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A Logic of Diversity

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  1. A Logic of Diversity Scott E Page Complex Systems, Political Science, Economics and Institute for Social Research University of Michigan Santa Fe Institute Michigania 02005

  2. The dim boy claps because the others clap. - Richard Hugo Michigania 02005

  3. A Logic of Diversity I am going to replace abstract concepts, metaphors, and mantras with formal frameworks to produce a logic of individual diversity and its aggregative implications. Michigania 02005

  4. Co-Authors Lu Hong: Mathematics of Diversity Jenna Bednar: Cultural Diversity and Institutional Path Dependence Michigania 02005

  5. The Diversity Mantra Identity Diversity Diverse Perspectives Michigania 02005

  6. Extending The Mantra Identity Diversity Diverse Perspectives Better Outcomes Michigania 02005

  7. Enlarging The Mantra Identity Diversity Diverse Perspectives Better Outcomes Michigania 02005

  8. Identity Michigania 02005

  9. Training Michigania 02005

  10. Experiential Michigania 02005

  11. Enlarging The Mantra Identity, Training, Experiential Diversity Diverse Perspectives Better Outcomes Michigania 02005

  12. Today’s Talk: Unpacking The First Box Diverse Perspectives Michigania 02005

  13. Wednesday’s Talk: Demonstrating Causality Better Outcomes Diverse Perspectives Michigania 02005

  14. Today’s Talk Describing the differences inside of our heads - cognitive differences. Michigania 02005

  15. Brief Intermission Link to training (calculus, physics, etc..) obvious. Link to experience (we reason based on past cases) also clear But what of identity and culture? Michigania 02005

  16. A Most Important Question Michigania 02005

  17. A Most Important Question Where do you keep your ketchup? Fridge? Cupboard? Michigania 02005

  18. The Follow-up Questions Shoes on or off in your house? Cross street when the red hand is flashing but no cars are present? Read newspaper at breakfast table? When you greet friends do you hug? Michigania 02005

  19. The Diversity Mantra Identity Diversity Diverse Perspectives Michigania 02005

  20. Diverse Perspectives? Perspectives Heuristics Interpretations Mental Models Michigania 02005

  21. Perspectives A perspective is a representation of the set of possible solutions. Michigania 02005

  22. The Value of Perspectives • Most great breakthroughs in science result from new perspectives. • Newton: Planetary Motion • Mendeleyev: Periodic Table Michigania 02005

  23. Diverse Perspectives Cartesian Polar (x,y) (r,) Michigania 02005

  24. Ben and Jerry chunk size number of chunks y x z Michigania 02005

  25. Consultant 1 caloric rank x z y Michigania 02005

  26. Consultant 2 masticity z x y Michigania 02005

  27. Rugged Landscapes Michigania 02005

  28. Perspectives and Difficulty A perspective creates a landscape where the elevation of each solution equals its value. The better the perspective, the less rugged the landscape. Michigania 02005

  29. Mt Fuji Landscape Michigania 02005

  30. Caloric Landscape Michigania 02005

  31. Chew Time Landscape Michigania 02005

  32. Value of Consultants Michigania 02005

  33. Perspectives in Strategic Contexts A perspective can also simplify a strategic context. What was hard can become easy. Michigania 02005

  34. Sum to Fifteen – Herb Simon Setup: Cards numbered 1-9 face up on table Play: Players alternate selecting cards Object: To hold exactly three cards that add up to fifteen Michigania 02005

  35. 4/29/98 Page-De Marchi Match D: 7 P: 6 D: 5 (12) P: 3 (9) D: 1 (6,8,12) P: 9 (12,9,15) De Marchi offers Draw!! Michigania 02005

  36. 7th Grade Algebra A Magic Square 8 3 4 1 5 9 6 7 2 Michigania 02005

  37. Page-De Marchi Again _ _ _ _ _ _ _ X _ Michigania 02005

  38. Page-De Marchi Again _ _ _ _ _ _ 0 X _ Michigania 02005

  39. Page-De Marchi Again _ _ _ _ X _ 0 X _ Michigania 02005

  40. Page-De Marchi Again _ 0 _ _ X _ 0 X _ Michigania 02005

  41. Page-De Marchi Again _ 0 _ X X _ 0 X _ Michigania 02005

  42. Page-De Marchi Again _ 0 _ X X 0 0 X _ Michigania 02005

  43. An Equivalence It can be shown that tic tac toe on the magic square is equivalent to sum to fifteen. In one perspective the game is hard. In the other perspective, the game is easy. Michigania 02005

  44. What Is Hard Can Be Easy Theorem: For any problem there exists a representation such that the problem of finding an optimal solution is easy. Michigania 02005

  45. Water Flow Problem Three valves (x,y,z): open = 1, closed = 0 Flow: x + y + z - 2xy - 2yz - 2xz + 4xyz Michigania 02005

  46. Walsh Functions Walsh Function #3 W(x,y,z) = 0 if #1’s is even W(x,y,z) = 1 if #1’s is odd W(x,y,z) = x + y + z - 2xy - 2yz - 2xz + 4xyz Michigania 02005

  47. Caution Diverse perspectives create more adjacencies, and therefore more solutions. Those additional solutions include better solutions only if the perspectives are appropriate to the problem. More need not imply more better. Michigania 02005

  48. Heuristics Heuristics are techniques that we use for finding solutions. They can take many forms - simulated annealing algorithms - rule of 72 - do the opposite Michigania 02005

  49. Heuristic Example Fill in the blank • 1 2 3 5 _ 13 Michigania 02005

  50. Answer 1 2 3 5 8 13 Michigania 02005