Bayes and Prejudice
Detlof von Winterfeldt
Professor of Industrial and Systems Engineering
Professor of Public Policy
Director, Center for Risk and Economic Analysis of Terroris Events
University of Southern California
EURO 2016
Poznan, Poland
July 4, 2016
Two Fundamental Errors in
Human Probability Judgment
• Equating P(H|D) with P(D|H)
– 90% of all CEOs of all Fortune 500 companies
(CEO) had a pet when they were young (Pet)
– P(Pet|CEO) = 0.90
– P(Pet|Not CEO) = 0.90
• Ignoring base rates
– Taxicab problem
– P(HIV|positive RAPID test)
Reverend Bayes to the Rescue
Bayes’ Theorem
or in odds-liklihood ratio form
Takeaway Points of this Presentation
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•
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These errors are common
They contribute to prejudice
Using Bayes theorem can fix these errors
We should find simple ways to eliminate them!
Pitbulls and Profiling
(Courtesy of Malcolm Gladwell, The New Yorker, 2007)
Would You Pet this Dog?
Let’s Look at the Data: Fatal Attacks by Dog Breed
Number of Fatal Dog Attacks (1979-1998)
Breed
Number
Pitbull
76
Rottweiler
44
German Shepard
27
Other
91
TOTAL
238
Percent
32%
18%
11%
38%
100%
A Simple Calculation
• P(Pitbull|Attack) = 0.32
• P(Attack|Pitbull)= P(Pitbull|Attack)*P(Attack)/P(Pitbull) = ?
• Inputs:
–
–
–
–
Attacks = 238/20years = 11.9/year
Number of dogs: 80 million/year
P(Attack) = 11.9/80m = 1.49*10-7
P(Pitbull) = 0.05 (about 4 million pitbulls)
• Answer = 0.32*1.49*10-7/0.05 ~ 10-6
• About the same as dying in a plane crash in 1 RT
Venn Diagram of Pitbull Attacks
80 million Dogs
~12 Fatal
~4
Attacks
Pitbull  Fatal Attack
4 million Pitbulls
Non-Breed Factors
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•
•
•
•
•
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Gender (male)
Reproductive state (not neutered)
Dog size
Dog’s past behavior
Owner behavior (trains agression; neglects; chains)
Owner not present during attack
Victim (defenseless or elderly)
A Terrorism Example
Recent Announcement at
Washington Dulles Airport:
“Will Muhammed Ramzi, Ali Azhar, and
Abdullah Saliba please proceed
immediately to boarding gate 84 – Your
plane to Munich is about to leave”
What Do We Know?
• Three men with Arab names
• Traveling from DC to Munich
• Late for the flight
________________________________
P(Terrorists|Arab Names) = ???
Application to Terrorists
All Passengers
Terrorists
Terrorists  Arab Name
150 Million People
With Arab Name
What To Do?
• Find more important and more powerful
distinguishing categories
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–
–
–
–
Age
Watch lists
Travel indicators
Past criminal record
Behavioral indicators
____________________________________
Given these indicators, the name or ethnicity may not
add much relevant information
Scientists Make Similar Mistakes
• “Childred with childhood leukemia are 20% more
likely to live near high-voltage power lines than
those that don’t”
• Should a family with two children worry about
buying a house near a powerline?
• P(Childhood Leukemia) ~ 1 in 10,000
• 20% increases this to 1.2 in 10,000
• Survival rate is 90%
Takeaway Points of this Presentation
• These errors are common
– Made by laypeople and experts
– Provide more dramatic reports of statistical findings
• They contribute to prejudice
– Used by people who pander to prejudice
– Provide drama and “human interest” to journalists
• Using Bayes’ Theorem can fix these errors
– Should we teach Bayes’ Theorem in elementary school?
• We should find simple ways to eliminate these errors
– Venn diagrams with simple counts?
– Similar approached by Gigerenzer and Hastie and Dawes