The Foundations of Expected Utility

1. Front Matter

   Pages i-xii

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2. Introduction

   1. Introduction

      • Peter C. Fishburn

      Pages 1-8

3. Expected Utility

   1. Front Matter

      Pages 9-9

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   2. Linear Utility on Mixture Sets

      • Peter C. Fishburn

      Pages 11-21

   3. Expected Utility for Probability Measures

      • Peter C. Fishburn

      Pages 23-34

   4. Lexicographic Quasilinear Utility

      • Peter C. Fishburn

      Pages 35-55

   5. Linear Utility for Partially Ordered Preferences

      • Peter C. Fishburn

      Pages 57-71

   6. Linear Utilities on Product Sets

      • Peter C. Fishburn

      Pages 73-84

   7. Multilinear Utility on Products of Mixture Sets

      • Peter C. Fishburn

      Pages 85-98

   8. Multilinear Utility for Probability Measures

      • Peter C. Fishburn

      Pages 99-103

4. Subjective Expected Utility

   1. Front Matter

      Pages 105-105

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   2. Subjective Linear Utility on Products of Mixture Sets

      • Peter C. Fishburn

      Pages 107-120

   3. Subjective Expected Utility for Arbitrary State Sets

      • Peter C. Fishburn

      Pages 121-134

   4. Subjective Linear Utility for Partially Ordered Preferences

      • Peter C. Fishburn

      Pages 135-147

   5. Subjective Linear Utility with Conditional Preference Comparisons

      • Peter C. Fishburn

      Pages 149-168

5. Back Matter

   Pages 169-178

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This book offers a unified treatment of my research in the foundations of expected utility theory from around 1965 to 1980. While parts are new, the presentation draws heavily on published articles and a few chapters in my 1970 monograph on utility theory. The diverse notations and styles of the sources have of course been reconciled here, and their topics arranged in a logical sequence. The two parts of the book take their respective cues from the von Neumann-Morgenstern axiomatization of preferences between risky options and from Savage's foundational treatment of decision making under uncertainty. Both parts are studies in the axiomatics of preferences for decision situations and in numerical representations for preferences. Proofs of the representation and uniqueness theorems appear at the ends of the chapters so as not to impede the flow of the discussion. A few warnings on notation are in order. The numbers for theorems cited within a chapter have no prefix if they appear in that chapter, but otherwise carry a chapter prefix (Theorem 3.2 is Theorem 2 in Chapter 3). All lower case Greek letters refer to numbers in the closed interval from o to 1. The same symbol in different chapters has essentially the same meaning with one major exception: x, y, ... mean quite different things in different chapters. I am indebted to many people for their help and encouragement.

• Flow
• research
• state
• treatment

`...this is the third masterpiece written by the author, ...as such, it is very highly recommended.' Mathematical Reviews

• Bell Telephone Laboratories, Inc., Murray Hill, USA

  Peter C. Fishburn

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