Title: A Logic of Diversity
1A Logic of Diversity
Scott E Page Complex Systems, Political Science,
Economics and Institute for Social
Research University of Michigan Santa Fe
Institute
2 The dim boy claps because the others
clap. - Richard Hugo
3A 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 Co-Authors
- Lu Hong Mathematics of Diversity
- Jenna Bednar Cultural Diversity and
Institutional Path Dependence -
5The Diversity Mantra
Identity Diversity
Diverse Perspectives
6Extending The Mantra
Identity Diversity
Diverse Perspectives
Better Outcomes
7Enlarging The Mantra
Identity Diversity
Diverse Perspectives
Better Outcomes
8Identity
9Training
10Experiential
11Enlarging The Mantra
Identity, Training, Experiential Diversity
Diverse Perspectives
Better Outcomes
12Todays Talk Unpacking The First Box
Diverse Perspectives
13Wednesdays Talk Demonstrating Causality
Better Outcomes
Diverse Perspectives
14Todays Talk
- Describing the differences inside of our heads -
cognitive differences.
15Brief 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?
16A Most Important Question
17A Most Important Question
- Where do you keep your ketchup?
- Fridge?
- Cupboard?
18The 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?
19The Diversity Mantra
Identity Diversity
Diverse Perspectives
20Diverse Perspectives?
- Perspectives
- Heuristics
- Interpretations
- Mental Models
21Perspectives
- A perspective is a representation of the set of
possible solutions.
22The Value of Perspectives
Most great breakthroughs in science result from
new perspectives. Newton Planetary
Motion Mendeleyev Periodic Table
23Diverse Perspectives
(x,y)
(r,?)
24Ben and Jerry
-
- chunk
- size
- number of chunks
y
x
z
25Consultant 1
z
x
y
26Consultant 2
z
x
y
27Rugged Landscapes
28Perspectives 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.
29Mt Fuji Landscape
30Caloric Landscape
31Chew Time Landscape
32Value of Consultants
33Perspectives in Strategic Contexts
- A perspective can also simplify a strategic
context. What was hard can become easy.
34Sum 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
354/29/98 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!!
367th Grade Algebra
- A Magic Square
- 8 3 4
- 1 5 9
- 6 7 2
37Page-De Marchi Again
38Page-De Marchi Again
39Page-De Marchi Again
40Page-De Marchi Again
41Page-De Marchi Again
42Page-De Marchi Again
43An 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.
44What Is Hard Can Be Easy
- Theorem For any problem there exists a
representation such that the problem of finding
an optimal solution is easy.
45Water Flow Problem
- Three valves (x,y,z) open 1, closed 0
- Flow x y z - 2xy - 2yz - 2xz 4xyz
46 Walsh Functions
- Walsh Function 3
- W(x,y,z) 0 if 1s is even
- W(x,y,z) 1 if 1s is odd
- W(x,y,z) x y z - 2xy - 2yz - 2xz 4xyz
47Caution
- 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 Heuristics
- Heuristics are techniques that we use for finding
solutions. They can take many forms - - simulated annealing algorithms
- - rule of 72
- - do the opposite
49Heuristic Example
- Fill in the blank
- 1 2 3 5 _ 13
50Answer
51Heuristic
52Next Question
53Answer
54Heuristic
55Last One!
56Answer
57Heuristic
- 1 2 6 42 1806
- xi1 xi xi 2
- 6 2 22
- 42 6 62
- 1806 42 422
58Combining Heuristics
-
- 1 2 6 42 1806
- xi1 xi xi 2
- This is a combination of the first two heuristics
59One plus one equals THREE
- By knowing two heuristics, you know three
heuristics The two individual heuristic plus
the combined heuristic.
60Interpretations
Reality consists of many variables or attributes.
People cannot include them all. Therefore, we
either - consider only some attributes - lump
things together
61Lump 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.
62Real Life Examples
- Kerry is a liberal
- Soccer moms and NASCAR Dads
- Price Earnings Ratios
- Autism
- Modern Art
- SKA
63An 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.
64The Outcome Function
student
O C A R
G
G
G
B
O
G
G
G
B
C
advisor
G
B
B
B
A
G
B
B
B
R
65Advisor Type Interpretation
prediction
G
G
G
B
O
G
C
G
G
G
B
G
advisor
B
G
B
B
B
A
R
B
G
B
B
B
66Student Type Interpretation
student
O C A R
G
G
G
B
G
G
B
G
G
B
B
B
G
B
B
B
prediction
G
G
B
B
67Making 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.
68Miles Davis
Experts parse the world more finely than the rest
of.
69Chicago El 1992
red line max 70K riders blue line max
80K riders
70Chicago El 1992
red line max 70K riders blue line max
80K riders
40K
80K
70K
30K
71Chicago El 1992
red line max 70K riders blue line max
80K riders
40K
80K
70K
30K
72Chicago El 1992
yellow line max 40K riders purple line max
80K riders
40K
80K
70K
30K
73Toolboxes vs Measuring Sticks
- We can think of a persons ability as her
collection of tools -- her perspectives, her
heuristics, and her mental models -- and not as
an IQ score.
74More 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!
75Toolboxes and IQs
- Suppose 50 possible tools
- Sarah knows 20
- Frank knows 12
- What are odds that Sarah knows all that Frank
knows?
76Toolboxes 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
77An Implicit Cheat
- I assumed that any tool can be acquired. (I
think Ill 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.
78Ladder 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.
-
79Many Ladders Model
- Probability
- of Ladders Sarah gt Frank
- 1 100
- 2 29
- 3 9
- 4 1
- 5 0.005
80A Puzzle
- Why do people in the humanities and the arts
believe in the value of diversity and why do
people in the sciences not?
81We Believe What We Know
-
- Discipline of Ladders
- Math Very Few
- Physics Very Few
- Economics Few
- Political Science Several
- Literature Many
82Summary
- We dont 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
83Whats Next
- Individual diversity influences collective
performance. - ExplainWisdom of Crowds
- See that diversity and ability merit equal
standing