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

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Presentation on theme: "Michigania 02005 A Logic of Diversity Scott E Page Complex Systems, Political Science, Economics and Institute for Social Research University of Michigan."— Presentation transcript:

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

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

3 Michigania 02005 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.

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

5 Michigania 02005 The Diversity Mantra Identity Diversity Diverse Perspectives

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

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

8 Michigania 02005 Identity

9 Michigania 02005 Training

10 Michigania 02005 Experiential

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

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

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

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

15 Michigania 02005 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?

16 Michigania 02005 A Most Important Question

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

18 Michigania 02005 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?

19 Michigania 02005 The Diversity Mantra Identity Diversity Diverse Perspectives

20 Michigania 02005 Diverse Perspectives? Perspectives Heuristics Interpretations Mental Models

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

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

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

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

25 Michigania 02005 Consultant 1 caloric rank zxy

26 Michigania 02005 Consultant 2 masticity zxy

27 Michigania 02005 Rugged Landscapes

28 Michigania 02005 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.

29 Michigania 02005 Mt Fuji Landscape

30 Michigania 02005 Caloric Landscape

31 Michigania 02005 Chew Time Landscape

32 Michigania 02005 Value of Consultants

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

34 Michigania 02005 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

35 Michigania 02005 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!!

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

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

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

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

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

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

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

43 Michigania 02005 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.

44 Michigania 02005 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.

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

46 Michigania 02005 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

47 Michigania 02005 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.

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

49 Michigania 02005 Heuristic Example Fill in the blank 1 235_13

50 Michigania 02005 Answer 1 2 35813

51 Michigania 02005 Heuristic 1 235813 –x i+2 - x i+1 =x i

52 Michigania 02005 Next Question 1 4_162536

53 Michigania 02005 Answer 1 49162536

54 Michigania 02005 Heuristic 1 4 9162536 –x i 2

55 Michigania 02005 Last One! 1 2 6 _1806

56 Michigania 02005 Answer 1 2 6421806

57 Michigania 02005 Heuristic 1 2 6 42 1806 –x i+1 – x i = x i 2 –6 – 2 = 2 2 – 42 – 6 = 6 2 – 1806 – 42 = 42 2

58 Michigania 02005 Combining Heuristics 1 2 6 42 1806 –x i+1 – x i = x i 2 This is a combination of the first two heuristics

59 Michigania 02005 One plus one equals THREE By knowing two heuristics, you know three heuristics: The two individual heuristic plus the combined heuristic.

60 Michigania 02005 Interpretations Reality consists of many variables or attributes. People cannot include them all. Therefore, we either - consider only some attributes - lump things together

61 Michigania 02005 “Lump to Live” If we did not lump various experiences, situations, and events into categories, we could not draw inferences, make generalities, or construct mental models.

62 Michigania 02005 Real Life Examples “Kerry is a liberal” Soccer moms and NASCAR Dads Price Earnings Ratios Autism Modern Art SKA

63 Michigania 02005 An Example Students and advisors can have one of four personality types: –Obsessive –Curious –Ambitious –Rule Following Outcome function F maps each pair into an outcome which is either good or bad.

64 Michigania 02005 The Outcome Function GG G G G G G B B B BB BBB O C A R O C A R student advisor G

65 Michigania 02005 Advisor Type Interpretation GG G G G G G B B B BB BBB O C A R advisor G prediction G G B B

66 Michigania 02005 Student Type Interpretation GG G G G G G B B B BB BBB G O C A R student prediction GGBB

67 Michigania 02005 Making Horse Races This is why we differ on our predictions of what will happen with stock prices, who will win sporting events, and who is a likely terrorist -- we look at the world differently.

68 Michigania 02005 Miles Davis Experts parse the world more finely than the rest of.

69 Michigania 02005 Chicago El 1992 red line max 70K riders blue line max 80K riders

70 Michigania 02005 Chicago El 1992 red line max 70K riders blue line max 80K riders 40K 70K 80K 30K

71 Michigania 02005 Chicago El 1992 red line max 70K riders blue line max 80K riders 40K 70K 80K 30K

72 Michigania 02005 Chicago El 1992 yellow line max 40K riders purple line max 80K riders 70K 80K 30K 40K

73 Michigania 02005 Toolboxes vs Measuring Sticks We can think of a person’s ability as her collection of tools -- her perspectives, her heuristics, and her mental models -- and not as an IQ score.

74 Michigania 02005 More Toolbox Combinatorics With one hundred tools, the number of collections of ten tools equals 17,310,309,456,440 Compare this to the number of I.Q.s!

75 Michigania 02005 Toolboxes and IQs Suppose 50 possible tools Sarah knows 20 Frank knows 12 What are odds that Sarah knows all that Frank knows?

76 Michigania 02005 Toolboxes and IQs Suppose 50 possible tools Sarah knows 20 Frank knows 12 What are odds that Sarah knows all that Frank knows? About 4 in a billion

77 Michigania 02005 An Implicit Cheat I assumed that any tool can be acquired. (“I think I’ll learn string theory.”) That may not be true. It could be that tools have an ordering - to learn one tool you must first learn another.

78 Michigania 02005 Ladder Model Suppose the tools are arranged in a ladder, so that to learn tool nine you must first learn tools 1-8. Sarah now knows tools 1-20 Frank now knows tools 1-15 Sarah is “smarter” than Frank.

79 Michigania 02005 Many Ladders Model Probability # of Ladders Sarah > Frank 1 100% 2 29% 3 9% 4 1% 5 0.005%

80 Michigania 02005 A Puzzle Why do people in the humanities and the arts believe in the value of diversity and why do people in the sciences not?

81 Michigania 02005 We Believe What We Know Discipline # of Ladders Math Very Few Physics Very Few Economics Few Political Science Several Literature Many

82 Michigania 02005 Summary -We don’t apply our IQ directly -We apply tools -Perspectives, heuristics, interpretations, mental models -Tools are superadditive (42) -Cannot universally compare intelligences -Can compare domain specific intelligence

83 Michigania 02005 What’s Next -Individual diversity influences collective performance. -Explain``Wisdom of Crowds” -See that diversity and ability merit equal standing


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