Foundations of Decision Analysis

Cover ... 1
Title ... 2
Copyright ... 3
Brief Contents ... 4
Contents ... 6
Chapter 1: Introduction to Quality Decision Making ... 24
	1.1 Introduction ... 24
	1.2 Normative Vs. Descriptive ... 24
	1.3 Declaring a Decision ... 27
	1.4 Thought Vs. Action ... 30
	1.5 What is a Decision? ... 31
	1.6 Decision Vs. Outcome ... 33
	1.7 Clarity of Action ... 36
	1.8 What is a Good Decision? ... 37
	1.9 Summary ... 41
		Key Terms ... 42
		Problems ... 43
Chapter 2: Experiencing a Decision ... 45
	2.1 Introduction ... 45
	2.2 Analysis of a Decision: The Thumbtack and the Medallion Example ... 45
	2.3 Lessons Learned from the Thumbtack and Medallion Example ... 54
	2.4 Summary ... 58
		Key Terms ... 58
		Appendix A: Results of the Thumbtack Demonstration ... 59
		Problems ... 60
Chapter 3: Clarifying Values ... 64
	3.1 Introduction ... 64
	3.2 Value in Use and Value in Exchange ... 64
	3.3 Values Around a Cycle of Ownership ... 68
	3.4 Summary ... 73
		Key Terms ... 74
		Problems ... 75
Chapter 4: Precise Decision Language ... 78
	4.1 Introduction ... 78
	4.2 Lego-Like Precision ... 78
	4.3 Precise Decision Language ... 79
	4.4 Experts and Distinctions ... 80
	4.5 Mastery ... 82
	4.6 Creating Your Own Distinctions ... 83
	4.7 Footnote ... 83
	4.8 Summary ... 83
		Key Terms ... 83
		Problems ... 84
Chapter 5: Possibilities ... 85
	5.1 Overview ... 85
	5.2 Creating Distinctions ... 85
	5.3 The Possibility Tree ... 88
	5.4 Measures ... 95
	5.5 Sumary ... 97
		Key Terms ... 98
		Problems ... 99
Chapter 6: Handling Uncertainty ... 101
	6.1 Introduction ... 101
	6.2 Describing Degree of Belief by Probability ... 101
	6.3 The Probability Tree ... 105
	6.4 Several Degrees of Distinction ... 114
	6.5 Multiple Degrees of Distinction ... 114
	6.6 Probability Trees Using Multiple Distinctions ... 117
	6.7 Adding Measures to the Probability Tree ... 124
	6.8 Multiple Measures ... 132
	6.9 Summary ... 134
		Key Terms ... 135
		Appendix A: The Chain Rule for Distinctions: Calculating Elemental Probabilities ... 136
		Appendix B: Let’s Make a Deal Commentary ... 138
		Appendix C: Further Discussion Related to the Example: At Least One Boy ... 141
		Problems ... 142
Chapter 7: Relevance ... 146
	7.1 Introduction ... 146
	7.2 Relevance with Simple Distinctions ... 146
	7.3 Is Relevance Mutual? ... 147
	7.4 Relevance Diagrams ... 149
	7.5 Alternate Asessment Orders ... 153
	7.6 Relevance Depends on Knowledge ... 155
	7.7 Distinctive Vs. Asociative Logic ... 160
	7.8 The Third Factor ... 161
	7.9 Multi-Degree Relevance ... 164
	7.10 Summary ... 164
		Key Terms ... 165
		Appendix A: More on Relevance Diagrams and Arrow Reversals ... 166
		Problems ... 169
Chapter 8: Rules of Actional Thought ... 179
	8.1 Introduction ... 179
	8.2 Using Rules for Decision Making ... 179
	8.3 The Decision Situation ... 181
	8.4 The Five Rules of Actional Thought ... 182
	8.5 Summary ... 188
		Key Terms ... 189
		Problems ... 190
Chapter 9: The Party Problem ... 199
	9.1 Introduction ... 199
	9.2 The Party Problem ... 199
	9.3 Simplifying the Rules: E-Value ... 205
	9.4 Understanding the Value of the Party Problem ... 210
	9.5 Summary ... 214
		Key Terms ... 214
		Appendix A ... 215
		Problems ... 216
Chapter 10: Using a Value Measure ... 217
	10.1 Introduction ... 217
	10.2 Money as a Value Measure ... 217
	10.3 u-curves ... 220
	10.4 Valuing Clairvoyance ... 224
	10.5 Jane’s Party Problem ... 228
	10.6 Attitudes toward Risk ... 231
	10.7 Mary’s Party Problem ... 234
	10.8 Summary ... 236
		Key Terms ... 236
		Problems ... 237
Chapter 11: Risk Attitude ... 240
	11.1 Introduction ... 240
	11.2 Wealth Risk Attitude ... 240
	11.3 Buying and Selling a Deal Around a Cycle of Ownership ... 241
	11.4 The Delta Property ... 244
	11.5 Risk Odds ... 247
	11.6 Delta Property Simplifications ... 252
	11.7 Other Forms of Exponential u-Curve ... 254
	11.8 Direct Assessment of Risk Tolerance ... 255
	11.9 Summary ... 261
		Key Terms ... 262
		Problems ... 263
Chapter 12: Sensitivity Analysis ... 270
	12.1 Introduction ... 270
	12.2 Kim’s Sensitivity to Probability of Sunshine ... 270
	12.3 Certain Equivalent Sensitivity ... 272
	12.4 Value of Clairvoyance Sensitivity to Probability of Sunshine ... 273
	12.5 Jane’s Sensitivity to Probability of Sunshine ... 274
	12.6 Comparison of Kim’s and Jane’s Value of Clairvoyance Sensitivities ... 275
	12.7 Risk Sensitivity Profile ... 277
	12.8 Summary ... 279
		Key Terms ... 279
		Problems ... 280
Chapter 13: Basic Information Gathering ... 288
	13.1 Introduction ... 288
	13.2 The Value of Information ... 288
	13.3 The Acme Rain Detector ... 290
	13.4 General Observations on Experiments ... 296
	13.5 Asymmetric Experiments ... 300
	13.6 Information Gathering Equivalents ... 303
	13.7 Summary ... 306
		Problems ... 308
Chapter 14: Decision Diagrams ... 315
	14.1 Introduction ... 315
	14.2 Nodes in the Decision Diagram ... 315
	14.3 Arrows in Decision Diagrams ... 316
	14.4 Value of Clairvoyance ... 318
	14.5 Imperfect Information ... 319
	14.6 Decision Tree Order ... 319
	14.7 Detector Use Decision ... 320
	14.8 Summary ... 323
		Key Terms ... 323
		Problems ... 324
Chapter 15: Encoding a Probability Distribution on a Measure ... 331
	15.1 Introduction ... 331
	15.2 Probability Encoding ... 333
	15.3 Fractiles of a Probability Distribution ... 339
	15.4 Summary ... 347
		Key Terms ... 347
		Problems ... 348
		Answers to Problem 2 ... 349
Chapter 16: From Phenomenon to Asesment ... 350
	16.1 Introduction ... 350
	16.2 Information Transmission ... 350
	16.3 Perception ... 351
	16.4 Cognition ... 352
	16.5 Motivation ... 356
	16.6 Summary ... 356
		Key Terms ... 356
Chapter 17: Framing a Decision ... 357
	17.1 Introduction ... 357
	17.2 Making a Decision ... 357
	17.3 Selecting a Frame ... 358
	17.4 Summary ... 369
		Key Terms ... 369
		Problems ... 370
Chapter 18: Valuing Information from Multiple Sources ... 371
	18.1 Introduction ... 371
	18.2 The Beta Rain Detector ... 371
	18.3 Clarifying the Value of Joint Clairvoyance on Two Distinctions ... 378
	18.4 Value of Information for Multiple Uncertainties ... 381
	18.5 Approaching Clairvoyance with Multiple Acme Detectors ... 386
	18.6 Valuing Individually Immaterial Multiple Detectors ... 395
	18.7 Summary ... 398
		Key Terms ... 399
		Problems ... 400
Chapter 19: Options ... 401
	19.1 Introduction ... 401
	19.2 Contractual and Non-Contractual Options ... 401
	19.3 Option Price, Exercise Price, and Option Value ... 402
	19.4 Simple Option Analysis ... 403
	19.5 Consequences of Failure to Recognize Options ... 406
	19.6 Jane’s Party Revisited ... 409
	19.7 Value of Clairvoyance as an Option ... 411
	19.8 Sequential Information Options ... 412
	19.9 Sequential Detector Options ... 415
	19.10 Creating Options ... 415
	19.11 Summary ... 420
		Key Terms ... 420
		Problems ... 421
Chapter 20: Detectors with Multiple Indications ... 422
	20.1 Introduction ... 422
	20.2 Detector with 100 Indications ... 423
	20.3 The Continuous Beta Detector ... 440
	20.4 Summary ... 446
		Key Terms ... 446
		Problems ... 447
Chapter 21: Decisions with Influences ... 448
	21.1 Introduction ... 448
	21.2 Shirley’s Problem ... 448
	21.3 Summary ... 463
		Key Terms ... 463
		Problems ... 464
Chapter 22: The Logarithmic u-Curve ... 465
	22.1 Introduction ... 465
	22.2 The Logarithmic u-Curve ... 466
	22.3 Deals with Large Monetary Prospects for a DeltaPerson ... 470
	22.4 Properties of the Logarithmic u-Curve ... 474
	22.5 Certain Equivalent of Two Mutually Irrelevant Deal ... 479
	22.6 The St. Petersburg Paradox ... 482
	22.7 Summary ... 485
		Key Terms ... 486
		Appendix A: The Logarithmic Function and Its Properties ... 487
		Appendix B: The Risk-Aversion Function ... 488
		Appendix C: A Student’s Question Following an Economist Article ... 489
		Problems ... 494
Chapter 23: The Linear Risk Tolerance u-Curve ... 496
	23.1 Introduction ... 496
	23.2 Linear Risk Tolerance ... 496
	23.3 Summary ... 504
		Key Terms ... 504
		Appendix A: Derivation of Linear Risk Tolerance u-Curve ... 505
		Appendix B: Student’s Problem Using Linear Risk Tolerance u-Curve ... 506
		Problems ... 508
Chapter 24: Aproximate Expresions for the Certain Equivalent ... 509
	24.1 Introduction ... 509
	24.2 Moments of a Measure ... 509
	24.3 Central Moments of a Measure ... 513
	24.4 Approximating the Certain Equivalent Using First and Second Central Moments ... 514
	24.5 Approximating the Certain Equivalent Using Higher Order Moments ... 516
	24.6 Cumulants ... 519
	24.7 Summary ... 519
		Key Terms ... 520
		Problems ... 521
Chapter 25: Deterministic and Probabilistic Dominance ... 522
	25.1 Introduction ... 522
	25.2 Deterministic Dominance ... 522
	25.3 First-Order Probabilistic Dominance ... 527
	25.4 Second-Order Probabilistic Dominance ... 531
	25.5 Dominance for Alternatives in the Party Problem ... 535
	25.6 Summary ... 538
		Key Terms ... 538
		Problems ... 539
Chapter 26: Decisions with Multiple Attributes (1)–Ordering Prospects with Preference and Value Functions ... 540
	26.1 Introduction ... 540
	26.2 Step 1: Direct Vs. Indirect Values ... 541
	26.3 Step 2: Ordering Prospects Characterized by Multiple “Direct Value” Attributes ... 545
	26.4 Summary ... 552
		Key Terms ... 553
		Appendix A: Deriving the Relation Between Increments in x and y as a Function of ? in the Preference Function ... 554
		Problems ... 555
Chapter 27: Decisions with Multiple Attributes (2)–Value Functions for Investment Cash Flows: Time Preference ... 556
	27.1 Introduction ... 556
	27.2 Rules for Evaluating Investment Cash Flows ... 557
	27.3 Methods Not Equivalent to the Present Equivalent ... 568
	27.4 Cash Flows: A Single Measure ... 571
	27.5 Summary ... 571
		Key Terms ... 571
		Problems ... 572
Chapter 28: Decisions With Multiple Attributes (3)–Preference Probabilities Over Value ... 573
	28.1 Introduction ... 573
	28.2 Stating Preference Probabilities with Two Attributes ... 574
	28.3 Stating Preference Probabilities with a Value Function ... 575
	28.4 Stating a u-Curve Over the Value Function ... 575
	28.5 The Value Certain Equivalent ... 577
	28.6 Other u-Function Approaches ... 579
	28.7 Stating a u-Curve Over an Individual Attribute within the Value Function ... 580
	28.8 Valuing Uncertain Cash Flows ... 583
	28.9 Discussion ... 587
	28.10 Summary ... 588
		Key Terms ... 588
		Problems ... 589
Chapter 29: Betting on Disparate Belief ... 590
	29.1 Introduction ... 590
	29.2 Betting on Disparate Probabilities ... 590
	29.3 Practical Use ... 594
	29.4 Summary ... 595
		Key Terms ... 595
		Problems ... 596
Chapter 30: Learning From Experimentation ... 597
	30.1 Introduction ... 597
	30.2 Assigning Probability of Head and Tail for the Thumbtack ... 598
	30.3 Probability of Heads on Next Two Tosses ... 599
	30.4 Probability of Any Number of Heads and Tails ... 600
	30.5 Learning from Observation ... 601
	30.6 Conjugate Distributions ... 604
	30.7 Does Observing a Head Make the Probability of a Head on the Next Toss More Likely? ... 605
	30.8 Another Thumbtack Demonstration ... 606
	30.9 Summary ... 609
		Key Terms ... 609
		Problems ... 610
Chapter 31: Auctions and Biding ... 611
	31.1 Introduction ... 611
	31.2 Another Thumbtack Demonstration ... 611
	31.3 Auctions 1 and 3 for a Deltaperson ... 616
	31.4 Non-Deltaperson Analysis ... 622
	31.5 The Value of the Bidding Opportunity for Auction 2 ... 624
	31.6 The Winner’s Curse ... 628
	31.7 Summary ... 640
		Key Terms ... 641
		Problems ... 642
Chapter 32: Evaluating, Scaling, and Sharing Uncertain Deals ... 644
	32.1 Introduction ... 644
	32.2 Scaling and Sharing Risk ... 644
	32.3 Scaling an Uncertain Deal ... 645
	32.4 Risk Sharing of Uncertain Deals ... 648
	32.5 Optimal Investment in a Portfolio ... 650
	32.6 Summary ... 659
		Key Terms ... 660
		Appendix A: Covariance and Correlation ... 661
		Appendix B: Scalar (Dot) Product of Vectors ... 666
		Appendix C: 2 × 2 and 3 × 3 Matrix Multiplications and Matrix Inversion ... 667
		Problems ... 670
Chapter 33: Making Risky Decisions ... 671
	33.1 Introduction ... 671
	33.2 A Painful Dilemma ... 671
	33.3 Small Probabilities ... 674
	33.4 Using Micromort Values ... 674
	33.5 Applications ... 676
	33.6 Facing Larger Probabilities of Death ... 678
	33.7 Summary ... 681
		Key Terms ... 681
		Problems ... 682
Chapter 34: Decisions with a High Probability of Death ... 684
	34.1 Introduction ... 684
	34.2 Value Function for Remaining Life Years and Consumption ... 684
	34.3 Assigning a u-Curve Over the Value Function ... 687
	34.4 Determining Micromort Values ... 690
	34.5 Equivalent Perfect Life Probability (EPlP) ... 696
	34.6 Summary ... 698
		Key Terms ... 698
		Appendix A: Mortality Table for 30-Year-Old Male ... 699
		Appendix B: Example of a Black Pill Calculation, x = 10,000 ... 702
		Appendix C: Example of a White Pill Calculation, x = 10,000 ... 705
		Problems ... 708
Chapter 35: Discretizing Continuous Probability Distributions ... 709
	35.1 Introduction ... 709
	35.2 Equal Areas Method ... 710
	35.3 Caution with Discretization ... 714
	35.4 Accuracy of 10–50–90 Approximate Method for Equal Areas ... 716
	35.5 Moments of Discrete and Continuous Measures ... 719
	35.6 Moment Matching Method ... 719
	35.7 Summary ... 721
		Key Terms ... 721
		Appendix A: Rationale for Equal Areas Method ... 722
		Problems ... 725
Chapter 36: Solving Decision Problems by Simulation ... 726
	36.1 Introduction ... 726
	36.2 Using Simulation for Solving Problems ... 726
	36.3 Simulating Decisions Having a Single Discrete Distinction ... 727
	36.4 Decisions with Multiple Discrete Distinctions ... 730
	36.5 Simulating a Measure with a Continuous Distribution ... 733
	36.6 Simulating Mutually Irrelevant Distinctions ... 737
	36.7 Value of Information with Simulation ... 739
	36.8 Simulating Multiple Distinctions with Relevance ... 743
	36.9 Summary ... 745
		Key Terms ... 745
		Problems ... 746
Chapter 37: The Decision Analysis Cycle ... 747
	37.1 Introduction ... 747
	37.2 The Decision Analysis Cycle ... 747
	37.3 The Model Sequence ... 757
	37.4 Summary ... 768
		Key Terms ... 768
		Appendix A: Open Loop and Closed Loop Sensitivity for the Bidding Decision ... 769
Chapter 38: Topics in Organizational Decision Making ... 776
	38.1 Introduction ... 776
	38.2 Operating to Maximize Value ... 777
	38.3 Issues When Operating with Budgets ... 779
	38.4 Issues with Incentive Structures ... 780
	38.5 A Common Issue: Multiple Specifications Vs. Tradeoffs ... 781
	38.6 Need for a Corporate Risk Tolerance ... 782
	38.7 Common Motivational Biases in Organizations ... 786
	38.8 Summary ... 788
		Key Terms ... 788
		Problems ... 789
Chapter 39: Coordinating the Decision Making of Large Groups ... 790
	39.1 Introduction ... 790
	39.2 Issues Contributing to Poor Group Decision Making ... 790
	39.3 Classifying Decision Problems ... 792
	39.4 Structuring Decision Problems within Organizations ... 795
	39.5 Example: The Fifth Generation Corvette ... 800
	39.6 Summary ... 803
		Key Terms ... 803
Chapter 40: Decisions and Ethics ... 804
	40.1 Introduction ... 804
	40.2 The Role of Ethics in Decision Making ... 805
	40.3 Ethical Distinctions ... 806
	40.4 Harming, Stealing, and Truth Telling ... 809
	40.5 Ethical Codes ... 812
	40.6 Ethical Situations ... 813
	40.7 Summary ... 815
		Key Terms ... 816
		Problems ... 817
Index ... 818
	A ... 818
	B ... 819
	C ... 819
	D ... 820
	E ... 821
	F ... 822
	G ... 822
	H ... 823
	I ... 823
	J ... 823
	L ... 823
	M ... 824
	N ... 824
	O ... 824
	P ... 825
	Q ... 826
	R ... 827
	S ... 827
	T ... 828
	U ... 828
	V ... 829
	W ... 830
	Z ... 830