Activity: Heuristics and Bias
Activity 1:
A. 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, also participated in antinuclear demonstrations. Please check the most likely alternative:
1. Linda is a bank teller.
2. Linda is a bank teller and is active in the feminist movement.
Answer to question A: : Put this question to 86 people and nearly 9 out of every 10 respondents answered #2. If you think about it, though, this response violates a fundamental rule of probability. The conjunction, or co-occurrence, of two events (e.g. bank teller and feminist) cannot be more likely than the probability of either event alone. This is referred to as the conjunctive fallacy.
B. Suppose an unbiased coin is flipped three times, and each time the coin lands on Heads. If you had to bet on the next toss, what side would you choose?
1. Heads
2. Tails
3. No Preference
Answer to question B: Because the coin is unbiased you should have had no preference between Heads and Tails. To think otherwise is to commit the "Gambler's Fallacy." The probability remains 50/50 regardless of previous coin tosses.
Activity 2:
A. Which of the following sequences of X's and O’s seems more like it was generated by a random process?
1. XOXXXOOOOXOXXOOOXXXOX
2. XOXOXOOOXXOXOXOOXXXOX
Answer to question A: The first string, in fact, alternates on half of all possible occasions, similar to what might be expected from a chance series, no illusions of "the hot hand" for you. If you thought the first string contained too many alternations to be random you fell victim to the illusion of "the hot hand". The first string alternates on half of all possible occasions (similar to what might be expected from a chance series). In contrast, this string represents an alternation probability of .70 – far higher than the .50 expected by chance alone.
B. Suppose a piece of paper is folded in half. It is folded in half again, and again. After 100 folds how think will it be?
Answer to question B: Only rarely do people give estimates larger than a few yards or meters, yet the correct answer, given an initial sheet of paper 0.1 millimeter thick, is roughly 1.27 X 1023 kilometers – more than 800,000,000,000 times the distance between earth and the sun. This answer surprises most people because they begin by imagining the first few folds (a very low anchor) and do not adjust their estimates upward sufficiently for the doubling effect of later folds.
C. Including February 29, there are 366 possible birthdays in a year. Consequently, a group would need to contain 367 members in order to be absolutely sure that at least two people shared the same birthday. How many people are necessary in order to be 50 percent certain?
Answer to question C: Most people give an answer around 183 (half the days). The correct answer is that only 23 people are needed. That is, any random grouping of 23 people has better than even odds of containing at least two people with the same birthday. To calculate try this formula: 365 X 364 X 363X … 344 Although this problem is difficult for reasons apart from anchoring, (366) 22 there is no question that many people first react by adopting a high anchor value (such as 83) and later find it hard to adjust that anchor downward as they think about the problem.
Activity 3:
Consider the two structures, A and B, which are displayed here.
Structure A
X X X X X X X X
X X X X X X X X
X X X X X X X X
Structure B
X X
X X
X X
X X
X X
X X
X X
X X
X X
A path is a line that connects X in the top row of a structure to an X in the bottom row by passing through one (and only one) X in each row. In other words, a path connects three Xs in Structure A (one in each of the three rows) and nine Xs in Structure B (one in each of the nine rows).
A. In which of the two structures are there more paths?
Answer to Question A: 15 percent of the original respondents believed that Structure B has more paths than A, while 85 percent believed A has more than B. The truth, they both have the same amount of paths.
B. Approximately how many paths are in Structure A? Structure B?
Answer to Question B: In Structure A there are eight elements to choose from in the top row, eight in the middle row, and eight in the third row. This yields 8 X 8 X 8 = 512 possible combinations. In Structure B there are 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 = 512 possible combinations.
Activity 4:
Suppose that scores on a high school academic achievement test are moderately related to college grade point averages (GPAs). Given the percentiles presented in this table, what GPA would you predict for a student who scored 725 on the achievement test?
Student Percentile Achievement Test GPA
Top 10% >750 >3.7
Top 20% >700 >3.5
Top 30% >650 >3.2
Top 40% >600 >2.9
Top 50% >500 >2.5
Student Percentile Achievement Test GPA
Top 10% >750 >3.7
Top 20% >700 >3.5
Top 30% >650 >3.2
Top 40% >600 >2.9
Top 50% >500 >2.5
Answer: Most people predict a GPA between 3.5 and 3.7 (a GPA highly "representative" of a 725 test score). This answer makes sense if the achievement test is perfectly diagnostic of a student's GPA. According to this problem, however, the achievement test is only moderately predictive of GPA, the best GPA prediction lies between 3.6 and the average GPA or 2.5 thereby allowing for regression to the mean.
Activity 5:
Reexamine all of your choices. What principles were demonstrated in each different situation? What do these principles and models imply about the ways in which we make decisions? Can any of these phenomena lead to critical errors in judgment? Why or why not? Consider your responses to these questions, revisit your assignment list and then share your ideas with others in the discussion room.
Questions and Answers:
Question 1: How can I reduce the chance of bias when I use representativeness as a rule of thumb?
Research suggests four tips for reducing error associated with the representativeness heuristic:
• Don’t Be Misled by Highly Detailed Scenarios . The very nature that makes the detailed scenarios seem representative also lessens the likelihood that they are. In general, the more specific a scenario is, the lower the chances are of occurring — even when the scenario seems a perfect fit or the most probable outcome.
• Whenever Possible, Pay attention to Base Rates . Base rates are very important when an event is very rare or common. When base rates are extreme, representativeness is often a fallible indicator of probability.
• Remember That Chance Is Not Self-Correcting . A run of bad luck is just that: a run of bad luck. It doesn’t mean that things are either going to be good all the time or stay the same. If a chance process has a certain probable outcome, past events will have no effect on future outcomes.
• Don’t Misinterpret Regression Toward the Mean . Extreme performances tend to be followed by more average performances. Regression toward the mean is typical whenever an outcome depends in part upon chance factors.
Question 2:
What is meant by regression to the mean?
Regression effect or regression to the mean is an example of representativeness bias. We, in fact, have substantial firsthand experience with regression effects in our daily lives (for example, sons of unusually tall fathers tend to be shorter than their fathers). Kahneman and Tversky noted, however, that we often fail to make adequate allowance for it in our judgment because, they conjectured, we feel intuitively that an output (for example, an offspring) should be representative of the input (for example, the parent) that produced it.
It has long been observed that the rookie of the year in the major league baseball (and in other sports as well) often has a mediocre second season. This has been attributed to the "sophomore jinx." A related phenomenon is the "sports illustrated jinx," which holds that an athlete whose picture appears on the cover of Sports Illustrated one week is destined to do poorly the next. Shirley Babashoff, a United States' Olympic swimming medalist, was once said to have refused to have her picture on the cover of Sports Illustrated for fear of the jinx. Both these supposed jinxes, however, are easily explained as the result of regression to the mean. Someone gets to be the rookie of the year only after having had an extraordinarily good season. Similarly, athletes appear on the cover of SI only after an unusually strong performance. Their subsequent performance, even if still well above average, will almost inevitably fall below the standard that earned them their accolades.
Question 3:
What is the Law of Small Numbers?
The law of small numbers says that random samples of a population will resemble each other and the population more closely than statistical sampling theory would predict. For example, when people are asked to write down a random sequence of coin tosses without actually flipping a coin, they often try to make the string look random at every point known as "local representativeness". As a consequence, they tend to exclude long runs and include more alterations between heads and tails than you would normally find in a chance sequence. In a chance sequence, there are many points at which the series does not look random at all. To verify this fact, you can approximate a chance sequence by tossing a coin 100 times and recording the patterns of heads and tails.
Question 4:
How can the availability heuristic lead to biased judgments?
Availability can lead to biased judgment when examples of one event are inherently more difficult to generate than examples of another. For instance, Tversky and Kahneman asked people if a sample text of English Language is more likely to start with the letter K or that K is its third letter. A vast majority thought that it started with the letter K. In truth, however, there are twice as many words with K in the third position as there were words that began with K. Because it is easier to generate words that start with K than have K as the third letter, most people overestimate the frequency of these words.
Still another way that availability can lead to biases is when one type of outcome is easier to visualize than other, either because an alternative is too negative or too pallid or abstract to imagine with equal force.
Question 5:
What is the gambler’s fallacy?
People often believe that chance is self-correcting. It isn’t. The representativeness heuristic leads people to commit the "gambler's fallacy" — the belief that a successful outcome is due after a run of bad luck (or, more generally, the belief that a series of independent trials with the same outcome will soon be followed by an opposite outcome). Suppose that a fair coin is flipped three times, and each time you get a head. If you had to bet $100 on the next toss, what side would you choose? Because the coin is fair, the normative correct answer is that you should have no preference between heads and tails. Some people erroneously believe, however, that tails are more probable after a run of three heads, when, in fact, the statistical probability for tails OR heads remains 50/50.
Question 6:
What can I do to reduce error caused by anchoring?
It is difficult to protect against the effects of anchoring, partly because incentives for accuracy seldom work, and partly because the anchor values themselves often go unnoticed. The best approach may be to generate an alternative anchor value that is equally extreme in the opposite direction. For example, before estimating the value of a used automobile that seems overpriced, imagine what the value would seem like if the selling price had been surprisingly low. Remember, however, that extreme anchor points are correlated with the largest anchoring effects, so using only the extreme ends as anchors may be problematic in some instances. In these cases, try using multiple anchor points before attempting to make a final estimate.
Question 7:
What is salience and why is it important?
Salience is, in many respects, similar to availability and vividness. Information that is salient, available, or vivid tends to have more impact than information which is not. Salience is important for understanding errors made in causal arguments or judgments. Salient actors or outcomes are often inappropriately viewed as the causal factor, only because of their perceptual dominance.
Question 8:
How can I avoid attributional biases?
One way of reducing error is to pay close attention to consensus data. If most people behave similarly when confronted by the same situation, a dispositional explanation is probably wrong. Instead, it would be better to conclude that something about the situation is causing the behavior. For example, most people experience anxiety when asked to speak in public, so the behaviors associated with anxiety such as rapid breathing, verbal intolerance for questioning, short attention spans, and so forth, are more accurately attributed to the performance anxiety (due to the situation) than to permanent self-absorption (trait-induced behavior) on the part of the speaker.
Another technique is to ask how you would have behaved if put into the same circumstance. Research suggests that perspective-taking can reverse actor-observer differences in attribution. Finally, because causal attributions often depend on what factors happen to be the most salient, it is also important to look for hidden causes.