## Decisions with Multiple Objectives: Preferences and Value Trade-OffsMany of the complex problems faced by decision makers involve multiple conflicting objectives. This book describes how a confused decision maker, who wishes to make a reasonable and responsible choice among alternatives, can systematically probe his true feelings in order to make those critically important, vexing trade-offs between incommensurable objectives. The theory is illustrated by many real concrete examples taken from a host of disciplinary settings. The standard approach in decision theory or decision analysis specifies a simplified single objective like monetary return to maximise. By generalising from the single objective case to the multiple objective case, this book considerably widens the range of applicability of decision analysis. |

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### Contents

THE PROBLEM | 1 |

12 Paradigm of Decision Analysis | 5 |

13 Comments About the Paradigm | 7 |

14 Complex Value Problems | 14 |

15 Classes of Examples and Methodological Nightmares | 19 |

16 Organization of Remaining Chapters | 26 |

THE STRUCTURING OF OBJECTIVES | 31 |

21 Objectives and Attributes | 32 |

65 The Additive Utility Function | 295 |

66 Assessing Multiattribute Utility Functions | 297 |

67 A Fundamental Relationship Between Preferential Independence and Utility Independence | 310 |

68 Relationships Among Utility Independence Assumptions | 316 |

69 Decomposition of Multiattribute Utility Functions | 319 |

610 Additional Representation Theorems | 324 |

611 Hierarchical Structures and Conditional Preferences | 332 |

612 Summary | 343 |

22 Generation of Objectives and Attributes | 34 |

23 Hierarchical Nature of Objectives | 41 |

24 Sets of Objectives and Attributes | 49 |

25 Proxy Attributes and Direct Preferences Measurements | 55 |

26 Summary and Perspective on the Practical Aspects of Specifying Objectives and Attributes | 64 |

TRADEOFFS UNDER CERTAINTY | 66 |

32 Choice Procedures That Do Not Formalize Preference Structures | 69 |

33 Structuring of Preferences and Value Functions | 77 |

34 Preference Structures and Value Functions for Two Attributes | 82 |

35 The Case of Three Attributes | 100 |

36 The Case of More Than Three Attributes | 108 |

An Abstract Hypothetical Example | 117 |

38 Willingness to Pay | 125 |

39 Brief Summary and Guide to Some Relevant Literature | 129 |

UNIDIMENSIONAL UTILITY THEORY | 131 |

42 Direct Assessment of Utilities for Consequences | 140 |

43 Unidimensional Utility Functions | 141 |

44 Risk Aversion | 148 |

45 A Measure of Risk Aversion | 159 |

46 Constant Decreasing and Increasing Risk Aversion | 165 |

47 Proportional Risk Aversion | 174 |

48 Monotonically Decreasing and Nonmonotonic Utility Functions | 179 |

49 A Procedure for Assessing Utility Functions | 188 |

410 Illustrations of the Assessment of Unidimensional Utility Functions | 203 |

411 Explicating a Single Attribute by Means of Multiple Attributes | 212 |

412 Conditional Unidimensional Utility Theory | 214 |

413 Where We Stand | 218 |

MULTIATTRIBUTE PREFERENCES UNDER UNCERTAINTY THE TWOATTRIBUTE CASE | 219 |

52 Utility Independence | 224 |

53 Additive Independence and the Additive Utility Function | 229 |

54 The Implications of Mutual Utility Independence | 232 |

55 Use of Certainty Equivalents | 242 |

56 Utility Functions with One UtilityIndependent Attribute | 243 |

57 What to Do if No Independence Properties Hold | 255 |

58 Assessment Procedure for Multiattribute Utility Functions | 261 |

59 Interpreting the Scaling Constants | 271 |

510 The Assessment of a Utility Function in a Hospital Blood Bank | 273 |

MULTIATTRIBUTE PREFERENCES UNDER UNCERTAINTY MORE THAN TWO ATTRIBUTES | 282 |

62 Utility Function with Three Attributes | 286 |

63 The Multiplicative Utility Function | 288 |

64 The Multilinear Utility Function | 293 |

Generalization of Preferential Independence and Utility Independence | 345 |

Evaluating the Scaling Constant in the Multiplicative Utility Function | 347 |

An Interactive Computer Program for Assessing and Using Multiattribute Utility Functions | 349 |

ILLUSTRATIVE APPLICATIONS | 354 |

71 Air Pollution Control | 355 |

72 Preference Tradeoffs among Instructional Programs | 365 |

73 Fire Departments Operations | 377 |

74 Structuring Corporate Preferences for Multiple Objectives | 390 |

75 Evaluating Computer Systems | 408 |

76 Siting and Licensing of Nuclear Power Facilities | 412 |

77 Other Applications | 417 |

AIRPORT DEVELOPMENT FOR MEXICO CITY A CASE STUDY | 436 |

82 Background Information | 437 |

83 Evolution of the Analysis | 441 |

84 The Static Model | 442 |

85 Specifying the Possible Impacts of Each Alternative | 445 |

86 Assessing the Multiattribute Utility Function | 451 |

87 The Analysis | 459 |

88 The Dynamic Analysis | 463 |

89 Impact of the Results | 470 |

PREFERENCES OVER TIME | 473 |

91 Characteristics of the Time Problem | 474 |

Value Functions over Time Streams | 476 |

Utility Functions over Time Streams | 488 |

94 Relaxing the Independence Assumptions | 493 |

95 Uncertain Horizon | 497 |

96 StateDependent Utilities | 501 |

97 Problems of Application | 503 |

98 Time Resolution of Uncertainty | 509 |

Derivation of a Utility Function for Consumption and Lifetime | 513 |

AGGREGATION OF INDIVIDUAL PREFERENCES | 515 |

101 The Decision Maker as Synthesizer or Amalgamator | 516 |

102 Aggregating Individuals Preferences under Certainty | 523 |

104 Additive Utility and Equity Considerations | 532 |

105 Appraisal of the Independence Assumptions | 536 |

106 Assessing Group Utility Functions | 539 |

107 Uses of Multiattribute Utility Analysis for Groups | 542 |

549 | |

561 | |

### Common terms and phrases

additive independence additive utility function additive value function air pollution airport alternatives amount appropriate assume cardinal utility certainty equivalent Chapter concerned conditional utility functions consider cost decision analysis decision maker decision maker's preferences decision problem decreasing define depend discussed equations evaluating example expected consequence expected utility follows formal given hierarchy illustrate impact implies important increasing utility functions independence conditions indicated indifference curves individual involved lottery measures of effectiveness Mexico City monetary multiattribute utility function multilinear multilinear form mutual utility independence net present value objectives pair possible preference structure preferentially independent probabilistic probabilistic independence probability distributions procedure proof proxy attributes questions relevant response result risk averse risk premium risk prone scaling constants Section set of attributes specified strategically equivalent strategy subjective suppose Texcoco Theorem tion tradeoffs uncertainty utility independent chain utility theory Zumpango