Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear rallies.

• Rank how likely is it that…– Linda is a teacher.

– Linda works in a bookstore and takes yoga classes.

– Linda is a bank teller.

– Linda sells insurance.

– Linda is a bank teller and is active in the feminist movement.

Judgment and DecisionsJudgment and Decisions

Outline• Heuristics

– Availability – Representativeness– Anchoring– Illusory Correlations & Confirmation bias

• Errors• Base Rate Neglect• Gambler’s Fallacy• Conjunction Fallacy

Heuristic: - a ‘rule of thumb’ for judgment and decision-making - it takes into account only a portion of the available evidence - it allows for fast and efficient decision-making, but- it is vulnerable to error.

Algorithm:- guarantees the correct answer- inefficient (computationally expensive)

Judgment: “how likely is that …?”Decision-Making (Choice): ‘should you take a coupon for $200 or $100 in cash, given that …”

The Availability Heuristic: Examples

Which is more frequent? Words that begin with “R”, or words with “R” as their third letter?

Which household chores do you do more frequently than your partner? (e.g. washing dishes, taking out the trash, etc.) - wives report 16/20 chores

- husbands report 16/20 chores Ross and Sicoly (1979)

Why? Availability!- I remember lots of instances of taking out the trash, washing dishes, but I do not remember lots of instance of my wife doing it

- I can come up with many examples of ‘R_ _ _’, but few of ‘_ _ R_’

The Availability Heuristic

Tendency to form a judgment on the basis of information is readily brought to mind.

Why is it useful?- Frequent events are easily brought to mind (words that start with X)

Why is it sometimes misleading?- Factors other than frequency can affect ease of remembering:

--Ease of Retrieval (the “r” example)

--Recency of the example (advertisement, news)

-- Familiarity (“what % of people go to college?”)

Testing the Availability Heuristic

- Keep frequency invariant - Experimentally manipulate availability

- Measure estimated frequency (dependent variable)

Subjects read a list of names- 50% of names are male names, the rest are female- Group A: Some male names famous (Bill Clinton)- Group B: Some female names famous

Test: Where there more men or women in the list?

The Representativeness Heuristic

The tendency to judge an event as likely if it “represents” the typical features of its category.

Why is it useful?- Typical features often are the most frequent ones Why is it sometimes misleading?- It fails to account for:

- prior odds- Conjunction Fallacy - Base Rate Neglect

- random process- Gambler’s Fallacy

Representativeness Heuristic

• The tendency to assume that categories are homogeneous, and therefore each member is a good example (representative) of the category

• Each individual should have the properties of the category ‘The country is divided 51% vs. 48% ….the average American wants moderation” (this is nonsense)

• The category should have the properties of the individual. This leads to a tendency to generalize from a few cases “I know a man who...”

• This heuristic is close to the similarity heuristic (tendency to judge events as likely if they “represent” the typical features of the category). Eg. Linda the bank teller, lottery # 9834024 vs.999999

Anchoring

• Tendency to reach an estimate by beginning with an initial guess and altering it based on new information.

• In general

– People rely too heavily on the anchor (initial value)

– Adjustments are too small

– even when the anchor (reference point) is known to be uninformative.

Anchoring: Example

“What is the proportion of African nations in the UN?Answer: ‘45%’

“65”

“10” “What is the proportion of African nations in the UN?Answer: ‘25%’

Illusory Correlations

--Does a college education lead to a higher paying job?

-- Are flaws in the personal arena --sexual escapades, DUI-- correlated with flaws in governing the country?

-- Do small dogs bite more often than big dogs?

The perceived correlation between two variables is influenced - by the data we observe - by our personal theories --> Illusory Correlations

When subjects had theories about what they would see….

- The estimates did not show as orderly a relationship with the data.- The correlation values were over-estimated!

Scientists are similarly affected by their theoretical biases

Jennings, Amabile, & Ross, 1982

When subjects observed data without preconceptions...

Illusory correlation: Possible Mechanisms

Confirmation bias. Tendency to notice and remember evidence that confirms our preconceptions.

Data consistent with one’s theories are more easily retrieved.

This increased availability biases our judgment.

Outline• Heuristics

– Availability – Representativeness– Anchoring– Illusory Correlations & Confirmation bias

• Errors• Base Rate Neglect• Gambler’s Fallacy• Conjunction Fallacy

• A single witness is found for a hit and run accident involving a taxi cab. • There are 2 cab companies in this town. • A huge blue cab company (with 1000 cars active at a time) and,• A small green cab company (with 50 cars active at a time).• The witness believes the cab was green. • Subsequent experiments show that this person is 90% accurate in determining the color of cabs.

Is it more likely that the cab was blue or green?

Base Rate Neglect: People’s tendency to neglect the overall frequency of an event when predicting its likelihood.

Base Rate Neglect: Example

1000 blue cabs

Suppose the witness were to identify all the cabs in the city...

50 green cabs

900 “blue”

What the witnesswould report

100 “green”

5 “blue”

45 “green”

“green” answersare more often wrong than right!(100/145 are wrong)

In this case, the base rate information overwhelms the diagnostic information.

Base rate neglect has real world consequences...

Suppose mammograms are 85% likely to detect breast cancer, if it’s really there (hit rate), and 90% likely to return a negative result if there is no breast cancer (correct rejection rate).

Suppose we are testing a patient population with an overall likelihood of cancer of 1%.

If the mammogram detects cancer, what are the odds that the patient really has cancer?

Mammogram Indicates Cancer No Cancer Total

cancer present 850 150 1,000cancer absent 9,900 89,100 99,000

In this case, when the mammogram indicates the presence of cancer, there is an 850/10,750 likelihood that the patient actually has cancer (only about an 8% chance).

While positive results on a mammogram surely indicate that more tests would be wise…they should be viewed in the context of the overall probability of the disease they are testing for.

Studies have shown that doctors have the same base rate neglect tendencies as the rest of the population.

What’s reallythere

From a sample of 30 engineers and 70 lawyers, you randomly draw Jack…(Base Rate Information)

Jack is 45 yrs old... He shows no interest in political or social issues and spends most of his free time on his many hobbies which include... mathematical puzzles. (Diagnostic Information)

How likely is it that Jack is an engineer?

- Diagnostic and Base Rate information are important- however, when both are provided, subjects ignore the Base rate

information and make their judgment based exclusively on the Diagnostic infromation

Base Rate Neglect: Another Example

Question: If a test to detect a disease whose prevalence is 1/1000 has a false positive rate of 5 percent, what is the chance that a person found to have a positive result actually has the disease, assuming that you know nothing about the person’s symptoms or signs?

Participants: Students at the Harvard Medical School

- 1000 people tested, one has the disease (1/1000). This should lead to:- 50 false positives (5%) and 1 hit (assuming perfect sensitivity)- The chance of having the disease if the result comes positive is 1/51 (1.96%) - This is due to the very low base rate (1/1000).

- Almost half of the participants responded 95%. - The average answer was 56%.

The Gambler’s Fallacy: Example

Which sequence of coin tosses is more likely?

1. H T T H H H T2. H H H H H H H

The Gambler’s Fallacy: the misconception that prior outcomes can influence the outcome of an independent probabilistic event. But why?!

Because in the long run heads & tails alternate, so a short run in which heads & tails alternate seems more typical (similar) member of the category.

The error becomes most obvious the shorter the run (or the smallest the sample).

Conjunction fallacy

• What is more likely?– Man has heart attack– Man overweight & 68 y-old has heart attack?

What can help improve the quality of these kinds of decisions?

--Overt cues in each situation can increase the likelihood that people will use probability information. (e.g. emphasizing the role of chance in the lawyers and engineers problem)

--Along the same lines, Agnoli and Krantz taught subjects how to use Venn diagrams to represent categories. This significantly reduced cases of conjunctive fallacy in this group.

--Statistical training increases people’s chances of making use of probability information (at least a little bit).

Hooray for psychology!!!

College Helps...

Spare ones

Base Rate Neglect

People’s tendency to neglect the overall frequency

of an event when predicting its likelihood.

Base Rate Neglect: Example

Steve is very shy and withdrawn, invariably helpful, but with little interest in people or in the world or reality. A meek and tidy soul, he has a need for order and structure, and a passion for detail.

Is Steve a Librarian or salesperson?

Anchoring Error: Example

Estimate as quickly as you can, the answer to this math problem:1 x 2 x 3 x 4 x 5 x 6 x 7 x 8=?

Correct answer: 40,320 Median answer: 512!!

When the problem was stated as8 x 7 x 6 x 5 x 4 x 3 x 2 x 1= ?

Median answer was 2250 (still low, but 4 times as higher)

Overview

• Decision-making: generating, evaluating, and selecting among a set of relevant choices, where the choices involve some uncertainty or risk.

• Algorithm – Specific rule or procedure, often detailed or

complex, that guarantees a correct answer.

• Heuristic– Informal strategy that works sometimes but does not

guarantee correct solution.

Streak Shooting

• Gilovich, Vallone & Tversky• Hot hand: basketball players get “hot” (91% of 76ers fans)• Analysis of 48 76ers home games during 1980-81 season

revealed no basis in fact.– Measured probability of making shot after

• making 1, 2, or 3 shots.• missing 1, 2 or 3 shots.

– Found no difference.

• How might the representativeness heuristic explain belief in streak shooting?

Simulation Heuristic

• Tendency to judge events that we can easily imagine occurring as more likely.

– Ms. C and Ms. T were scheduled to leave the airport on different flights, at the same time. They traveled in the same taxi, were caught in traffic, and arrived 30 minutes after their flights were scheduled to leave. Ms. C is told that her flight left on time, 30 minutes ago. Ms. T is told that her flight was delayed, and left 5 minutes ago.

– Who is more upset?

Heuristics & Errors

• Heuristics are not errors, they are strategies.

• A type of error can be driven by more than one heuristic – The Conjunctive Fallacy is driven by:

• Representativeness heuristic (old smoker)

• Availability heuristic (Words ending in “----ing” vs. “-----n-”)

• A heuristic can lead to several types of errors– The representativeness heuristic leads to:

• Conjunctive Fallacy (described above)

• Base Rate Fallacy: Ignoring overall frequency of events.