Judgment Heuristics and Biases

Try these cases yourself.

A. A cab was involved in a hit-and-run accident. Two cab companies serve the city: the Green, which operates 85% of the cabs, and the Blue, which operates the remaining 15%. A witness identifies the hit-and-run cab as Blue. When the court tests the reliability of the witness under circumstances similar to those on the night of the accident, he correctly identifies the color of the cab 80% of the time and misidentifies it 20% of the time. What is the probability that the cab involved in the accident was Blue, as the witness stated?

B. You've reserved a seat for a Broadway play for which the ticket price is $40. As you enter the theater to buy your ticket, you discover you've lost $40 from your pocket. Would you still buy the ticket? (Assume you still have enough left to do so.)

C. Linda is 31, single, outspoken, and very bright. She majored in philosophy in college. As a student, she was deeply concerned with discrimination and other social issues, and participated in anti-nuclear demonstrations. Which statement is more likely?

a. Linda is a bank teller.

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

D. Threatened by a superior force, the general faces a dilemma. Her intelligence officers say her soldiers will be caught in an ambush in which 600 of them will die unless she leads them to safety by one of two available routes. If she takes the first route, 200 of her soldiers will be saved. If she takes the second, there's a one-third chance that 600 soldiers will be saved and a two-thirds chance that none will be saved. Which route should she take?

E. A certain town is served by two hospitals. In the larger hospital about 45 babies are born each day, and in the smaller hospital about 15 babies are born each day. Although the overall proportion of boys is about 50%, that actual proportion at either hospital may be greater or less that 50% on any given day. At the end of the year, which hospital will have the greater number of days on which more that 60% of the babies born were boys?

a. the large hospital

b. the small hospital

c. neither, it is equally probable

F. An urn is filled with with white balls and black balls. You know that two-thirds of the balls are of one color and one-third are of the other, but you don't know which color predominates. One blindfolded person plunges a hand into the urn and comes up with three black balls and one white ball. Another uses both hands and comes up with 14 black balls and ten white balls. Both samples suggest that black balls are more numerous. But which sample produces the more convincing evidence?

G. Choose between

a) a sure gain of $3000, and

b) an 80% chance of winning $4000 and a 20% chance of winning nothing

H. You've decided to see a Broadway play and have bought a $40 ticket. As you enter the theater, you realize you've lost your ticket. you can't remember the seat number so you can't prove to the management that you bought a ticket. Would you spend $40 for a new ticket?

I. Threatened by a superior force, the general has to choose between two escape routes. Her aides tell her that if she takes the first, 400 soldiers will die. If she takes the second, there's a one-third chance that no soldier will die, and a two-thirds chance that 600 soldiers will die. Which route should she take?

J. Choose between

a) a sure loss of $3000, and

b) an 80% chance of losing $4000 and a 20% chance of losing nothing

Outline

I. What is a "judgment heuristic?" II. The representativeness heuristic III. The availability heuristic IV. Adjustment and anchoring V. Risk and loss aversion

I. What is a "judgment heuristic?"

A. Judgemental heuristics are principles or methods by which one makes assessments or judgements of probability simpler.

B. These heuristic are often very useful but sometimes they lead to systematic errors.

II. The representativeness heuristic

A. An event is judged to be probable to the extent that it represents the essential features of the parent population or of its generating process.
B. The heuristic is useful in inductive reasoning. For example, if we want to know how likely it is that Jones will pass the course we might consider the degree to which Jones represents that group of students who pass.
C. The use of this heuristic can, however, systematically lead one to make poor judgements in some circumstances.

1. Sometimes the manner in which the object or event is represented makes one insensitive to the prior probabilities involved.

2. Sometimes the manner in which the object or event is represented leads one to ignore the basic rules of the probability calculus, e.g., that the likelihood of a conjunction is always less than the likelihood of each conjunct taken singly.

3. Sometimes the manner in which the object or event is represented makes one insensitive to the fact that small samples are less representative than large samples are.

4. Sometimes the manner in which the object or event is represented leads one to misconceive the outcome of chance. For example, some outcomes of a random selection are taken to "look more random" than equally likely alternatives.

5. Sometimes the manner in which the object or event is represented makes one insensitive to the fact that, in circumstances in which random events cluster around a mean or average, extraordinary events are likely to be followed by more ordinary ones (regression to the mean). People tend to think that extreme instances are representative of future instances.

III. The availability heuristic

A. One's judgement about the relative frequency of an event often depends upon the availability or accessability of objects or events in the processes of perception, memory or construction in the imagination.
B. This heuristic is useful in inductive reasoning because (1) typically instances of large classes are recalled better and faster than instances of small groups, (2) likely events are often easier to imagine, (3) causal connections are repeatable and therefore more likely to be remembered. When the availability is associated with the objective likelihood of an event, this heuristic is trustworthy.
C. The use of this heuristic can, however, systematically lead one to make poor judgements in some circumstances.

1. A class whose instances are readily available might appear to be more numerous than it is.

2. Events that easily come to mind might be judged more likely than they are.

3. The availability of certain information may be biased because one has had limited exposure to events of a certain kind, or because the events are more graphic, remarkable or noticable and attract more attention, or because one has stored the information in a particular fashion.

IV. Adjustment and anchoring

A. Conservativism is sometime recommended when adjusting our beliefs or methods in light of new information. A well established belief should be overthrown only when one has solid evidence against it. An otherwise reliable method should be changed only when it meets significant failure.
B. Insufficient adjustment due to anchoring can lead to mistakes.

1. Sometimes reasoners hold fast to some piece of information and ignore the consequences of additional information.

2. When solving a problem involving probabilities, reasoners may start with an initial value and adjust it to reach a final value. The anchoring phenomenon results when their results are biased toward the initial value.

3. Sometimes reasoners anchor to an initial problem-solving method when a change in methods would be recommended.

V. Risk and loss aversion

A. Many people are adverse to taking risks. People tend not to bet $500 on a 50% chance of winning $1,000, even though that is the fair price.
B. But studies show that people would rather take a risk than suffer a loss. Equivalent problems get different responses depending on whether the problem is framed in terms of losses or gains.