Many of the complex problems faced by decision makers involve uncertainty as well as multiple conflicting objectives. This book provides a complete understanding of the types of objective functions that should be used in multiattribute decision making. By using tools such as preference, value, and utility functions, readers will learn state-of-the-art methods to analyze prospects to guide decision making and will develop a process that guarantees a defensible analysis to rationalize choices. Summarizing and distilling classical techniques and providing extensive coverage of recent advances in the field, the author offers practical guidance on how to make good decisions in the face of uncertainty. This text will appeal to graduate students and practitioners alike in systems engineering, operations research, business, management, government, climate change, energy, and healthcare. 'Ali E. Abbas' new book on utility theory is a comprehensive treatment ranging from simple distinctions about facing uncertainty to general multiattribute utility theory. Beginning with a general approach to MAU, it then specializes to show how popular versions, such as additive utility, are actually very restrictive and other simple approaches, such as additive value functions with risk aversion, are much more general. He derives the complete forms of multiattribute utility functions having additive value functions. With utility transversality, he also demonstrates that there is only one dimension of risk attitude, as the value function translates risk attitude across dimensions. Abbas's book promises to be the standard reference work for decades to come.' Jim Matheson, Chairman and CFO, SmartOrg, Inc. 'Foundations of Multiattribute Utility
provides a much-needed update, a comprehensive structure, and indeed a vision for a field that has blossomed in the forty years since Keeney and Raiffa's Decisions with Multiple Objectives. The book synthesizes recent results by others and by the author, including an elegant copula representation. Thanks to the book's accessible style - which even includes Socratic dialogues - readers will appreciate its place within the rich mathematics of preference and economic utility theory and the rich practice of decision analysis. The book offers many rewards for modelers in these fields, while for researchers it is required reading.' Jeffrey M. Keisler, University of Massachusetts, Boston 'The definitive work on preference, value, and utility that can serve the full range of decision situations. If you need to
Foundations of Multiattribute Utility
Part I. Foundations of Preference, Value, and Utility: 1. Preference, value, and utility; 2. Foundations of expected utility; 3. Some flawed methods of decision making; Part II. Deterministic Decisions: 4. The order rule: preferences for deterministic consequences; 5. Getting the attributes right; 6. Preference functions for single attributes; 7. Preference functions for multiple attributes; 8. Additive preference functions; 9. Valuing deterministic consequences - value functions; Part III. Decisions with Uncertainty: Multi-attribute Utility Functions Using a Value Measure: 10. Single-attribute utility function; 11. Multi-attribute utility functions using preference and value functions; 12. Utility functions over additive preference or value functions; Part IV. Decisions with Uncertainty: Properties of Single-Attribute Utility Functions: 13. The role of the utility function in valuing uncertain deals; 14. The risk aversion function; 15. Scale transformations applied to lottery outcomes; 16. The invariant transformation of a utility function; 17. Valuing changes in investment opportunities; 18. One-switch utility functions; 19. Utility transversality; 20. Multi-attribute risk aversion; Part V. Decisions with Uncertainty: Multi-attribute Utility Functions without Preference or Value Functions: 21. Attribute dominance utility; 22. The two-attribute utility tree; 23. Independence conditions for two attributes; 24. The multi-attribute utility tree; 25. Independence conditions for three or more attributes; 26. Higher-order independence conditions; 27. One-switch utility independence; Part VI. Utility Copula Formulations: 28. Multi-attribute utility copulas; 29. Archimedean utility copulas; 30. Assessing Archimedean utility copulas; 31. Utility copula functions matching all boundary assessments; 32. Bidirectional one-switch ordinal copulas; 33. Reflections of what we have learned.