3Wisdom of the Crowd Information Aggregation On Who Wants to be a Millionaire, the lifeline is correct 2/3 of the time. The audience is correct 9/10 times!
4Goldcorp ChallengeIn 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.
5Galton’s SteerAt 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.
10In the case of Galton’s 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.
11When Diversity Matters If Average Error is small, the task is easy. Diversity doesn’t help.Group-think and deference to experts reduce the quality of the decisions.
12Cognitive Diversity Matters in Problem Solving Page Distinguishes: Diversity in Perspective Diversity in Heuristics
13Sum to Fifteen (Herb Simon, Nobel Prize in Economics) 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.
17Perspectives Trig functions If y = sin(x), is x a) an angle b) a distance around the unit circlec) a position on the real axis?Coordinate Systems: Cartesian, Polar, SphericalFunctional representations: recursive, parametric, vector
19Einstein and BohrEvery Tuesday from 3:00 to 4:00 in the afternoon, Niels Bohr and Albert Einstein would play duets together when they were both at Princeton.Einstein would playthe violin and Bohrwould play the piano.How would the history of science be different if Einstein had played the discrete instrument and Bohr the continuous instrument?
23PerspectivesWhen 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.
24HeuristicsProcess by which solutions are found within a perspective. Problem Solving Techniques.CalculusDo the Opposite (Castanza Rule Princeline.com)Error Allowing Heuristics (Explore vs Exploit)Simulated Annealing(aka Brainstorming)
25IQ Test Question or 1+1=3In each sequence, replace the X with the unique number that makes the sequence logically consistent.Sequence 1: X 36Sequence 2: X 13Sequence 3: X
271+1 = 3 or maybe 4Sequence 3: X Differences and Squares 2 – 1 = 12 6 – 2 = 22 X – 6 = – X = 422
28Perspectives are ways of seeing the problem 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.
29Innovations 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.
30Multiple Perspectives and Heuristics are Essential We Now Work in Teams
40Condition #1 “Calculus Condition” All Problem Solvers are Smart(relevant cognitive skills)All problem solvers can move theball up or, at least, keep itat the same level.
41No individual problem solver always locates the global optimum Condition #2The Problem is DifficultNo individual problem solver always locates the global optimum
42Condition #3 DiversityAny solution other than the global optimum is not a local optimum for some non-zero percentage of problem solvers.When one agent gets stuck, there is always another agent that canfind an improvement using adifferent perspective or heurisitic.The intersection of all local maxcontains only the global max.
43Condition #4Good-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.
44Diversity 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.)
48Making 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 don’t.Academy of Mangement Perspecitves, Nov. 2007, page 11
49Making 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 don’t.Scott Page, from Academy of Management Perspectives, Nov. 2007, page 11
50Making 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 Management Perspectives, Nov. 2007, page 11
51Problems of Diversity Communication Misunderstanding and Mistrust (Problem solvers with diverse perspectives may have difficulty understanding each other)Misunderstanding and MistrustLess comfortable atmosphere(We are all more comfortable with like-minded individualsIf people do not believe in the value of diversity, then when part of a diverse team, they are not as likely to produce good outcomes.)
52Final 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.
53ReferencesScott Page, The Difference, Princeton University Press, 2007.Scott Page, Making the Difference: Applying a Logic of Diversity, Academy of Mangement Perspecitves, Nov (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, vol no – (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.