r + p; y, q). (2) If S = (x, p; y, q; z, r) R = (x, p; y, q; z, r) then S = (x, p + q; y, r) R = (x, p; y, q + r), where 0 < z < x < x < y < y < y < z.Violations contradict any utility theory satisfying transivity, outcome monotonicity, coalescing, and comonotonic independence. Because rank-and sign-dependent utility theories, including cumulative prospect theory (CPT), satisfy these properties, they cannot explain these results.However, the configural weight model of Birnbaum and McIntosh (1996) predicted the observed violations of stochastic dominance, cumulative independence, and branch independence. This model assumes the utility of a gamble is a weighted average of outcomes\' utilities, where each configural weight is a function of the rank order of the outcome\'s value among distinct values and that outcome\'s probability. The configural weight, TAX model with the same number of parameters as CPT fit the data of most individuals better than the model of CPT.     

Five legitimate definitions of correlated equilibrium in games with incomplete information

Aumann's (1987) theorem shows that correlated equilibrium is an expression of Bayesian rationality. We extend this result to games with incomplete information.First, we rely on Harsanyi's (1967) model and represent the underlying multiperson decision problem as a fixed game with imperfect information. We survey four definitions of correlated equilibrium which have appeared in the literature. We show that these definitions are not equivalent to each other. We prove that one of them fits Aumann's framework; the agents normal form correlated equilibrium is an expression of Bayesian rationality in games with incomplete information.We also follow a universal Bayesian approach based on Mertens and Zamir's (1985) construction of the universal beliefs space. Hierarchies of beliefs over independent variables (states of nature) and dependent variables (actions) are then constructed simultaneously. We establish that the universal set of Bayesian solutions satisfies another extension of Aumann's theorem.We get the following corollary: once the types of the players are not fixed by the model, the various definitions of correlated equilibrium previously considered are equivalent.     

Fairness,Public Good,and Emotional Aspects of Punishment Behavior

We report an experiment on two treatments of an ultimatum minigame. In one treatment, responders reactions are hidden to proposers. We observe high rejection rates reflecting responders intrinsic resistance to unfairness. In the second treatment, proposers are informed, allowing for dynamic effects over eight rounds of play. The higher rejection rates can be attributed to responders provision of a public good: Punishment creates a group reputation for being tough and effectively educate proposers. Since rejection rates with informed proposers drop to the level of the treatment with non-informed proposers, the hypothesis of responders enjoyment of overt punishment is not supported.     

Singular causal explanations

Singular causal explanations cite explicitly, or may be paraphrased to cite explicitly, a particular factor as the cause of another particular factor. During recent years there has emerged a consensus account of the nature of an important feature of such explanations, the distinction between a factor regarded correctly in a given context of inquiry as the cause of a given result and those other causally relevant factors, sometimes called mere conditions, which are not regarded correctly in that context of inquiry as the cause of that result. In this paper that consensus account is characterized and developed. The developed version is then used to illuminate some recent discussions of singular causal explanations.Work on this paper was supported by a University of Maryland Faculty Research Award. Earlier versions were read at the University of Minnesota and at the 1971 Western Division meetings of the American Philosophical Association. I have profited from criticisms raised on these occasions. I am especially grateful for the comments of James Lesher, Peter Machamer, John Vollrath, and the students in my Macalester College seminar.     

Utility theory and the Bayesian paradigm

In this paper, a problem for utility theory - that it would have an agent who was compelled to play Russian Roulette with one revolver or another, to pay as much to have a six-shooter with four bullets relieved of one bullet before playing with it, as he would be willing to pay to have a six-shooter with two bullets emptied - is reviewed. A less demanding Bayesian theory is described, that would have an agent maximize expected values of possible total consequence of his actions. And utility theory is located within that theory as valid for agents who satisfy certain formal conditions, that is, for agents who are, in terms of that more general theory, indifferent to certain dimensions of risk. Raiffa- and Savage-style arguments for its more general validity are then resisted. Addenda are concerned with implications for game theory, and relations between utilities and values.     

Constructs and empirical basis in theories of economic behavior

Theories of economic behavior often use as-if-languages: for example, analytical sentences or definitions are used as if they were synthetic and factual-normative theoretical constructs are used as if they were empirical concepts. Such as-if-languages impede the acquisition of knowledge and are apt to encourage the wrong assessment of actual research strategies. The author's criticism is first leveled at revealed-preference theory. In this theory observed behavior is often understood in an empirical sense although it is a pure theoretical construct. Another example can be found in von Mises' representations on marketing behavior: here theoretical valuations are used to achieve a spurious streamlining of reality. Result: Scientists should not ogle with reality if they have nothing to say about it.