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## A Logic of Diversity

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**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**The dim boy claps because the others clap.**- Richard Hugo 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. Michigania 02005**Co-Authors**Lu Hong: Mathematics of Diversity Jenna Bednar: Cultural Diversity and Institutional Path Dependence Michigania 02005**The Diversity Mantra**Identity Diversity Diverse Perspectives Michigania 02005**Extending The Mantra**Identity Diversity Diverse Perspectives Better Outcomes Michigania 02005**Enlarging The Mantra**Identity Diversity Diverse Perspectives Better Outcomes Michigania 02005**Identity**Michigania 02005**Training**Michigania 02005**Experiential**Michigania 02005**Enlarging The Mantra**Identity, Training, Experiential Diversity Diverse Perspectives Better Outcomes Michigania 02005**Today’s Talk: Unpacking The First Box**Diverse Perspectives Michigania 02005**Wednesday’s Talk: Demonstrating Causality**Better Outcomes Diverse Perspectives Michigania 02005**Today’s Talk**Describing the differences inside of our heads - cognitive differences. 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? Michigania 02005**A Most Important Question**Michigania 02005**A Most Important Question**Where do you keep your ketchup? Fridge? Cupboard? 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? Michigania 02005**The Diversity Mantra**Identity Diversity Diverse Perspectives Michigania 02005**Diverse Perspectives?**Perspectives Heuristics Interpretations Mental Models Michigania 02005**Perspectives**A perspective is a representation of the set of possible solutions. Michigania 02005**The Value of Perspectives**• Most great breakthroughs in science result from new perspectives. • Newton: Planetary Motion • Mendeleyev: Periodic Table Michigania 02005**Diverse Perspectives**Cartesian Polar (x,y) (r,) Michigania 02005**Ben and Jerry**chunk size number of chunks y x z Michigania 02005**Consultant 1**caloric rank x z y Michigania 02005**Consultant 2**masticity z x y Michigania 02005**Rugged Landscapes**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. Michigania 02005**Mt Fuji Landscape**Michigania 02005**Caloric Landscape**Michigania 02005**Chew Time Landscape**Michigania 02005**Value of Consultants**Michigania 02005**Perspectives in Strategic Contexts**A perspective can also simplify a strategic context. What was hard can become easy. 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 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!! Michigania 02005**7th Grade Algebra**A Magic Square 8 3 4 1 5 9 6 7 2 Michigania 02005**Page-De Marchi Again**_ _ _ _ _ _ _ X _ Michigania 02005**Page-De Marchi Again**_ _ _ _ _ _ 0 X _ Michigania 02005**Page-De Marchi Again**_ _ _ _ X _ 0 X _ Michigania 02005**Page-De Marchi Again**_ 0 _ _ X _ 0 X _ Michigania 02005**Page-De Marchi Again**_ 0 _ X X _ 0 X _ Michigania 02005**Page-De Marchi Again**_ 0 _ X X 0 0 X _ 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. 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. Michigania 02005**Water Flow Problem**Three valves (x,y,z): open = 1, closed = 0 Flow: x + y + z - 2xy - 2yz - 2xz + 4xyz 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 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. 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 Michigania 02005**Heuristic Example**Fill in the blank • 1 2 3 5 _ 13 Michigania 02005**Answer**1 2 3 5 8 13 Michigania 02005