Bayesian decision theory,rule utilitarianism,and Arrow's impossibility theorem

The first part of this paper reexamines the logical foundations of Bayesian decision theory and argues that the Bayesian criterion of expected-utility maximization is the only decision criterion consistent with rationality. On the other hand, the Bayesian criterion, together with the Pareto optimality requirement, inescapably entails a utilitarian theory of morality. The next sections discuss the role both of cardinal utility and of cardinal interpersonal comparisons of utility in ethics. It is shown that the utilitarian welfare function satisfies all of Arrow's social choice postulates avoiding the celebrated impossibility theorem by making use of information which is unavailable in Arrow's original framework. Finally, rule utilitarianism is contrasted with act utilitarianism and judged to be preferable for the purposes of ethical theory.     

Risk-adjusted martingales and the design of “indifference” gambles

In the probability literature, a martingale is often referred to as a “fair game.” A martingale investment is a stochastic sequence of wealth levels, whose expected value at any future stage is equal to the investor’s current wealth. In decision theory, a risk neutral investor would therefore be indifferent between holding on to a martingale investment, and receiving its payoff at any future stage, or giving it up and maintaining his current wealth. But a risk-averse decision maker would not be indifferent between a martingale investment and his current wealth level, since he values uncertain deals less than their mean. A risk seeking decision maker, on the other hand, would readily accept a martingale investment in exchange for his current wealth, and would repeat this investment any number of times. These ideas lead us to introduce the notion of a “risk-adjusted martingale”; a stochastic sequence of wealth levels that a rational decision maker with any attitude toward risk would value constantly with time, and would be indifferent between receiving its pay-off at any future stage, or giving it up and maintaining his current wealth level. We show how to construct such risk-adjusted investments for any decision maker with a continuous monotonic utility function. The fundamental result we derive is that a pay-off structure of an investment (i) is a risk-adjusted martingale and (ii) can be represented by a lattice if and only if the pay-off functions are invariant transformations of the given utility function.     

The chain store paradox

The chain store game is a simple game in extensive form which produces an inconsistency between game theoretical reasoning and plausible human behavior. Well-informed players must be expected to disobey game theoretical recommendations.The chain store paradox throws new light on the well-known difficulties arising in connection with finite repetitions of the prisoners dilemma game. Whereas these difficulties can be resolved by the assumption of secondary utilities arising in the course of playing the game, a similar approach to the chain store paradox is less satisfactory.It is argued that the explanation of the paradox requires a limited rationality view of human decision behavior. For this purpose a three-level theory of decision making is developed, where decisions can be made on different levels of rationality. This theory explains why insight into the rational solution of a decision problem does not necessarily mean that the corresponding course of action will be taken.     

G.H. Mead: Theorist of the Social Act

ABSTRACT: There have been many readings of Mead's work, and this paper proposes yet another: Mead, theorist of the social act. It is argued that Mead's core theory of the social act has been neglected, and that without this theory, the concept of taking the attitude of the other is inexplicable and the contemporary relevance of the concept of the significant symbol is obfuscated. The paper traces the development of the social act out of Dewey's theory of the act. According to Mead, Dewey's theory does not sufficiently account for consciousness. Grappling with this problematic leads Mead to several key ideas, which culminate in his theory of the social act. The social act and taking the attitude of the other are then illustrated by the analysis of a game of football. The interpretation presented has two novel aspects: first, symbolisation arises not simply through self taking the attitude of the other, but through the pairing of this attitude with the complementary attitude in self; second, self is able to take the attitude of the other to the extent that self has in actuality or in imagination previously been in the social position of the other. From this standpoint the key issue is how the attitude of self and other become integrated. New directions for empirical research, aimed at advancing this question are outlined. Finally, the paper shows how the social act can contribute to our contemporary concerns about the nature of the symbolic.     

Even Risk-Averters may Love Risk

A decision maker bets on the outcomes of a sequence of coin-tossings. At the beginning of the game the decision maker can choose one of two coins to play the game. This initial choice is irreversible. The coins can be biased and the player is uncertain about the nature of one (or possibly both) coin(s). If the player is an expected-utility maximizer, her choice of the coin will depend on different elements: the nature of the game (namely, whether she can observe the outcomes of the previous tosses before making her next decision), her utility function, the prior distribution on the bias of the coin. We will show that even a risk averter might optimally choose a riskier coin when learning is allowed. We will express most of our results in the language of stochastic orderings, allowing comparisons that are valid for large classes of utility functions.     

On the existence of stable states in game problems

Each individual or group of individuals unified by some common interests often have to either accept an offer or reject it. The choice is made on the basis of not only individual or group preferences but on the basis of the reaction to this choice by other people whose preferences are dependent to some extent on this choice. The following question is to be answered: under what conditions is an offer stable, i.e. will it be accepted by each participant in a group with non-coincident interests? To answer this question is to specify in the set of all feasible offers (options or situations) those ones which would be rejected by no participant. According to this intuitive understanding of stable offers a sequence of weak and strong equilibria referred to as active equilibria was defined. A weak equilibrium satisfies the following conditions: (1) It defines stable situations which cannot be changed by a participant because of certain retaliatory actions by the other participants, which would worsen his initial situation. (2) It always exists. (3) Under comparatively wide conditions it has a non-empty intersection with the Pareto set. (4) It includes non-cooperative equilibria well known in the game theory and does not lead to any paradoxes (as, for example, the Nash equilibrium does). These conditions, and especially the third and fourth ones, indicate that the active equilibria can be successfully used in the game theory as well. Strong equilibria define a more stable situation but they do not necessarily meet all four conditions listed above.     

Justice,liberty, unanimity and the axioms of identity

Two new justice constraints on liberal rights and the Pareto rule are proposed and analysed. Each resolves both Sen and Gibbard paradoxes. The first, following Hammond, requires no axiom of identity. The second, following Sen and Suppes, resolves Sen Paradoxes for two rights, but requires the axiom of complete identity to resolve Gibbard paradoxes and Sen Paradoxes with three or more rights. This second constraint therefore turns social conflicts over rights into disagreements about interpersonal and intersituational comparisons. By itself it solves the majoritarian paradox and the all-but-one-person-is-decisive paradox.     

We-thinking and vacillation between frames: filling a gap in Bacharach’s theory

We-thinking theories allow groups to deliberate as agents. They have been introduced into the economic domain for both theoretical and empirical reasons. Among the few scholars who have proposed formal approaches to illustrate how we-thinking arises, Bacharach offers one of the most developed theories from the game theoretic point of view. He presents a number of intuitions, not always mutually consistent and not fully developed. In this article, I propose a way to complete Bacharach??s theory, generalizing the interdependence hypothesis and building on his intuition about vacillation. It is a simple model of vacillation between the I and we-modes of reasoning, as a way in which we-thinking can come to mind in the face of a decision problem. The vacillation model makes we-reasoning more easily usable in game theory.     

Instrumental rationality and cognitive rationality

Beside instrumental rationality, concerned with consistency between available means and pursued objectives, cognitive rationality, concerned with consistency between current beliefs and detained information, is nowadays bursting in economic theory. For an individual decision, the two notions are expressed structurally in similar forms, but they heavily interact in the deliberation process, especially when the agent is searching relevant information on his environment and his own determiners. In a game framework, the players' representations are formalized in a more and more sophisticated way, and are closely interwoven with their preferences in contemporary equilibrium notions as well as in selection between corresponding equilibrium points.     

滕尼斯与齐美尔:社会伦理同文化伦理的分流

作为德国社会学的两位奠基人,滕尼斯和齐美尔奠定了截然相反的两种现代伦理生活格局。伦理世界观的分流源于他们各自对时代处境的体验以及对思想史的独特解释。从近代自然法的角度出发,滕尼斯的社会伦理的核心是重建政治社会的秩序与风尚,一切价值最终都要融入社会;与此相反,齐美尔的社会学思考从一开始就以对社会伦理的批评作为前提,他将超越社会的个体生命视作伦理的目的,对他来说,生命不仅意味着身处社会之中的个体具有饱满个性,而且从自身孕育出客观的、适用于他自己的伦理责任。从帝制时期到魏玛时期,德国社会伦理同文化伦理的分流、交织与合流为我们提供了一条理解德国社会学史的清晰主线。     

Choice under risk and the security factor: An axiomatic model

The particular attention paid by decision makers to the security level ensured by each decision under risk, which is responsible for the certainty effect, can be taken into account by weakening the independence and continuity axioms of expected utility theory. In the resulting model, preferences depend on: (i) the security level, (ii) the expected utility, offered by each decision. Choices are partially determined by security level comparison and completed by the maximization of a function, which express the existing tradeoffs between expected utility and security level, and is, at a given security level, an affine function of the expected utility. In the model, risk neutrality at a given security level implies risk aversion.     

Justice,utility, and interpersonal comparisons

One of the most common objections against utilitarianism is that it cannot account for the claims of distributive justice. This objection can be answered by appeal to the principle of Diminishing Marginal Utility (DMU), which says that the value of a given portion of a commodity tends to increase as a person's supply of the commodity decreases. DMU implies that, other things equal, the way to maximize the value of a commodity is to distribute it equally. Some economists have objected to DMU on the ground that it presupposes interpersonal comparisons of utility, but the arguments which they have advanced against the objectivity of such comparisons are unsound. Moreover, the interpersonal comparisons presupposed by DMU are ordinal, rather than cardinal, and there are reasons for believing that ordinal comparisons, at least, do have an objective basis.     

Nontransitive preferences in decision theory

Intransitive preferences have been a topic of curiosity, study, and debate over the past 40 years. Many economists and decision theorists insist on transitivity as the cornerstone of rational choice, and even in behavioral decision theory intransitivities are often attributed to faulty experiments, random or sloppy choices, poor judgment, or unexamined biases. But others see intransitive preferences as potential truths of reasoned comparisons and propose representations of preferences that accommodate intransitivities. This article offers a partial survey of models for intransitive preferences in a variety of decisional contexts. These include economic consumer theory, multiattribute utility theory, game theory, preference between time streams, and decision making under risk and uncertainty. The survey is preceded by a discussion of issues that bear on the relevance and reasonableness of intransitivity.     

Nonlinear social welfare functions

It is argued that Bayesian decision theory is a solution of an important philosophical problem, viz. the problem of how to define rational behavior under risk and uncertainty. The author has shown in earlier papers that if we take the Bayesian rationality postulates seriously, and take an individualistic point of view about social welfare, then our social welfare function must be a linear function of individual utilities: indeed, it must be their arithmetic mean. The present paper criticizes Diamond's and Sen's contention that one of the Bayesian postulates (viz. the sure-thing principle) does not apply to social decisions, even though it may apply to individual decisions. It also criticizes Sen's proposal of making social welfare a nonlinear function of individual utilities. The social welfare function proposed by the author depends on interpersonal utility comparisons. The use of such comparisons is defended. It is also argued that anybody who feels that the utilitarian (i.e., linear) form of the social welfare function is not egalitarian enough, should reject the author's individualism axiom, instead of trying to reject the Bayesian rationality axioms. However, this would be equivalent to giving egalitarian considerations a priority in many cases over humanitarian considerations. Finally, the paper discusses the reasons why even full agreement on the mathematical form of the social welfare function would not give rise to a Utopian state of moral consensus: moral controversies arising from disagreements about what predictions to make about future empirical facts would still remain.     

Minimum cost spanning tree games and spillover stability

This article discusses interactive minimum cost spanning tree problems and argues that the standard approach of using a transferable utility game to come up with a fair allocation of the total costs has some flaws. A new model of spillover games is presented, in which each player??s decision whether or not to cooperate is properly taken into account.     

Interpersonal comparisons of utility for 2 of 3 types of people

This article argues that there is a natural solution to carry out interpersonal comparisons of utility when the theory of gambles is supplemented with a group operation of joint receipts. If so, three types of people can exist, and the two types having multiplicative representations of joint receipt have, in contrast to most utility theories, absolute scales of utility. This makes possible, at least in principle, meaningful interpersonal comparisons of utility with desirable properties, thus resolving a long standing philosophical problem and having potentially important implications in economics. Two behavioral criteria are given for the three classes of people. At this point the relative class sizes are unknown.     

Alcoholism and Drug Dependence: Planning a New Service

An outline is given of some of the background ideas and experiences that a new mental health administrator brings to his task of planning innovative services for alcoholic and drug-dependent persons. Familial and interpersonal factors are overviewed, and an account is given of the concepts and principles being adopted in the planning of a treatment service in the Australian Capital Territory.     

A differential approach to the repeated prisoner's dilemma

The repeated prisoner's dilemma game is converted into a differential game by assuming that the players, instead of making decisions individually for each repetition of the prisoner's dilemma game, make decisions on the ratio of cooperative and noncooperative games that they wish to play over the next few moves, and that the actual plays are then determined using this ratio and a randomizing procedure. Although it sounds like a significant departure, this assumption is probably not too different from reality.Since each player can always obtain by his own action at least the payoff which he would receive from the noncooperative-noncooperative pair of strategies, that part of the differential game which is dominated by such a dual noncooperative strategy for either player is an unlikely outcome. This dominated area can be readily computed for any game, including those with more than two players.Formal testing with empirical data was impossible because of uncertainty about the proper null hypothesis. Nevertheless, experimental results reported by Rapoport are consistent with the theory.The authors are, respectively, Graduate Research Asistant in Economics and Professor of Economics and Public Choice at Virginia Polytechnic Institute and State University.     

A note on the prisoner's dilemma

This paper clarifies some basic concepts or assumptions of the prisoner's dilemma, asserts the independence between the two agentsA andB, and advocates the application of the dominance principle of decision theory to the prisoner's dilemma. It discusses several versions of the prisoner's dilemma, including the one-shot and repeated cases of a noncooperative game from a purely egoistic point of view. The main part of this paper, however, is a study of the problem from a moral point of view through a special decision-theoretic approach. Morality is taken into account by incorporating the utility of the feeling of moral satisfaction for the agent, as a part of the total utility for the agent, into the decision-theoretic model. In this way the problem will appear as a purely technical decision problem, and the conflicts between various assumptions, or the dilemma caused by the problem, will no longer exist. It is also pointed out that in a more general case, for some values of the coefficient of moralityk, dominance will not exist so that the dominance principle will not be applicable.     

环境伦理学研究中的几种伦理境界及其意义

环境伦理学的产生和发展来自对西方传统伦理学的批判和超越。从对传统的强人类中心主义的伦理学的批判到弱人类中心主义的伦理学,西方传统伦理学不得不将自然资源和环境纳入到伦理学的研究视域中,体现了人们对生态环境的伦理应对,这无疑是人的伦理境界的进步。而从动物解放/权利论到生物平等主义、再到生态整体主义,伦理的对象已逐步从人及其社会扩展到了动物界、生物界以及整个生态系统;尽管这使人在自然中的地位越来越低,但人的伦理境界也在被不断提升,充分展示了人的伦理潜力和对人与自然和谐关系的伦理追求,体现了人对自身的超越,也为生态环境问题的最终解决提供了伦理支持。