When Can Diversity Trump Ability?

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When Can Diversity TrumpAbility?

• Dan Teague
• NC School of Science
• and Mathematics

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Scott Page, Lu Hong, John Miller
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Wisdom of the CrowdInformation Aggregation

• On Who Wants to be a Millionaire, the lifeline is
  correct 2/3 of the time.
• The audience is
• correct 9/10
• times!

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Identify the non-Monkee

• a) Peter Tork
• b) Michael Nesmith
• c) Roger Noll
• d) Davy Jones

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Crowd of 100 people

• 7 know all three of the Monkees listed
• 10 know two of the Monkees listed
• 15 know only one of the Monkees listed
• 68 know nothing about the Monkess
• What would the wisdom of the crowd show?

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The Vote

• 7 know all three of the Monkees
• 7 votes for Roger Noll
• 10 know two of the Monkees
• Expect 5 Votes for Roger Noll
• 15 know only one of the Monkees
• Expect 5 Votes for Roger Noll
• 68 know nothing about the Monkees
• Expect 17 Votes for Roger Noll
• 34 votes for Roger Noll

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Goldcorp Challenge

• In 1999 CEO Rob McEwen instructed his geologists
  to release all geological records to the public.
  The Goldcorp Challenge offered 575k to anyone
  who could find the gold and drew 1,200 people
  from 50 countries.
• Results
• 110 sites identified 50 new, 80 produced gold.
• 8 million ounces found.
• Company value up from 100 million to 9 billion.
•  

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Galtons Steer

• At the 1906
• West of England
• Fat Stock and Poultry Exhibition, 787 people
  guessed the weight of a steer. Francis Galton
  collected the data and found the average guess
  was 1,197 pounds. The actual weight of the steer
  was 1,198 pounds.

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Accuracy of Group Predictions
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Computing the Squared Error(Variance)
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Computing the Crowds Diversity
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Diversity Prediction Theorem 38
39 - 1
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• In the case of Galtons steer, the collective
  accuracy was approximately 1, the average
  accuracy was 2,956 and the diversity was 2,955.
  This means that individuals missed by about 55 or
  60 pounds each. The fairgoers owe their
  collective accuracy more to their remarkable
  diversity than to the prescient individual
  abilities.

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When Diversity Matters

• If Average Error is small, the task is easy.
  Diversity doesnt help.
• Group-think and deference to experts reduce the
  quality of the decisions.

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Cognitive Diversity Matters in Problem Solving

• Page Distinguishes
• Diversity in Perspective
• Diversity in Heuristics

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Sum to Fifteen (Herb Simon, Nobel Prize in
Econmics)

• One player randomly chosen to go first.
• Alternate turns selecting cards.
• The winner is the first player who has
• exactly 3 cards which sum to 15.

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Picnic Basket Game

• Nachos (N)
• Eggs (E)
• Sausage (S)
• Water (W)
• Hot Dogs (H)
• Vinegar (V)
• Lemons (L)
• Raisins (R) Goal is to Collect all 3
  
• Copies of One Food Item

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Tic Tac Toe
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Perspectives

• Trig functions
• If y sin(x), is x
• a) an angle
• b) a distance around the unit circle
• c) a position on the real axis?
• Coordinate Systems Cartesian, Polar, Spherical
• Functional representations recursive,
  parametric, vector

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Mendeleyevs Periodic Table
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Einstein and Bohr

• Every Tuesday from 300 to 400 in the afternoon,
  Niels Bohr and Albert Einstein would play duets
  together when they were both at Princeton.
• Einstein would play
• the violin and Bohr
• would play the piano.
• How would the history of science be different if
  Einstein had played the discrete instrument and
  Bohr the continuous instrument?

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Differing Perspectives
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Perspectives

• When people see a problem from the same
  perspective, they are likely to get stuck on the
  same local peaks.
• New perspectives can clarify or muddy. Sum to 15
  can be seen as Tic Tac Toe or as the Unpacking
  Game.

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Heuristics

• Process by which solutions are found within a
  perspective. Problem Solving Techniques.
• Calculus
• Do the Opposite (Castanza Rule Princeline.com)
• Error Allowing Heuristics (Explore vs Exploit)
• Simulated Annealing
• (aka Brainstorming)

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IQ Test Question or 113

• In each sequence, replace the X with the unique
  number that makes the sequence logically
  consistent.
• Sequence 1 1 4 9 16 X 36
• Sequence 2 1 2 3 5 X 13
• Sequence 3 1 2 6 X 1,806

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• Sequence 1 1 4 9 16 25 36
• Square
• Sequence 2 1 2 3 5 8 13
• Differences 1 2 3
  5
• Sequence 3 1 2 6 X 1,806

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11 3 or maybe 4

• Sequence 3 1 2 6 X 1,806
• 42
• Differences and Squares
• 2 1 12
• 6 2 22
• X 6 62
• 1,806 X 422

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• Perspectives are ways of seeing the problem. They
  create different landscapes.
• Heuristics are ways of constructing solutions.
• The more productively a perspective organizes
  reality, the more heuristics people can create to
  work in that perspective.

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• Innovations can arise from rearranging the box
  with a new perspective or from exploring parts of
  the box that have been ignored with new
  heuristics.
• Diverse perspectives are more likely to lead to
  breakthroughs diverse heuristics are more likely
  to leader to iterative improvements.

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Multiple Perspectives and Heuristics are
Essential We Now Work in Teams
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and when working in teams
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Selecting Talent (how we think about whos
good)Scores vs Toolkits
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Two Views of Ability
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Under what conditions does diversity trump
ability?
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Pages Initial Experiments
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Condition 1 Calculus Condition

• All Problem Solvers are Smart
• (relevant congnitive skills)
• All problem solvers can move the
• ball up or, at least, keep it
• at the same level.

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Condition 2

• The Problem is Difficult
• No individual problem solver always locates the
  global optimum

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Condition 3 Diversity

• Any solution other than the global optimum is not
  a local optimum for some non-zero percentage of
  problem solvers.
• When one agent gets stuck, thereis always
  another agent that can
• find an improvement using a
• different perspective or heurisitic.
• The intersection of all local max
• contains only the global max.

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Condition 4

• Good-sized collections drawn at random from large
  population of potential problem solvers.
• The initial population of problem solvers must be
  large and the collections of problem solvers
  working together must contain more than a handful
  of problem solvers.

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Diversity Trumps Ability Theorem

• Given conditions 1-4, a randomly selected
  collection of problem solvers outperforms,
• on average,
• a collection of the best individual problem
  solvers. (in practice, a.s.)

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The Theorem
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The Basic Idea of the Proof
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Making a Difference Applying the Logic of
Diversity

• The best problem solvers likely have similar
  perspectives and heuristics. The random problem
  solvers bring diverse ways of thinking.
• The best problem solvers all get stuck at the
  same place. The random problems solvers dont.
• Academy of Mangement Perspecitves, Nov. 2007,
  page 11

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Making a Difference Applying the Logic of
Diversity

• The best problem solvers likely have similar
  perspectives and heuristics. The random problem
  solvers bring diverse ways of thinking.
• The best problem solvers all get stuck at the
  same place. The random problems solvers dont.
• Scott Page, from Academy of Mangement
  Perspecitves, Nov. 2007, page 11

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Making a Difference Applying the Logic of
Diversity

• The logic of the theorem does not imply the
  irrelevance of ability. Ability still matters,
  but so does diversity.
• And, as the theorem shows, once an ability
  threshold has been met, diversity matters more
  than ability.
• Scott Page, from Academy of Mangement
  Perspecitves, Nov. 2007, page 11

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Problems of Diversity

• Communication
• (Problem solvers with diverse perspectives may
  have difficulty understanding each other)
• Misunderstanding and Mistrust
• Less comfortable atmosphere
• (We are all more comfortable with like-minded
  individuals
• If people do not believe in the value of
  diversity, then when part of a diverse team, they
  are not as likly to produce good outcomes.)

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Final Thoughts from Scott Page

• Our individual abilities are not likely to growth
  much anytime soon.
• Our collective diversity can grow.
• Diversity is our best hope to solve problems and
  to create innovations.

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References

• Scott Page, The Difference, Princeton University
  Press, 2007.
• Scott Page, Making the Difference Applying a
  Logic of Diversity, Academy of Mangement
  Perspecitves, Nov. 2007. (Google Scott Page
  Academy of Mangement )
• Lu Hong and Scott Page, Groups of diverse problem
  solvers can outperform groups of high-ability
  problem solvers , PNAS November 16, 2004 vol.
  101 no. 46 1638516389. (Google Hong and Page)
• Scott Page, Diversity and Complexity, Princeton
  University Press, 2011.
• John Miller and Scott Page, Complex Adaptive
  Systems, Princeton University Press, 2007.