Foundations of Multiattribute Utility

Ali E. Abbas is Professor of Industrial and Systems Engineering and Professor of Public Policy and Governance at the University of Southern California. He directs the Center for Decisions and Ethics (DECIDE) and previously directed the Center for Risk and Economic Analysis of Terrorism Events (CREATE). His research covers all aspects of decision making under uncertainty broadly defined. He has written two books and edited two others, and has more than 100 refereed publications in the field of decision analysis. He is editor of numerous professional journals and has extensive media coverage on all aspects of decision making and risk.

'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.

• 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.