## Utility theory for decision makingDeveloped as part of RAC's Advanced Research Department work program in decision and value theory. Presents a concise yet mathematically complete treatment of modern utility theories that covers nonprobabilistic preference theory, the von Neumann-Morgenstern expected-utility theory and its extensions, and the joint axiomatization of utility and subjective probability. |

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### Contents

Introduction and Preview lNvlI | 1 |

Preference Orders and Utility Functions for Countable Sets | 9 |

Utility Theory for Uncountable Sets | 26 |

Copyright | |

14 other sections not shown

### Common terms and phrases

aé Q alternatives Archimedean assume axioms binary relation Boolean algebra bounded Chapter consequences continuous contradiction convex convex combinations convex cone countably additive Debreu deﬁned Deﬁnition denumerable elements equivalence expected utility extraneous probabilities f E F factors ﬁnite ﬁrst following theorem function f g given gamble Hence holds horse lotteries hypotheses of Theorem imply indifference indifference curve inﬁnite interval order irreﬂexive Lemma n-tuples negatively transitive nonempty null obtains open set order dense ordered group ot)Q ot)R partition persistent positive integer positive linear transformation proof of Theorem Prove rational numbers real numbers reﬂexive satisﬁes satisfy Savage’s Section sequence similar positive linear simple probability measures speciﬁed strict order strict partial order sufﬁcient Suppose symmetric Theorem 4.1 topological space topology unique utility function utility theory verify weak order X1 X X2