Engineering Systems Analysis for Design Richard de Neufville © Massachusetts Institute of Technology Primitive Decisions Models Slide 1 of 16 Primitive Decision Models l Still widely used l Illustrate problems with intuitive approach l Provide base for appreciating advantages of decision analysis

Engineering Systems Analysis for Design Richard de Neufville © Massachusetts Institute of Technology Primitive Decisions Models Slide 2 of 16 Payoff Matrix as Basic Framework BASIS: Payoff Matrix Alternative State of “nature” S 1 S 2... S M A1A2ANA1A2AN Value of outcomes ONMONM

Engineering Systems Analysis for Design Richard de Neufville © Massachusetts Institute of Technology Primitive Decisions Models Slide 3 of 16 Primitive Model: Laplace (1) l Decision Rule: a)Assume each state of nature equally probable => p m = 1/m b)Use these probabilities to calculate an “expected” value for each alternative c)Maximize “expected” value

Engineering Systems Analysis for Design Richard de Neufville © Massachusetts Institute of Technology Primitive Decisions Models Slide 4 of 16 Primitive Model: Laplace (2) l Example l Ex: A1, A2 = weekend at Beach or in NY City l S1, S2 = the sunny and rainy scenarios S 1 S 2 “expected” value A A

Engineering Systems Analysis for Design Richard de Neufville © Massachusetts Institute of Technology Primitive Decisions Models Slide 5 of 16 Primitive Model: Laplace (3) l Problem: Sensitivity to framing ==> “irrelevant states” l Ex: A1, A2 = weekend at Beach or in NY City l S1A, S1B = Sunny or Saturday or Sunday S 1A S 1A S 2 “expected” value A A

Engineering Systems Analysis for Design Richard de Neufville © Massachusetts Institute of Technology Primitive Decisions Models Slide 6 of 16 Maximin or Maximax Rules (1) l Decision Rule: a)Identify minimum or maximum outcomes for each alternative b)Choose alternative that maximizes the global minimum or maximum

Engineering Systems Analysis for Design Richard de Neufville © Massachusetts Institute of Technology Primitive Decisions Models Slide 7 of 16 Maximin or Maximax Rules (2) l Example: S 1 S 2 S 3 maximinmaximax A A A l Problems - discards most information - focuses in extremes

Engineering Systems Analysis for Design Richard de Neufville © Massachusetts Institute of Technology Primitive Decisions Models Slide 8 of 16 Regret (1) l Decision Rule a)Regret = (max outcome for state i) - (value for that alternative) b)Rewrite payoff matrix in terms of regret c)Minimize maximum regret (minimax)

Engineering Systems Analysis for Design Richard de Neufville © Massachusetts Institute of Technology Primitive Decisions Models Slide 9 of 16 Regret (2) l Example: l Original Payoff Matrix Regret Matrix S 1 S 2 S 3 A A A

Engineering Systems Analysis for Design Richard de Neufville © Massachusetts Institute of Technology Primitive Decisions Models Slide 10 of 16 Regret (3) l Problem: Sensitivity to Irrelevant Alternatives => Potential Intransitivities A A NOTE: Reversal of evaluation if alternative dropped ! What is A3 is “vaporware” – meant to keep customer from switching from A1 to A2? (this happens!)

Engineering Systems Analysis for Design Richard de Neufville © Massachusetts Institute of Technology Primitive Decisions Models Slide 11 of 16 Weighted Index Approach (1) l Decision Rule a)Portray each choice with its deterministic attribute -- different from payoff matrix For example: MaterialCostDensity A$5011 B$609

Engineering Systems Analysis for Design Richard de Neufville © Massachusetts Institute of Technology Primitive Decisions Models Slide 12 of 16 Weighted Index Approach (2) b)Normalize table entries on some standard, to reduce the effect of differences in units. This could be a material (A or B); an average or extreme value, etc. For example, normalizing on A: MaterialCostDensity A B c)Decide according to weighted average of normalized attributes.

Engineering Systems Analysis for Design Richard de Neufville © Massachusetts Institute of Technology Primitive Decisions Models Slide 13 of 16 Weighted Index Approach (3) l Problem 1: Sensitivity to Normalization Example: Normalize on ANormalize on B Matl $Density $Density A B Weighting both equally, we have A > B (2.00 vs ) B > A (2.00 vs. 2.05) Depending on basis of normalization

Engineering Systems Analysis for Design Richard de Neufville © Massachusetts Institute of Technology Primitive Decisions Models Slide 14 of 16 Weighted Index Approach (4) l Problem 2: Sensitivity to Irrelevant Alternatives As above, evident when introducing a new alternative, and thus, new normalization standards. l Problem 3: Sensitivity to Framing “irrelevant attributes” similar to Laplace criterion (or any other using weights)

Engineering Systems Analysis for Design Richard de Neufville © Massachusetts Institute of Technology Primitive Decisions Models Slide 15 of 16 Example from Practice l Sydney Environmental Impact Statement l 10 potential sites for Second Airport l About 80 characteristics l The choice from first solution l … not chosen when poor choices dropped l … best choices depended on aggregation of attributes l Procedure a mess -- totally dropped

Engineering Systems Analysis for Design Richard de Neufville © Massachusetts Institute of Technology Primitive Decisions Models Slide 16 of 16 Summary l Primitive Models are full of problems l Yet they are popular because people have complex spreadsheet data they seem to provide simple answers l Now you should know why to avoid them!