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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. The dim boy claps because the others clap. - Richard Hugo. A Logic of Diversity.

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a logic of diversity

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

slide2

The dim boy claps because the others clap.

- Richard Hugo

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a logic of diversity3
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.

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slide4

Co-Authors

Lu Hong: Mathematics of Diversity

Jenna Bednar: Cultural Diversity and Institutional Path Dependence

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the diversity mantra
The Diversity Mantra

Identity

Diversity

Diverse

Perspectives

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extending the mantra
Extending The Mantra

Identity

Diversity

Diverse

Perspectives

Better

Outcomes

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enlarging the mantra
Enlarging The Mantra

Identity

Diversity

Diverse

Perspectives

Better

Outcomes

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slide8

Identity

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slide9

Training

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slide10

Experiential

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enlarging the mantra11
Enlarging The Mantra

Identity,

Training,

Experiential

Diversity

Diverse

Perspectives

Better

Outcomes

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today s talk unpacking the first box
Today’s Talk: Unpacking The First Box

Diverse

Perspectives

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wednesday s talk demonstrating causality
Wednesday’s Talk: Demonstrating Causality

Better

Outcomes

Diverse

Perspectives

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today s talk
Today’s Talk

Describing the differences inside of our heads - cognitive differences.

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brief intermission
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?

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a most important question17
A Most Important Question

Where do you keep your ketchup?

Fridge?

Cupboard?

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the follow up questions
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?

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the diversity mantra19
The Diversity Mantra

Identity

Diversity

Diverse

Perspectives

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diverse perspectives
Diverse Perspectives?

Perspectives

Heuristics

Interpretations

Mental Models

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perspectives
Perspectives

A perspective is a representation of the set of possible solutions.

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

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diverse perspectives23
Diverse Perspectives

Cartesian Polar

(x,y)

(r,)

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ben and jerry
Ben and Jerry

chunk

size

number of chunks

y

x

z

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consultant 1
Consultant 1

caloric rank

x

z

y

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consultant 2
Consultant 2

masticity

z

x

y

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rugged landscapes
Rugged Landscapes

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perspectives and difficulty
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.

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mt fuji landscape
Mt Fuji Landscape

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caloric landscape
Caloric Landscape

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chew time landscape
Chew Time Landscape

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value of consultants
Value of Consultants

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perspectives in strategic contexts
Perspectives in Strategic Contexts

A perspective can also simplify a strategic context. What was hard can become easy.

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sum to fifteen herb simon
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

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4 29 98 page de marchi match
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!!

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7 th grade algebra
7th Grade Algebra

A Magic Square

8 3 4

1 5 9

6 7 2

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page de marchi again
Page-De Marchi Again

_ _ _

_ _ _

_ X _

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page de marchi again38
Page-De Marchi Again

_ _ _

_ _ _

0 X _

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page de marchi again39
Page-De Marchi Again

_ _ _

_ X _

0 X _

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page de marchi again40
Page-De Marchi Again

_ 0 _

_ X _

0 X _

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page de marchi again41
Page-De Marchi Again

_ 0 _

X X _

0 X _

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page de marchi again42
Page-De Marchi Again

_ 0 _

X X 0

0 X _

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an equivalence
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.

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what is hard can be easy
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.

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water flow problem
Water Flow Problem

Three valves (x,y,z): open = 1, closed = 0

Flow: x + y + z - 2xy - 2yz - 2xz + 4xyz

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walsh functions
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

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caution
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.

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heuristics
Heuristics

Heuristics are techniques that we use for finding solutions. They can take many forms

- simulated annealing algorithms

- rule of 72

- do the opposite

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heuristic example
Heuristic Example

Fill in the blank

  • 1 2 3 5 _ 13

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answer
Answer

1 2 3 5 8 13

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heuristic
Heuristic

1 2 3 5 8 13

  • xi+2- xi+1 =xi

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next question
Next Question

1 4 _ 16 25 36

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answer53
Answer

1 4 9 16 25 36

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heuristic54
Heuristic

1 4 9 16 25 36

  • xi2

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last one
Last One!

1 2 6 _ 1806

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answer56
Answer

1 2 6 42 1806

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heuristic57
Heuristic

1 2 6 42 1806

  • xi+1 – xi = xi 2
  • 6 – 2 =22
  • 42 – 6 =62
  • 1806 – 42 =422

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combining heuristics
Combining Heuristics

1 2 6 42 1806

  • xi+1 – xi = xi 2

This is a combination of the first two heuristics

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one plus one equals three
One plus one equals THREE

By knowing two heuristics, you know three heuristics: The two individual heuristic plus the combined heuristic.

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interpretations
Interpretations

Reality consists of many variables or attributes. People cannot include them all. Therefore, we either

- consider only some attributes

- lump things together

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lump to live
“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.

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real life examples
Real Life Examples

“Kerry is a liberal”

Soccer moms and NASCAR Dads

Price Earnings Ratios

Autism

Modern Art

SKA

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an example
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.

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the outcome function
The Outcome Function

student

O C A R

G

G

G

B

O

G

G

C

G

B

advisor

B

G

B

B

A

R

G

B

B

B

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advisor type interpretation
Advisor Type Interpretation

prediction

O

G

G

G

B

G

C

G

G

G

B

G

advisor

B

A

B

G

B

B

R

B

G

B

B

B

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student type interpretation
Student Type Interpretation

student

O C A R

G

G

G

B

G

G

B

G

B

G

B

B

G

B

B

B

prediction

G

G

B

B

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making horse races
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.

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miles davis
Miles Davis

Experts parse the world more finely than the rest of.

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chicago el 1992
Chicago El 1992

red line max 70K riders blue line max 80K riders

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chicago el 199270
Chicago El 1992

red line max 70K riders blue line max 80K riders

40K

80K

70K

30K

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chicago el 199271
Chicago El 1992

red line max 70K riders blue line max 80K riders

40K

80K

70K

30K

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chicago el 199272
Chicago El 1992

yellow line max 40K riderspurple line max 80K riders

40K

80K

70K

30K

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toolboxes vs measuring sticks
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.

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more toolbox combinatorics
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!

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toolboxes and iqs
Toolboxes and IQs

Suppose 50 possible tools

Sarah knows 20

Frank knows 12

What are odds that Sarah knows all that Frank knows?

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toolboxes and iqs76
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

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an implicit cheat
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.

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ladder model
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.

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many ladders model
Many Ladders Model

Probability

# of LaddersSarah > Frank

1 100%

2 29%

3 9%

4 1%

5 0.005%

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a puzzle
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?

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we believe what we know
We Believe What We Know

Discipline# of Ladders

Math Very Few

Physics Very Few

Economics Few

Political Science Several

Literature Many

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summary
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

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what s next
What’s Next
  • Individual diversity influences collective performance.
  • Explain``Wisdom of Crowds”
  • See that diversity and ability merit equal standing

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