Heuristics and biases: prospect theory

Question 1

What is prospect theory?

Answer 1

A descriptive theory of decision making.

Question 2

What did Kahneman and Tversky document?

Answer 2

Numerous deviations from normative decision making.

Question 3

How did Kahneman and Tversky explain deviations from normative decision making?

Answer 3

People often rely on heuristics to make decisions, which create systematic biases.

Question 4

What did the research programme resulting from Kahneman and Tversky’s claims become known as?

Answer 4

Heuristics and biases.

Question 5

What is the representativeness heuristic?

Answer 5

Most people believe that two things are likely to occur than one, which can’t be true according to probabilities (the conjunction fallacy).

Question 6

Give two examples of the representativeness heuristic.

Answer 6

1. Nuclear war, vs. nuclear war triggered by a third country.
2. Linda - bank teller or bank teller and active in the feminist movement.

Question 7

What is the conjunction fallacy?

Answer 7

The conjunction or co-occurrence of two events cannot be more likely than the probability of either event alone.

Question 8

What did Tversky & Kahneman (1982) state about the conjunction fallacy?

Answer 8

• The fallacy occurs because specific scenarios appear more likely than general ones
• This is because they appear more representative than they really are
• “As the amount of detail in a scenario increases, its probability can only decrease steadily, but its representativeness and hence its apparent likelihood may increase” (p.98)

Question 9

Give an example where people incorrectly use ‘the law of small numbers’.

Answer 9

The mean IQ of the population of 8th graders is known to be 100, what’s the mean IQ in a sample of 50 pupils where the first child tested has an IQ of 150?
Most people incorrectly answer 100, whereas if the first IQ is 150 and the rest have a mean of 100 = total of 5050 = average IQ of 101.

Question 10

What did Tversky & Kahneman (1971) state about people’s use of the law of small numbers?

Answer 10

That people who respond 100 assume there would be some low IQs to balance out the high ones - they believe that chance is self-correcting, whereas the law of small numbers is non-existent.

Question 11

What is the ‘law of small numbers’?

Answer 11

The false idea that random samples of a population will resemble each other more closely than statistical sampling theory would predict.

Question 12

What is the law of large numbers?

Answer 12

The larger the sample you draw from a population, the closer its average will be to the population average.

Question 13

What is local representativeness (Kahneman and Tversky, 1972)?

Answer 13

An example of the law of small numbers - when people are asked to write down random sequences of numbers/letters/coin tosses, they tend to try to make the sequence look random at every point

Question 14

What gives rise to the gamblers fallacy?

Answer 14

The representativeness heuristic, through the law of small numbers.

Question 15

What is the gamblers fallacy?

Answer 15

The that a series of independent trials with the same outcome will be followed by an opposite outcome sooner than is expected by chance, for example when given the sequence “tails, heads, tails, heads, heads, heads, heads…” most people think tails follows.

Question 16

What is the ‘hot hand’?

Answer 16

People’s perceptions of lucky streaks in games.

Question 17

What did Gillovich, Vallone & Tversky (1985) do?

Answer 17

They examined people’s perceptions of the hot hand in basketball, reporting statistical analyses of lucky streaks.

Question 18

What did Gillovich, Vallone & Tversky (1985) find?

Answer 18

‘Lucky streaks’ were simply misconceptions - successful shots during lucky streaks are actually no more likely than that player’s overall probability of a lucky streak… Lucky streaks are an illusion.7

Question 19

What do judgements of Xs and Os show about the ‘hot hand’?

Answer 19

When the probability of alternation was set at .4, .5, .6, .7, .8 or .9, subjects thought that the higher probability of alternation sequences are more likely to be chance, when in fact the opposite is true.

Question 20

What is the availability heuristic?

Answer 20

The bias towards options that we have more information about.

Question 21

Give an example of the availability heuristic.

Answer 21

Most believe you’re more likely to die on a plane than by being kicked by a donkey, whereas the latter is true; in short it’s a memory effect affected by media coverage etc.

Question 22

What do decision makers do when using the availability heuristic, according to Tversky & Kahneman, (1974)?

Answer 22

“assess the frequency of a class or the probability of an event by the ease with which instances or occurrences can be brought to mind”

Question 23

What did Tversky & Kahneman (1973) do?

Answer 23

Asked subjects if there were more words with K as the 3rd or 1st letter in English.

Question 24

What did Tversky & Kahneman (1973) find?

Answer 24

69% of people answered incorrectly: there are twice as many words with K as the 3rd letter than the 1st.

Question 25

How did Tversky & Kahneman (1973) explain their results?

Answer 25

They argued that because our lexicon is organised by spelling (or at least phonetics) more words beginning with K are available for retrieval.

Question 26

What is availability influenced by, other than memory?

Answer 26

Imagination.

Question 27

What did Caroll (1978) reason?

Answer 27

If easily imagined events are judged to be more probable than the very act of imagination might increase availability and consequently judgements of probability.

Question 28

What is an example of the availability heuristic being improved by imagination?

Answer 28

Participants, a day before the 1976 presidential election, were asked to imagine one of two scenarios involving either candidate winning, and when asked who they thought would win their beliefs were consistent with the imagined scenario.

Question 29

What heuristic is hindsight bias part of?

Answer 29

The availability heuristic.

Question 30

What is hindsight bias?

Answer 30

The tendency to view what has already happened as inevitable and obvious without realising that retrospective knowledge the outcome is influencing one’s judgement.

Question 31

What did Fischoff (1975) do?

Answer 31

Had participants read true historical accounts of incidents which they were unfamiliar with e.g. the battle between the British and Nepalese Ghurkhas in 1814. Half were told the outcome, they then had to assign probabilities to outcomes

Question 32

What did Fischoff (1975) find?

Answer 32

Participants who were told the outcome gave higher probability to the actual outcome than those who were uninformed.

Question 33

What did Fischoff and Beyth (1975) do?

Answer 33

Asked Israeli participants to estimate the probability of 15 different outcomes of Nixon’s (1972) trips to China and the USSR before they took place.
2 weeks - 6 months after the trips participants had to recall their original ratings and indicate if the event occurred.

Question 34

What did Fischoff and Beyth (1975) find?

Answer 34

75% of participants remembered assigned higher probabilities than they had to events they thought had occurred.

Question 35

What are Kahneman and Tversky’s three heuristics?

Answer 35

The representativeness heuristic, the availability heuristic and anchoring and adjustment.

Question 36

What is anchoring and adjustment?

Answer 36

The heuristic where numerical estimates (e.g. probabilities) are formed by taking an initial value (an anchor) and adjusting it.

Question 37

How did Tversky & Kahneman (1974) demonstrate anchoring and adjustment?

Answer 37

They asked high school students to estimate answers to 1x2x3x4x5x6x7x8 and 8x7x6x5x4x3x2x1 within 5secs, and found that mean estimates were 512 and 2250 respectively but the answer is 40,320; the anchor was determined by left to right calculation.

Question 38

What did Tversky & Kahneman (1974) state about anchors?

Answer 38

The anchor “may be suggested by the formulation of the problem, or it may be the result of a partial computation”

Question 39

What did Tversky & Kahneman (1974) do with random number generation?

Answer 39

Produced a number 0-100, then asked participants to estimate the percentage of African countries in the UN and indicate whether the estimate was greater or less than the random number.

Question 40

What did Tversky & Kahneman (1974) find with random number generation?

Answer 40

Participants given high random numbers produced higher estimates than those given low numbers. Modifications of the estimate are always too small because of the anchor effect.

Question 41

Who first described the Asian disease problem?

Answer 41

Tversky & Kahneman, 1981.

Question 42

What is the Asian disease problem?

Answer 42

Imagine the UK is preparing for the outbreak of an unusual Asian disease which is expected to kill 60,000 people. Two programs have been proposed.

Question 43

What are the two proposed programs for the Asian disease problem?

Answer 43

Program A: 20,000 will be saved OR Program C: 40,000 will die
Program B: 1/3 chance 60,000 will be saved but a 2/3 chance that no one will be saved OR Program D: 1/3 chance no one will die but a 2/3 chance that 60,000 will die

Question 44

What did Tversky and Kahneman (1981) find with the Asian disease problem?

Answer 44

The framing of the question reverses the decisions participants make - people are risk averse for gains (lives seen as gains), so 70% choose A over B, but risk seeking for losses (loss aversion), so 20% choose C over D.

Question 45

What is another example of how framing of questions affects their answers?

Answer 45

Rugg (1941) - asked US citizens if public speeches against democracy should be either allowed or forbidden. 62% said no to the allowed question, but only 46% said yes to the forbid question.

Question 46

Give examples of deviations from rational choice theory that prospect theory aimed to explain.

Answer 46

The Allais paradox, Ellseberg paradox and the framing effect.

Question 47

What are the two main components of prospect theory?

Answer 47

Utility and probability.

Question 48

Describe the value function proposed by Tversky and Kahneman in 1981.

Answer 48

Where the x-axis is gains and losses and the y axis utility, functions for gains and losses are asymmetric. Utility is larger for losses than gains.

Question 49

What choices demonstrate the value function (being risk averse for gains and risk seeking for losses)?

Answer 49

Choice 1: A) Sure gain of £240 or B) 25% of £100, 75% of nothing
- People choose A
Choice 2: C) Sure loss of £750 or D) 75% of £1000, 25% of nothing
- People choose D
However analysis shows it’s better to choose B and C over A and D (Tversky and Kahneman, 1981).

Question 50

What is the π function?

Answer 50

The certainty effect - we don’t treat probabilities as they’re stated, the pi function distorts them (objective p -> subjective π).

Question 51

Give an example of the π function in action.

Answer 51

Given a choice between p(1)£30 or p(0.8)£45, most people select A despite B having a higher EV. However given a choice between p(0.2)£45 or p(0.25)£30, most people choose A which this time does have a higher EV.

Question 52

How are subjective probabilities < 1.0 are weighted relative to objective probabilities?

Answer 52

They’re underweighted.

Question 53

What is explained by the certainty effect (π function)?

Answer 53

The Allais paradox and Zeckhauser problem (subjects tend to pay more to remove the only bullet from a gun in Russian roulette than to remove one out of 4).

Question 54

What did Kahneman & Tversky (1979) do to demonstrate the π function?

Answer 54

Asked participants to suppose they were evaluating insurance policies against theft or damage to properties and to weight premiums against benefits, then to consider a policy in which the premiums were halved but only paid out in 50% of claims.

Question 55

What did Kahneman & Tversky (1979) find about the π function?

Answer 55

80% of participants wouldn’t buy the probabilistic insurance, therefore halving the probability of a loss is less valuable than reducing the probability from half to 0. I.e. we prefer to eliminate risk than to reduce it.

Question 56

What is a consequence of the pi function for very low probabilities?

Answer 56

Each additional unit is over-weighted, e.g. people tend to believe that their chances of winning the lottery are larger than they actually are.

Question 57

What is a consequence of the pi function for very large probabilities?

Answer 57

Additional units are under-weighted, as shown by Lichtenstein et al. (1978), who compared participants’ estimated frequencies of deaths as a function of actual frequencies. They estimated less than is true for low frequency e.g. botulism and more than is true for high frequency e.g. cancer.

Question 58

Give evidence that some people are more confident than others despite being ‘experts’ in their field.

Answer 58

Comparison of confidence and actual probability of:
a) weather forecasters’ predictions of precipitation
b) doctors’ diagnoses of pneumonia
Shows that doctors show substantial overconfidence.

Question 59

What have studies on confidence using Superpowers A and B situations related to the cold war found?

Answer 59

People couldn’t distinguish between the military actions of the USA and USSR, and confidence was unrelated to accuracy - even high confidence responders couldn’t discriminate above chance.

Question 60

What is a limitation of prospect theory?

Answer 60

It doesn’t give any psychological reasons for the shapes of functions - neither RCT nor prospect theory consider alternative outcomes.

Question 61

According to regret theory, what do we do?

Answer 61

Compare outcomes, particularly after the fact, so we regret a decision if an alternative outcome would have led to a higher payoff, even when the prospect was better. We also rejoice if our choice let to a better outcome than other alternatives. I.e. when we make a decision we also consider the emotional outcomes.

Question 62

How does regret theory influence utility and value?

Answer 62

Anticipated emotional states contaminate our subjective estimation of utility, bending the value function.