Foundations of Multiattribute Utility
By: By Ali E. Abbas.
Edition: First Edition
Publisher: Cambridge University Press
Published: May 31, 2018
Place of publication: Cambridge, Massachusetts
Language: eng
Format: Paperback
Number of pages: 698
ISBN-13: 9781316596739; 9781108548687; 9781108547581; 9781107150904
Copyright date: 2018
Subjects: Decision making
Description: 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.
Table of contents: title: Machine generated contents note: 1.Preference, Value, and Utility; title: 1.1.Characterizing Prospects of a Decision; title: 1.2.Preference for a Deterministic Prospect; title: 1.3.Value of a Deterministic Prospect; title: 1.4.Utility of a Deterministic Prospect; title: 1.5.Using Value Statements to Help with the Utility of a Deterministic Prospect; title: 1.6.Summary; title: 2.Foundations of Expected Utility; title: 2.1.The Five Rules of Actional Thought: The Decision Calculator; title: 2.2.Using the Five Rules with Multiattribute Prospects: The Same Rules Apply; title: 2.3.Dealing with Uncertainty: Probability Assignment; title: 2.4.Dealing with Both Uncertainty and Trade-Offs; title: 2.5.Summary; title: 3.Some Flawed Methods of Decision-Making; title: 3.1.Introduction: Approximate vs. Fundamentally Flawed Methods of Decision-Making; title: 3.2.Using Pairwise Comparisons of Prospects and the Method of Elimination; title: 3.3.Majority Votes over the Individual Attributes; title: 3.4.The Min-Max Regret Criterion; title: 3.5.Summary Note continued: 4.The Order Rule: Preference for Deterministic Prospects; title: 4.1.Introduction; title: 4.2.Ordering Prospects by Visualization; title: 4.3.Summary; title: 5.Getting the Attributes Right; title: 5.1.Introduction; title: 5.2.Direct vs. Indirect Values; title: 5.3.Do Not Mix the Direct and Indirect Values in a Deterministic Objective Function; title: 5.4.Using Meaningful and Measurable Attributes; title: 5.5.Using Structural Models to Order Prospects (and to Characterize Direct Value Attributes); title: 5.6.Converting Meaningful and Measurable Attributes into Dollar Equivalents; title: 5.7.Summary; title: 6.Preferences for Prospects with a Single Direct Value Attribute; title: 6.1.Introduction; title: 6.2.Prospects Characterized by a Single Numeric Measure; title: 6.3.Preference Functions Obtained by Thinking Qualitatively about Your Preferences; title: 6.4.The Vertical Scale of the Preference Function; title: 6.5.Effects of a Preference Function Applied to a Direct Value Attribute on Its Components in the Structural Model Note continued: 6.6.Interpreting Preference Functions by Thinking about Changes in Preferences; title: 6.7.A Note on the Types of Preference Functions That We Have Presented; title: 6.8.Summary; title: 7.Preferences for Prospects with Multiple Direct Value Attributes; title: 7.1.Introduction; title: 7.2.Basic Notation and Definitions; title: 7.3.Isopreference Contours: The Added Complexity with Multiple Attributes; title: 7.4.Constructing Preference Functions for Multiple Attributes; title: 7.5.Assessment of Trade-Offs Using a Functional Form for the Isopreference Contours; title: 7.6.Constructing Preference Functions by Capturing Important Features of the Problem; title: 7.7.Constructing Preference Functions by Thinking about Changes in Preferences; title: 7.8.Summary; title: 8.Additive Preference Functions; title: 8.1.Introduction; title: 8.2.The Additive Preference Function; title: 8.3.Verifying the Additive Form by Preference Switches: Preferential Independence Note continued: 8.4.Alternate Representation: Archimedean Combinations of Individual Functions; title: 8.5.Elasticity of Substitution; title: 8.6.Summary; title: 9.Valuing Deterministic Prospects; title: 9.1.Introduction: The Benefits of a Value Measure; title: 9.2.Value Functions from Structural Models of Physics, Engineering, or Accounting Principles; title: 9.3.Value Functions Obtained by Applying a Monotone Transformation to the Preference Function; title: 9.4.Monotone Transformations of the Archimedean Preference Function: Archimedean Value Function; title: 9.5.Incorporating Time Preference into the Valuation of Prospects; title: 9.6.No Regrets; title: 9.7.Summary; title: 10.Single-Attribute Utility Functions; title: 10.1.Introduction; title: 10.2.Assessing Utility Functions over Value Measures; title: 10.3.Determining the Functional Form of a Utility Function; title: 10.4.Utility over Value versus Utility over an Attribute; title: 10.5.Incorporating Time Preference; title: 10.6.Summary Note continued: 11.Multiattribute Utility Functions Using Preference or Value Functions; title: 11.1.Introduction: The Good News; title: 11.2.Constructing Multiattribute Utility Functions Using Preference Functions; title: 11.3.Constructing Multiattribute Utility Functions Using Value Functions; title: 11.4.Historical Document from Early Phases of Decision Analysis; title: 11.5.Change of Variables in Utility Assignment; title: 11.6.Important Remark; title: 11.7.Summary; title: 12.Utility Functions over Additive Preference or Value Functions; title: 12.1.Introduction: What Is So Special about This Formulation?; title: 12.2.Exponential Utility Functions over Value; title: 12.3.Logarithmic Utility Functions over Value; title: 12.4.Archimedean Combinations of Utility Functions: General Utility Functions over Additive Preference Functions; title: 12.5.Assessing Multiattribute Utility Functions with Additive Ordinal Preferences Using Archimedean Combinations of Utility Functions; title: 12.6.Summary Note continued: 13.The Role of the Utility Function in Valuing Uncertain Deals; title: 13.1.Introduction; title: 13.2.Basic Definitions and Notation; title: 13.3.Assessing Utility Functions over Value Measures; title: 13.4.Valuing a Decision Alternative Using the Utility Function (The Certain Equivalent); title: 13.5.Effects of the Shape of the Utility Function on the Certain Equivalent; title: 13.6.Effects of Applying a Concave or Convex Transformation to the Utility Function; title: 13.7.Effects of Incrementing All Lottery Outcomes by the Same Shift Amount; title: 13.8.Summary; title: 14.The Risk Aversion Function; title: 14.1.Introduction; title: 14.2.The Absolute Risk Aversion Function; title: 14.3.Determining the Utility Function from the Absolute Risk Aversion Function; title: 14.4.Applications of the Absolute Risk Aversion Function; title: 14.5.When One Certain Equivalent Is Always Lower Than Another; title: 14.6.The Inclination of the Risk Aversion Function (Increasing or Decreasing with Wealth); title: 14.7.Summary Note continued: 15.Scale Transformations Applied to a Lottery; title: 15.1.Introduction; title: 15.2.The Multiplicative Delta Property; title: 15.3.The Multiplicative Sub-Delta Property; title: 15.4.The Multiplicative Super-Delta Property; title: 15.5.The Relative Risk Aversion Function; title: 15.6.Summary; title: 16.The Invariant Transformation of a Utility Function; title: 16.1.Introduction; title: 16.2.The Invariant Transformation of a Utility Function; title: 16.3.Determining the Invariant Transformation of a Utility Function; title: 16.4.The g-Risk Aversion Function; title: 16.5.Summary; title: 17.Valuing Changes in Uncertain Deals (In the Small and in the Large); title: 17.1.Introduction; title: 17.2.Problem Formulation: Bounds on the Wealth Equivalent; title: 17.3.The Characteristic Transformation of a Utility Function, U, and a Transformation, g; title: 17.4.Modifying Lotteries by Shift Transformations; title: 17.5.A Measure of Change in Wealth Equivalent; title: 17.6.Valuing Changes in the Small; title: 17.7.Jensen's Inequality Gap for Small Variance Note continued: 17.8.Summary; title: 18.One-Switch Utility Functions; title: 18.1.Introduction; title: 18.2.Relating the Delta Property to Zero-Switch Utility Functions; title: 18.3.One-Switch Utility Functions; title: 18.4.Additional Characterization of One-Switch Utility Functions; title: 18.5.N-Switch Utility Functions; title: 18.6.Extensions to Two Attributes; title: 18.7.Summary; title: 19.Utility Transversality; title: 19.1.Introduction; title: 19.2.Deriving the Conditional Utility Function at Different Levels; title: 19.3.The Chain Rule for Risk Aversion; title: 19.4.Utility Transversality; title: 19.5.Implications of Utility Transversality; title: 19.6.Summary; title: 20.Multiattribute Risk Aversion; title: 20.1.Introduction; title: 20.2.The Sign of the Cross-Derivative of a Preference Function; title: 20.3.The Sign of the Cross-Derivative of a Multiattribute Utility Function: Implications for Lotteries; title: 20.4.Relating Two-Attribute Risk Aversion and Correlation Aversion; title: 20.5.Relating Risk Aversion and Two-Attribute Risk Aversion Note continued: 20.6.The Implications of Additive Utility Functions; title: 20.7.Summary; title: 21.Attribute Dominance Utility Functions; title: 21.1.Introduction; title: 21.2.Properties of Attribute Dominance Utility Functions (No Attributes); title: 21.3.Marginal-Conditional Expansion of Attribute Dominance Utility Functions; title: 21.4.Trade-Offs Implied by Utility-Dominant Attributes; title: 21.5.Attribute Dominance Utility Functions with Multiple Attributes; title: 21.6.Attribute Dominance Utility Diagrams; title: 21.7.Attribute Dominance Utility Copulas; title: 21.8.Constructing Attribute Dominance Utility Functions with Various Independence Conditions; title: 21.9.Summary; title: 22.Basic Expansion Theorem for Two-Attribute Utility Functions; title: 22.1.Relaxing the Attribute Dominance Conditions; title: 22.2.Two-Attribute Utility Trees on a Continuous Domain; title: 22.3.Utility Inference for Two Attributes; title: 22.4.General Expression and Notation for Utility Inference Note continued: 22.5.Reversing the Order of the Attributes in the Conditioning Statements; title: 22.6.Summary; title: 23.Basic Independence Conditions for Two Attributes; title: 23.1.Introduction; title: 23.2.Utility Independence (Keeney and Raiffa 1976); title: 23.3.Boundary Independence (Abbas 2011); title: 23.4.Interpolation Independence (Bell 1979); title: 23.5.Relating Utility, Boundary, and Interpolation Independence; title: 23.6.Graphical Representations of Independence Relations; title: 23.7.Summary; title: 24.Basic Expansion Theorem for Multiattribute Utility Functions; title: 24.1.Introduction; title: 24.2.The Three-Attribute Utility Tree on a Continuous Domain; title: 24.3.The Conditional Utility Function of the First Attribute in the Expansion; title: 24.4.The Conditional Utility Function of the Second Attribute in the Expansion; title: 24.5.The Conditional Utility Function of the Third Attribute in the Expansion; title: 24.6.Extensions to Multiple Attributes Note continued: 24.7.Reversing the Order of the Attributes in the Conditioning Statements; title: 24.8.Utility Tree Networks for Three or More Attributes; title: 24.9.Summary; title: 25.Multiattribute Utility Functions with Partial Utility Independence; title: 25.1.Introduction; title: 25.2.Capturing Independence Relations Using Utility Trees; title: 25.3.Bidirectional Utility Diagrams with Three or More Attributes; title: 25.4.The Simplest Utility Diagram: A Diagram with No Arrows; title: 25.5.Deriving the Functional Forms with Partial Utility Independence; title: 25.6.Iteratively Determining the Utility Assessments Needed for Partial Independence; title: 25.7.Summary; title: 26.Higher-Order Independence Relations; title: 26.1.Introduction; title: 26.2.Higher-Order Utility Assessments; title: 26.3.Higher-Order Utility Independence; title: 26.4.Relating Higher-Order Utility Independence to Lower-Order Utility Independence; title: 26.5.Additional Conditions to Assert Higher-Order Independence from Lower-Order Independence Note continued: 26.6.When Every Subset of the Attributes Is Utility Independent of Its Complement; title: 26.7.Summary; title: 27.One-Switch Utility Independence; title: 27.1.Introduction: Relating Three Different Notions; title: 27.2.Zero-Switch Formulations; title: 27.3.One-Switch Utility Formulations; title: 27.4.One-Switch Utility Independence; title: 27.5.Assessing the Functional Form for One-Switch Utility Independence; title: 27.6.N-Switch Utility Independence; title: 27.7.Summary; title: 28.Multiattribute Utility Copulas; title: 28.1.Introduction; title: 28.2.What Is a Multiattribute Utility Copula?; title: 28.3.Why Do We Need Both Class 1 and Class 0 Utility Copulas?; title: 28.4.Extensions to Multiple Attributes; title: 28.5.The Inverse Problem: Calculating the Utility Copula Function for a Given Multiattribute Utility Function; title: 28.6.Be Careful with the Consistency Conditions; title: 28.7.Summary; title: 29.Archimedean Utility Copulas; title: 29.1.Introduction; title: 29.2.Archimedean Utility Copulas; title: 29.3.Class 0 Archimedean Utility Copulas Note continued: 29.4.Archimedean Utility Copulas with Improper Generating Functions; title: 29.5.Summary; title: 30.Assessing an Archimedean Utility Copula; title: 30.1.Introduction; title: 30.2.Assessing an Archimedean Multiattribute Utility Function; title: 30.3.Assessments Needed for Constructing a Two-Attribute Utility Function Using an Archimedean Utility Copula; title: 30.4.Determining the Generating Function; title: 30.5.Summary of the Approach; title: 30.6.Convergence and Comparison with Other Approaches; title: 30.7.Summary; title: 31.Utility Copula Functions Matching All Boundary Assessments; title: 31.1.Introduction: The Need for Copula Functions Matching All Boundary Assessments; title: 31.2.Archimedean Copulas Match Only One Boundary Assessment for Each Attribute; title: 31.3.Double-Sided Utility Copulas; title: 31.4.Double-Sided Utility Copulas Using Three Grounded Surfaces; title: 31.5.Utility Copula Functions Using a Single Grounded Surface; title: 31.6.Summary; title: 32.Preference and Value Copulas; title: 32.1.Introduction Note continued: 32.2.Single-Sided Preference and Value Copulas; title: 32.3.Double-Sided Preference and Value Copulas; title: 32.4.The Ordinal One-Switch Property; title: 32.5.Double-Sided Value Copulas Satisfying Ordinal One-Switch Independence; title: 32.6.Summary; title: 33.Reflections on What We Have Learned; title: 33.1.Introduction: Review of Some Important Concepts