a logic of diversity ii
DESCRIPTION
A Logic of Diversity II. Scott E Page Complex Systems, Political Science, Economics and Institute for Social Research University of Michigan Santa Fe Institute. Enlarging The Mantra. Identity, Training, Experiential Diversity. Diverse Perspectives. Better Outcomes. - PowerPoint PPT PresentationTRANSCRIPT
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Michigania 02005
A Logic of Diversity II
Scott E Page
Complex Systems, Political Science, Economics and
Institute for Social Research
University of MichiganSanta Fe Institute
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Michigania 02005
Enlarging The Mantra
Identity,
Training,
Experiential
Diversity
Diverse
Perspectives
Better
Outcomes
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Monday’s Talk: Unpacking The First Box
Diverse
Perspectives
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Monday’s Talk: Unpacking The First Box
Perspectives
Heuristics
Interpretations
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Today’s Talk: Demonstrating Causality
Diverse
Perspectives
Better
Outcomes
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Specific Tasks
Problem SolvingPrediction
Preference Aggregation
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Why Construct Models?Models allow us to provide conditions for
when a statement is true.
The Pythagorean Theorem: ``A-squared equals B-squared plus C squared’’ only holds for right triangles.
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Finding the Conditions``Two heads are better than one!’’
``Too many cooks spoil the broth’’
Which one wins? Which do we apply in a given setting.
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Finding the Conditions``Two heads are better than one!’’
``Too many cooks spoil the broth’’
Condition: For an irreversible process, too many cooks spoil the broth.
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Swarm of BeesAlmost all of social science looks at
averages and changes in those averages.
Analogy: if you look at a swarm of bees, the path of any one bee is hard to predict and understand, but in the swarm all of those idiosyncratic behaviors cancel out and we can identify general trends.
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The BuzzBee hives must stay around 96 degrees in
order for bees to reach maturation. Bees achieve this by genetic mechanisms that drive two behaviors:
When hot: fan out or leave the hiveWhen cool: huddle together
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Diversity and HomeostasisGenetically homogeneous bees: All
get cool (or hot) at the same time. Temperature in hive fluctuates wildly. (1930’s heating system)
Genetically diverse bees: Get cool (or hot) at different temperatures. Temperature stabilizes.
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Rethinking the SwarmThe logic of cancellation does not hold
because there are feedbacks between the bees. Those feedbacks imply we cannot look at averages.
Groups of people solving problems, making predictions, and making choices create feedbacks in abundance.
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Problem Solving
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Problem Solving
Perspectives
Heuristics
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The Idea
135 91 A,b,x x,M
Thermometer: Toolbox: SAT,IQ skills, heuristics
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Perspectivenumber of chunks
size
Ben & Jerry’s Ice Cream Array
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Heuristicnumber of chunks
size
Ben & Jerry’s Ice Cream Array
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Consultant
perspective: caloric rank
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Consultant
perspective: caloric rankheuristic: look left and
right
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Performance
• Average Performance Given– solution in perspective– application of heuristics
• Ben and Jerry– average quality of solution = 82
• Consultant- average quality of solution = 74
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Perspective Diversity
8375
7381
80
Ben and Jerrystuck at 83
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Perspective Diversity
8375
7381
80
86 8380 74
Ben and Jerrystuck at 83
consultantGets to 86
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Diversity or Ability: A Test
Create a bunch of artificial problem solving agents and rank these agents by their average performances on a difficult problem.
All of the agents must be “smart”
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Two Groups• Group 1: Best 20 agents• Group 2: Random 20 agents
Have each group work collectively - when one agent gets stuck at a point, another agent tries to find a further improvement. Group stops when no one can find a better solution.
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The IQ View
138
75
121 84
Alpha Group Diverse Group
132 135
139
135
137
135
111
31
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And the winner is..
“Most of the time” the diverse group outperforms the group of the best by a substantial margin.
See Lu Hong and Scott Page Proceedings of the National Academy of Sciences (2002)
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The Toolbox View
ABD
EZ
AHK FD
Alpha Group Diverse Group
ADE BCD
ABC
BCD
ACD
BCD
AEG
IL
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Formal Version
Theorem: Given a set of diverse problem solvers, a random collection outperforms a collection of the “best” individual problem solvers provided
-the set is large-the problem is hard-the problem solvers are smart
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Prediction.
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Prediction.
Interpretations Mental Models
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The Madness of Crowds
We tend to think of crowds of people as irrational mobs. And that can be true. When people hear the ideas and opinions of others, they often succumb to peer pressure rather than speaking their own minds.
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Which Line is Longer?
A: _____________
B: ___________
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The dim boy claps because the others clap.
- Richard Hugo
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The Wisdom of Crowds
If people do not hear the opinions of others, or if they render their true predictions anyway crowds can be incredibly wise.
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Suroweicki’s Examples
Morton Thiokol’s stock plungePrediction Markets
Hollywood Stock ExchangeIowa Electronic MarketSports Betting Markets
Who Wants to be a Millionaire1906 West of England Fat Stock and
Poultry Exhibition
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Two Separate Phenomena1. Information known by part of the crowd
2. Aggregative diverse predictive models
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Revealing Known Information
Which of the following books would you NOT find in the Point o’ Pines Library
A. The Periwinkle Steamboat - LancasterB. Curtains - Agatha ChristieC. Unabridged Crossword Puzzle DictionaryD. I am Charlotte Simmons - Tom Wolfe
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Information RisingSuppose that no one know the answer but
that 18 people know one of the books on the list is in the library and that 18 people know two of the books on the list are in the library. This means that 64 people guess randomly.
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Information Rising
Of 64 Clueless: Correct answer gets 16Of 18 know one: Correct answer gets 6Of 18 know two: Correct answer gets 9
Total 31
Other answers get 23 (on average)
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The Answer Is…Which of the following books would you NOT find in
the Point o’ Pines Library
B. Curtains - Agatha Christie
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Aggregating Diverse Predictions
In most of the situations described, people do not know the answer yet. We can assume that people have diverse predictive models. We’d like to understand how that aggregation occurs and what roles diversity and ability play.
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Reality
CharismaH MH ML L
H Experience
MH ML
L
G G G
G G G G
G
G
B
B
B
B
B
B
B
B
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Experience Interpretation
HExperience MH
ML
L
G G G
G G G G
G
G
B
B
B
B
B
B
B
B
B
B
B
B
B G
G
75 % Correct
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Charisma Interpretation
H MH ML L
75% Correct
G B
G BBBG
G G
BG G
BG G
BG G
G
G
B
B
B
B B
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Balanced Interpretation
H MH ML L
75% Correct H
Good to beextreme on one MHmeasure, bad on other ML
L
G G G
G B G G
G
G
B
B
B
B
B
B
B
B
B
G
G
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Voting OutcomeCharisma
H MH ML L
H
MH ML
L
GGB GGG GBG
GGG GGB G GBG
BGG
BGG
BGB
GBB
BBG
BBB
BBB
BBG
BBG
BGB
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The Mathematics of Prediction
Prediction: # runs scored by winning softball team
Mon Tue WedBrad 8 10 9Matt 10 12 8
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“Crowd’’ Prediction
Mon Tue WedBrad 8 10 10Matt 10 12 8Crowd 9 11 9
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Actual Numbers
Mon Tue WedBrad 8 10 10Matt 10 12 8Crowd 9 11 9Actual 8 12 9
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Squared Errors
Brad: (8-8)2 +(10-12)2 +(10-9)2 = 5
Matt : (10-8)2 +(12-12)2 +(8-9)2 = 5
Crowd: (9-8)2 +(11-12)2 +(9-9)2 = 2
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Diversity of Predictions
(Brad-Crowd)2 = 1 + 1 + 1 = 3 (Matt-Crowd)2 = 1 + 1 + 1 = 3
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Notice: 2 = 5 - 3
Crowd Error = Average Error - Diversity
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Diversity Prediction Theorem
Crowd Error = Average Error - Diversity
(note: proven by statisticians, computer scientists, and economists)
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Crowd = Average - Diversity
• Diversity as important as ability
• Limit to how much diversity(otherwise crowd error would be negative)
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Experts on NFL DraftPlayer #1 #2 #3 #4 #5 #6 #7 #8 Alex Smith 1 1 1 1 1 1 1 2 Ronnie Brown 2 2 4 2 2 5 2 6 Braylon Edwards 3 3 2 7 3 2 3 3 Cedric Benson 4 4 13 4 8 4 8 4 Carnell Williams 8 5 5 5 4 13 4 8 Adam Jones 16 9 6 8 6 6 9 17
Error^2 158 89 210 235 112 82 39 300
Average Error: 153.13Diversity: 101.52
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Crowd of Experts on NFL Draft
Player CrowdAlex Smith 1.13 Ronnie Brown 3.13Braylon Edwards 3.25Cedric Benson 6.13Carnell Williams 6.50Adam Jones 9.63
Error^2 51.61
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Crowds Beat Averages Law
Crowd Error < Average Error
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Does Crowd Beat Best?
In the NFL draft example, the best predictor Pete Brisco had an error of only 39. He outperformed the crowd, which had an error of 51.6.
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Novices and Experts
Novices: Base their models on only a few variables or a few boxes.
Experts: Base their models on many variables or many boxes.
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In Praise of Experts
Theorem: If an expert contains every variable considered by any one of the novices, the expert predicts better than the crowd of novices.
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Crowds vs Experts
Test Set: Linear functions defined over 20 variables.
Crowd: Each of 100 novices looks at N randomly chosen variables
Expert: Looks at E>N variablesTraining: 300 independent
variablesContest: 300 independent variables
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Crowds vs Experts% of Time
N E Expert Wins3 20 94.66%3 15 34.66%5 10 29.33%5 7 9%
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What’s Happening
Expert: Getting best fit over all his variables.
Crowd: Getting an average of many fits over many distinct subsets of variables.
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Put Another Way
Expert: Great partial view
Crowd: So-so complete view
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Diversity and Prediction
Diverse predictors generate better predictions unless someone’s head is large enough and data is sufficient enough for a complete model.
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Preference Aggregation
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Instrumental vs Fundamental
Fundamental Preferences: Preferences over outcomes
Instrumental Preferences: Preferences over policies to attain outcomes
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Instrumental Politics“I am the _____ candidate”
A.Pro crimeB.Anti childC.Anti environmentalD.Pro drug addictionE. Higher health care costs
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Preference Diversity Problems
• Preference Cycles
• Manipulation
• Underprovision
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Preference Cycle
A = Arts & Crafts, B = Boating, T = Tennis
Lindsey: A > B > T Samuel: B > T > ABecca : T > A > B
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Preference Cycle
Lindsey: A > B > T Samuel: B > T > ABecca : T > A > B
• Majority Vote Outcome: A > B > T > A
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ManipulationGiven any voting rule, people with
diverse preferences will always have an incentive to misrepresent themselves.
Implication: People in diverse groups will not trust one another as much.
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Under Provision
If we want different outcomes and have a fixed budget, we are likely to spread our money too thin.
Idea: Rather than have a good car or a nice boat, we have a lousy car and a lousy boat.
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Theoretical Summary
Tasks involve- Solution Generation (problem solving)- Evaluation (prediction)- Choice (preference aggregation)
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Michigania 02005
“Diversity is Ability”
To be different is to be able to make a contribution.
Diversity Trumps Ability: Diverse group does better than “able” group at problem solving
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Michigania 02005
“Diversity is Ability”
Diversity Prediction TheoremCrowd Error = individual error -
diversity
(ability and diversity enter equally)
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Michigania 02005
ComplicationPreference diversity creates cycles.
It creates incentives to act strategically and to manipulate agendas.
At the same time, preference diversity may be a primary cause of the other types of diversity.
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Michigania 02005
SummaryThe empirical evidence suggests
that diverse perspectives, mental models, and tools lead to “better outcomes” but that value diversity creates problems.
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Michigania 02005
Pudding
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Michigania 02005
Quick Look at the ``Facts’’• Growth of modern civilization• National level GDP• City level productivity• Diverse team performance
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Michigania 02005
Rise of Modern Civilization• Jared Diamond: diversity/easy
problems• Joel Mokyr: exploiting diversity• Michael Kremer: 1 million years of
data shows growth and population size correlated
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Michigania 02005
National Level GDP• Paul Romer: Diversity crucial to
economic growth• Ethnic Linguistic Fractionalization
(ELF): strongly negatively correlated with economic growth
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Michigania 02005
Performance of Cities (42)• Doubling of city size increases
productivity by 6% to 20%• Arrow, Lucas: spillovers within an
industry (silicon valley)• Jacobs, Auerbach: spillovers
between industries (just in time)*
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Michigania 02005
Identity Diverse Teams• Generate more solutions (many
worse)• Thomas and Ely: do better if they
have diverse heuristics and perspectives
• People in diverse groups are less happy - world views are challenged - feel like outcomes were
manipulated
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Michigania 02005
The End of Great Scientists First 10
Physics Nobels: 14 Chemistry Nobels: 10
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Michigania 02005
The End of Great Scientists First 10 Last 10
Physics Nobels: 14 28Chemistry Nobels: 10 27
(There’s a maximum of three)
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Michigania 02005
Final ThoughtIndividual ability not likely to grow
much.
Collective diversity can grow.
Diversity is our best hope to solve problems and to create innovations.
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Michigania 02005
www.cscs.umich.edu/~spage