70-386 Behavioral Decision Making

70-386 Behavioral Decision Making Lecture 4: More Biases

Administrative • Quiz • More review questions posted tonight • Although many of them will come from last week’s problem set. • Paper presentations • Groups assigned • First paper presentation this week • We’re going to be off schedule a bit • I’ll post an update soon • Seeing that almost no one had seen Bayes theorem, I’m going to go over it today. You’ll be required to know it.

Improper Linear Models • Assigned reading: Dawes (1979) and see RCUW Chp 3 for more info. • Linear model • Y = a + bX +cW + dZ • Proper linear model • (a,b,c,d) are calculated via some optimal (statistical) procedure • Improper linear model • (a,b,c,d) are not optimally calculated (can be random, equal weighting, etc). • Take away: interviews can fail to be diagnostic

Bayes’ Theorem:The Decision Analysis Version • Alternatively you think of Bayes’ Theorem as involving hypotheses (“H”) and observations (or tests, “T”)

False Positives and Negatives • Accuracy is a function of minimizing the probability of false positives and negatives • Accuracy is often stated as a simple percentage: 95% accurate • Unless otherwise qualified, we’ll assume that it’s symmetric: P(T= true | H=true) = P(T=false | H=false) = 0.95 • Viewing the problem this way suggests a four-fold partition

Conditional Probability as a Matrix Test Actual Illness

An Example: HIV Testing • P(HIV = true) = 0.0076 • P(“Positive” | HIV=true) = 0.976 • P(“Negative” | HIV=false) = 0.995 • Note that P(HIV = true) = 1 – P(HIV = false) • Given the test’s accuracy, P(“Positive” | HIV=true), what is P(HIV=true | “Positive”)?

Bayes Table • Fill out the table, given: • P(HIV = true) = 0.0076 • P(“Positive” | HIV = true) = 0.976 • P(“Negative” | HIV = false) = 0.995 • What is P(HIV=true |“Positive”)? P(HIV=true &“Positive”) P(“Positive”)

The Bayes Table 1 – Rate of True Positives (“False Negatives”) Rate of True Positives (“Accuracy”)

The Bayes Table 1 – Rate of True Positives (“False Negatives”) =1-0.9760 Rate of True Positives (“Accuracy”)

The Bayes Table 1 – Rate of True Positives (“False Negatives”) Rate of True Positives (“Accuracy”) Joint Probability 0.024 × 0.0076

The Bayes Table 1 – Rate of True Positives (“False Negatives”) Rate of True Positives (“Accuracy”) Joint Probability 0.024 × 0.0076 Joint Probability 0.976 × 0.0076

The Bayes Table 1 – Rate of True Positives (“False Negatives”) Rate of True Positives (“Accuracy”) Joint Probability 0.024 × 0.0076 Joint Probability 0.976 × 0.0076 1 – Rate of True Negatives (“False Positives”) = 1-0.995

The Bayes Table 1 – Rate of True Positives (“False Negatives”) Rate of True Positives (“Accuracy”) Joint Probability 0.024 × 0.0076 Joint Probability 0.976 × 0.0076 1 – Rate of True Negatives (“False Positives”) = 1-0.995 Joint Probability 0.99.5 × 0.9924

The Bayes Table 1 – Rate of True Positives (“False Negatives”) Rate of True Positives (“Accuracy”) Joint Probability 0.024 × 0.0076 Joint Probability 0.976 × 0.0076 Joint Probability 0.9924 × 0.005 1 – Rate of True Negatives (“False Positives”) = 1-0.995 Joint Probability 0.99.5 × 0.9924

The Bayes Table 1 – Rate of True Positives (“False Negatives”) Rate of True Positives (“Accuracy”) Joint Probability 0.024 × 0.0076 1 – Rate of True Negatives (“False Positives”) Probability Test Says NOT HIV+ 0.0002 + 0.9874

Now What? • To calculate P(HIV = true |“Positive”), divide entries in this table • P(HIV|“Positive”) = 0.0074/0.0124 = 0.5992

Testing Results • Note that despite the seemingly high accuracy of the test, the probability of actually being HIV+ given a positive test result is not that high: ~60% • By comparison, the probability of NOT being HIV+ given the test indicates you are not HIV+ is very high: 99.98% (0.9874/0.9876) • The rate of false positives is 40.08% (0.0050/0.0124)

Using Bayes’ Formula

Representativeness Heuristic:Base Rates Back to our problem: • Lisa takes the Triple Screen and obtains a positive result for Down syndrome. Given this test result, what are the chances that her baby has Down syndrome? • Most people would say that it’s very likely that the baby has Down syndrome – they neglect the prior, or base rate, information: Down syndrome is rare. • Actual posterior probability: 1.69% • Base Rate Neglect can often be thought of as reasoning without thinking • Background vs Foreground information • The base rate of Down syndrome was in the background, neglected • The results of the test were in the foreground, more readily accessible

Misconceptions of Chance • Pattern recognition is a fundamental human strength • Taken too far, however, it becomes a weakness • We often see patterns where none actually exist because we are “programmed” to seek patterns • Actual patterns can appear in random sequences, but that doesn’t change the fact that they’re still random • Which is sequence is more likely to be random: • A B A B B A B B A B B A B A A B A B A A • A B B A AA B B A B BB A A B B A A B B

Misconceptions of Chance • Which is sequence is more likely to be random: • A B A B B A B B A B B A B A A B A B A A • A B B A AA B B A B BB A A B B A A B B • Out of 19 possible alternations, (1) has 14 changes, and (2) has 9 changes. For a truly random sequence, how many changes should be expected – regardless of our perception of ‘patterns’? • Runs Test: 9.5

Misconceptions of Chance • The mechanism behind the failure to understand randomness drives what’s called the “gambler’s fallacy” • Winning hands are due. • KT: Chance is seen as self-correcting. A deviation in one direction is counterbalanced by a move in the other. • “Hot hands” in sports • Business applications?

Regression to the Mean • We’re generally really bad at understanding the probabilistic nature of most random events. • It’s not that bad outcomes will follow good ones, or visa versa. Average outcomes follow either • Examples: aka the ‘sophomore jinx’ • Movie sequels are often worse than the great movies by which they are prompted • Athletes who appear on Sports Illustrated covers often then experience worse performance (the “SI curse”) • Punishment works; praise doesn’t Business applications? • Performance evaluations

Conjunction Fallacy Linda is 31 years old, single, outspoken, and very smart. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and she participated in antinuclear demonstrations. • Rank the following eight descriptions in order of probability (likelihood) that they describe Linda: • ___a. Linda is a teacher in elementary school. • ___b. Linda works in a bookstore and takes yoga classes. • ___c. Linda is active in the feminist movement. • ___d. Linda is a psychiatric social worker. • ___e. Linda is a member of the League of Women Voters. • ___f. Linda is a bank teller. • ___g. Linda is an insurance salesperson. • ___h. Linda is a bank teller who is active in the feminist movement.

Conjunction Fallacy Most people rank 3 > 2. Actually, 100% of you did. • Linda is active in the feminist movement. • Linda is a bank teller. • Linda is a bank teller who is active in the feminist movement. Can’t be. Why? • P(A &B) ≤P(A) and P(A & B) ≤P(B) • Being a subset (bank teller AND feminist) can’t be larger than the set that includes it (bank teller) • The conjunction of two events is always equal or less probable than the individual events • But…conjunction often provides or completes the “story” Implications? • People find it very difficult to reason about isolated events • People in business often reason by anecdote (e.g., case studies, “war stories”), but such reasoning is often grossly biased when it comes to communicating probabilistic information

Representativeness Results of a recent survey of 74 Fortune 500 CEOs indicate that there may be a link between childhood pet ownership and future career success. Fully 94% of them had possessed a dog, or cat, or both as youngsters . . . . The respondents asserted that pet ownership had helped them develop positive character traits that make them good managers today: responsibility, empathy, generosity, and good communication skills.” -Management Focus, November 1984 • How about this? • “Fully 100% of the CEOs brushed their teeth as children…” • Why not make that assertion?

70-386 Behavioral Decision Making