1. Decision Support Systems INF421 & IS341 1

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3. Introduction To distinguish between normative theories, descriptive studies and prescriptive analysis; To set up the frameworks that are used in later chapters when outlining the processes of decision analysis and support; To indicate how rationality in decision making might be defined; and To define and categorize the decision support systems, software and tools that are used in these processes. 3

4. Normative and Descriptive Models Normative models suggest how people should make decisions. Descriptive models describe how they actually do. Much of this book focuses on drawing these perspectives on decision making together to build prescriptive decision analysis and support. 4

5. Normative and Descriptive Models These models provide the DMs with informative perspectives on the issues, – bring them understanding; and – through this understanding their judgments evolve and they reach a decision. 5

6. Normative and Descriptive Models 6

7. An introduction to normative modeling Normative decision theories begin by making assumptions about the characteristics of rational decision making. They then explore the implications of these assumptions. Normative decision theories lie at the interface between philosophy, mathematics and economics. 7

8. Normative modeling under certainty We focus in this section on decisions under certainty – i.e. we assume that each available action leads to an unambiguous consequence, and the DM has full knowledge of everything that she considers relevant to her problem. 8

9. Notations & Assumptions Let us introduce some notation. We write a ≽ b to mean that the DM weakly prefers a to b. – An alternative, perhaps more expressive interpretation is that she holds a to be at least as good as b. We demand that ≽ is complete: Axiom WOl (completeness): For all objects a, b in A, either a ≽ b or b ≽ a. 9

10. Notations & Assumptions Axiom W02 (transitivity): For all objects a, b, c in A, if a ≽ b and b ≽ c, then a ≽ c. There are two further preference orders related to weak preference: – Indifference: DM is indifferent between a and b a 〜 b – Strict preference: DM strictly prefers a to b a ≻ b 10

11. Notations & Assumptions Axiom WO3: a ≻ b if and only if a ≽ b and b ⋡ a. Axiom W04: a 〜 b if and only if a ≽ b and b ≽ a. 11

12. Example 1 An agency has three secretaries a, b, c. An employer has interviewed them all and strictly prefers a to b, b to c and c to a. Suppose that, between the interviews and the appointment, c becomes unavailable. The employer's choice now being between a and b, she will employ a. 12

13. Example 1 Next the agency 'discovers' that c was not unavailable after all, but b has gone off after another job. The employer has selected a; but she strictly prefers c to a. The agency will not find it difficult to persuade her to swap a for c for a suitably small charge, say a penny. 13

14. Example 1 At this point the agency discovers that b did not get the other job after all, but that a is no longer available. Since the employer strictly prefers b to c, she will need little persuasion to part with a further penny and swap c for b. Clearly, the 'irrationality' of the employer holding intransitive strict preferences. 14

15. Example 2 Consider: no real person could discriminate between an air temperature and one 0.001°C higher. ( i.e. 20°C 〜 20.001°C ). Thus, 20°C 〜 20.001°C 〜 20.002°C 〜 20.003°C 〜 … 〜 100°C Obviously, this is nonsense; but this argument muddles a descriptive perspective with a normative one. 15

16. The Rule of the Value Function We can also quickly perceive the ordering of the underlying alternatives. Analysis can become conceptually easier. For instance, most of us would find it simpler to identify a most preferred object by maximizing a value function than by searching through the alternatives. Optimization methods are central to much of decision analysis and OR. 16

17. Process of DS and analysis 17

18. DSS Levels 18

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20. Subjective Expected Utility Model Subjective Expected Utility (SEU) Model can be used to represent the decision problem with risks. SEU Model has two elements: – Subjective Probability Distribution, P(.). Give a probability for a state. – Utility Function, u(.). Give preferences for consequences. 20

21. Expected Utility Function The SEU model asserts that to combine her beliefs and preferences coherently in order to rank the actions the DM should form expected utilities 21

22. Questions? 22