## Game Theory, Social Choice and EthicsThere are problems to whose solution I would attach an infinitely greater import ancf! than to those of mathematics, for example touching ethics, or our relation to God, or conceming our destiny and our future; but their solution lies wholly beyond us and completely outside the province 0 f science. J. F. C. Gauss For a1l his prescience in matters physical and mathematieal, the great Gauss apparently did not foresee one development peculiar to OUT own time. The development I have in mind is the use of mathematical reasoning - in partieu lar the axiomatic method - to explicate alternative concepts of rationality and morality. The present bipartite collection of essays (Vol. 11, Nos. 2 and 3 of this journal) is entitled 'Game Theory, Social Choiee, and Ethics'. The eight papers represent state-of-the-art research in formal moral theory. Their intended aim is to demonstrate how the methods of game theory, decision theory, and axiomatic social choice theory can help to illuminate ethical questions central not only to moral theory, but also to normative public policy analysis. Before discussion of the contents of the papers, it should prove helpful to recall a number of pioneering papers that appeared during the decade of the 1950s. These papers contained aseries of mathematical and conceptual break through which laid the basis for much of today's research in formal moral theory. The papers deal with two somewhat distinct topics: the concept of individual and collective rationality, and the concept of social justiee. |

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### Contents

THOMAS SCHWARTZ Welfare Judgments and Future Generations | 181 |

STEVENSTRASNICK Moral Structures and Axiomatic Theory | 195 |

DONALD WITTMANA Diagrammatic Exposition of Justice | 207 |

HORACE W BROCK A Game Theoretic Account of Social Justice | 239 |

HARSANYI Bayesian Decision Theory Rule Utilitarianism | 304 |

ERIC MASKIN Decisionmaking Under Ignorance with Implications | 319 |

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adopted allocation alternative argued Arrow assumption axiomatic axioms bargaining baseline basic economic structure Braithwaite cacophony cardinal utility functions choose comparisons of utility concept constraints cooperative game criteria criterion f decision problem decision-making defined difference principle discussion distributive justice equal ethical theory example expected utility fair division feasible game theory Harsanyi impartiality income index of primary indifference curve interpersonal comparisons interpersonal utility comparisons lexicographic maximin lotteries Lucas Luke playing Matthew and Luke maximin criterion maximin strategy maximize measure n-person n-tuple Nash solution norms outcome Pareto frontier pareto optimal Pareto principle partial empathy payoff person players position possible rational choice Rawls relative needs rule utilitarian satisfies properties Shapley Value silence situation social choice theory social contract social preference social welfare function society status quo sum of utilities Suppose Theorem Theory and Decision Theory of Justice utilitarian theory utilities criterion veil of ignorance worst-off