## Rational Consensus in Science and Society: A Philosophical and Mathematical StudyTItis book is the joint project of a philosopher, Lehrer, and a mathematician, Wagner. The book is, therefore, divided into a first part written by Lehrer, which is primarily philosophical, and a second part written by Wagner that is primarily formal. The authors were, however, influenced by each other throughout. Our book articulates a theory of rational consensus in science and society. The theory is applied to politics, ethics, science, and language. We begin our exposition with an elementary mathematical model of consensus developed by Lehrer in a series of articles [1976a, 1976b, 1977, 1978]. Chapter 3 contains material from [1978]. Lehrer formulated the elementary model when he was a Fellow of the Center for Advanced Study in the Be havioral Sciences, Stanford, in 1973 with the invaluable mathematical assist of Kit Fine, Gerald Kramer and Lionel McKenzie. In the summer of ance 1977, Lehrer and Wagner met at the Center in a Summer Seminar on Freedom and Causality supported by the Andrew W. Mellon Foundation. Wagner read the manuscript of Lehrer [1978] and subsequently solved some mathematical problems of the elementary model. After discussions of philosophical prob lems associated with that model, Wagner developed the foundations for the extended model. These results were reported in Wagner [1978, 1981a]. |

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### Contents

CONSENSUS AND PHILOSOPHICAL ISSUES | 3 |

THE ELEMENTARY METHOD AND CONSENSUAL PROBABILITY | 19 |

THE ELEMENTARY METHOD AND SOCIAL CHOICE | 38 |

THE EXTENDED MODEL | 53 |

APPLICATIONS OF THE CONSENSUS MODEL | 73 |

THE FORMAL FOUNDATIONS OF RATIONAL CONSENSUS | 105 |

ALLOCATION AND ORDERING BY WEIGHTED ARITHMETIC AVERAGING AN AXIOMATIC APPROACH | 107 |

CONVERGENCE TO CONSENSUS THE ELEMENTARY MODEL | 125 |

CONVERGENCE TO CONSENSUS THE EXTENDED MODEL | 142 |

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Rational Consensus in Science and Society: A Philosophical and Mathematical ... Keith Lehrer,C. Wagner No preview available - 1981 |

### Common terms and phrases

affine transformation aggregation alternatives amalgamation application articulate assign a weight assigns positive weight assumption chain of respect chapter column communication of respect condition consensual assignment consensual opinion consensual ordering consensual probability assignment consensual utility consensual weights consensus matrix consider converges to consensus decision problem discount elementary model epistemology ethics evaluation example expected extended model fixed point weight function hypothesis idiolects iterated judges of physicists justice Markov chains mathematical method Moreover noted obtain person assigns philosophical point weight vector positive respect preferences probability or utility question rational consensus rationally committed reasonable result scientific scores semantic probability set of consensual set of weights simple social choice social welfare function solar astronomers summary Suppose Theorem 6.4 theory tion total information unique fixed point utility assignments values assigned weight assigned weight matrix weight of zero weighted arithmetic averaging weighted arithmetic mean weighted average weighted geometric means yield