A descriptive theory of decision making.
Heuristics & biases
-From numerous deviations in normative decision-making, we can see that people often rely on heuristics to make decisions and these lead to systematic biases.
The representative heuristics
-->Used when making judgements about the probability of an event under uncertainty.
-->People rely on the representativeness (a special representing event in its parent population) to make judgements
The conjunction fallacy
1. Which of the following two scenarios is more likely?
- An all out nuclear war between the United States and Russia.
- Neither country intends to attack the other side with nuclear weapons, but an all out nuclear war between the US and Russia is triggered by the actions of a third country.
2. 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 anti-war demonstrations.
- Linda is a bank teller.
- Linda is a bank teller and is active in the feminist movement.
90% of subjects feel that Linda is more likely to be a feminist bank teller than just a bank teller.
-->The conjunction/co-occurrence of two events cannot be more likely than the possibility of either event alone.
-->The fallacy occurs because specific scenarios more likely that general one due to they are more representative of how we imagine them.
-->When the amount of details in a scenarios increases, its probability can only steadily decrease; however its representativeness and hence its apparent likelihood may increase. We would thought that a specific event could occur more likely than it should be.
The law of numbers
1. The mean IQ of the population of eighth graders in a city is known to be 100. You have selected a random sample of 50 children for a study of educational achievements. The first child to be tested has an IQ of 150. What do you expect the mean IQ to be for the whole sample?
The majority of people incorrectly respond 100.
If the first child has an IQ of 150 and we can expect the remainder to have the mean IQ of 100 each, we have a total of 5050 IQ points, which when divided by the 50 children gives us an average expected IQ of 101.
People who respond 100 assume that there would be some low IQ scores to balance out the high ones (the bottoms tail of the distribution would be the same shape as the top tail). Generally, people believe that chance is self-correcting.
People behave as they belief in a non-existent law of small numbers.
--which in fact is a judgemental bias that the characteristics of a sample population can be estimated from a small number of observations/data points.
--suggests that a random sample of a population could predict the population more accurate than statistical sampling theory could.
In fact, the opposite law of large number is correct.
--The larger the sample you draw from a population, the closer its average will be to the population average.
2. If participants are asked to write down a random sequence of numbers/letters/coin tosses, they try to make the sequence look random at every point. Local representativeness.
- People exclude long runs like 1312222222311
- They would try to make each number more equifrequent than would be expected by chance.
3. What comes next?
- Tail, Head Tail Head, Head, Head, Head, Head, (?)
The representativeness heuristic give rise to the gambler's fallacy by means of the law of small numbers.
--That a series of independent trials with the same outcome will be followed by an opposite outcome sooner than expected by chance (a successful outcome is due to after a run of bad luck).
The availability heuristics
-->Mental shortcuts that rely on immediate examples that comes to one's mind when evaluating a certain topic, method or decision.
-->Operates in a principle that if something could be recalled, then it must be important (or at least more important than what is not as readily recalled).
-->Decision-makers assess the frequency of a class/the probability of an event by the ease with which instances/occurrences can be brought to mind.
1. Which of the following are more likely:
- Being killed by a shark?
- Being killed by falling airplane parts?
- Car accident
- Stomach cancer
Most people get these wrong because more information are available about the wrong answer, largely due to the media coverage. In short it is a memory effect
2. State a word in English has K as:
- the 1st letter
- the 3rd lettter
69% answered incorrectly. In fact, there are twice as many words with K as the 3rd letter as there are with K as the 1st.
Tversky & Kahneman argue that because our lexicon is organised by spelling (or at least phonetics), thus more words beginning with K are available for retrieval.
Not only by information stored in memory, imagination could influence availability too.
Caroll (1978) suggested that if easily imagined events are judged to be more probable then the imagination might increase availability and consequently judgements of probability.
--One day before the 1976 US presidential election, participants were asked to imagine the result. Half of them imagined Ford won the election while the other half were asked to imagine that Carter won the election.
--When asked about the participants' thought about who would win, the beliefs were consistent with the imaginative scenario.
Hindsight Bias
--the tendency to view what has already happened as unavoidable and obvious without realising that retrospective knowledge of the outcome in influencing one's judgement
--I knew it all along.
Fischhhoff (1975) asked participants to read true historical accounts of incidents which they were unfamiliar with. Half of them were told the outcome. they were then asked to assign probabilities to possible outcomes. Those who were told the outcome gave a higher probability to the actual outcome than those who were not told.
Anchoring and adjustment
-->Numerical estimates(probabilities) are formed by taking an initial value(an anchor) and adjusting it.
1. Tversky & Kahnerman asked high school students to estimate the values of products in 5 seconds:
- 1x2x3x4x5x6x7x8
- 8x7x6x5x4x3x2x1
Mean estimates were 512 & 2250 respectively. However the correct answer is 40320.
The anchor might be (i) the suggestion by the formulation of the problem, or (ii) the result of a partial computation.
--In this case, the anchor was determined by left-to-right calculation.
2. A number was selected randomly from 1to 100. Participants were asked to estimate the percentage of African countries in US and o indicate whether the estimate was greater or smaller than the random number.
Those who are given high random numbers produced higher estimates than hose given low number.
Modifications of the estimated are always too small because of the anchor effect.
3. The Asian Disease Problem: Imagine the UK is preparing for the outbreak of an unusual Asian disease, which is expected to kill 60000 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimates of the consequences of the program are as follows:
- If program A is adopted, 20000 people will be saved.
- If program B is adopted, there is 1/3 that 6000 people will be saved, and 2/3 probability that ni people will be saved.
- If program C is adopted, 40000 people will die.
- If program D is adopted, there is 1/3 probability that nobody will die, and 2/3 probability that 60000 people will die.
More people chose A over B (certain over gamble) and D over C (gamble over certain).
Although A=C, and B=D the framing of the questions reverses the responses subjects make.
--People are risk averse for gains (lives saved are seen as gains) and risk seeking/loss aversion for losses (deaths are seen as losses as the current reference no-one has died).
The Prospect Theory
=>a descriptive model of decision making.
=>intended to account for deviations from rational choice theory such as the Allais and Ellsberg paradoxes, and the framing effect mentioned.
=>Two components; Utility and Probability.
=>Instead of the final outcome, people make decision by evaluating the potential value of losses/gains using heuristics.
The value function.
>>proposed by T&K (1981).
>>differ from gains and losses.
>>Instead of the total wealth as Bernoulli described, the x-axis reflects gains to the right and losses to the left.The midpoint is ones current reference point.
>>The y-axis as utility.
>>Function for gains &losses are asymmetric. This explains why we treat treat losses as more serious than gains.
-->In the example, gains and losses of people to money were presented. The horizontal distance from 0 to any value is identical to that of relative negative value on x-axia, because objectively the difference is the same.
-->However, the respective vertical distance that reflects utility is larger for losses that the utility of losing $500 is greater than the utility of $500 gain.
Choose
- A. A sure gain of $240
- B. A 25% chance to gain $1000, and a 75% to gain nothing.
- C. A sure loss of $750
- D. A 75% chance to lose $1000, and a 25% to lose nothing.
This is a classic example of people being risk averse for gains and risk seeking for losses. Despite the irrationality of the inconsistent behaviour, on analysis options B and C are better.
To see this add the alternatives together:
- A+C=240-750=sure loss $510
- A+D=75% chance of losing 760 and a 25% chance of gaining $240
- B+C=25% chance to gain $250 and a 75% chance to lose $750
- B+D=18.75% chance of no gain or loss, 6.25% chance of gaining $1000, 56.25% chance of losing $1000 and another 18.75 chance of no gain or loss.
B+C would be the best option.
The pi function (π)
-->Some people prefer certainty which is the certain effect.
-->According to prospect theory we do not treat probabilities as they are stated, but they are distorted by the π function thus an objective p becomes a subjective π.
-->Subjective probabilities <1 are underweighted relative to objective probabilities.
1.
- A. $30, p=1, EV=$30
- B. $45, p=0.8, EV=$36
Though EV of B is higher, most people chose A
2.
- A. $45, p=0.2, EV=9
- B. $30, p=0.25, EV=$7.5
Now most people choose A.
-->The pi function lead to overweight of each additional unit for very low probabilities, and this is why people believe that their chance of winning the lottery are larger than they really are.
-->While in very high probabilities, additional unit are underweighted.
-->The certainty effect explains the Allais paradox/Zeckhauser problem.
-->K&T(1979) asked participants to evaluate insurance policies against theft/damage to property, and to weigh the premium against the benefits. They were asked to consider a policy that the premiums were halved but only paid out in 50% of claims (there's a 50:50 chance of whether your claim is paid).
-->80% of the participants would not buy the probabilistic insurance. Reducing probability of a loss(p) to 0.5(p) is less valuable than reaching the probability from 0.5*p to 0.
We prefer to eliminate risk than to reduce it.
Confidence:
->Most people could not distinguish between military activities between the USSR and the USA during the cold war.
->Physicians displayed substantial overconfidence in diagnosing that patients have pneumonia with unwanted certainty, when compared to whether forecaster's predictions of precipitation.
->Some people are more confident than others despite being experts in their field.
->Confidence was unrelated to accuracy. even high confidence responders could not discriminate above chance.
->Implications for eyewitness testimony.
The Regret Theory
=>The prospect theory does not give any psychological reasons for the shape of its functions.
=>Both RCT and prospect theory do not consider alternative outcomes.
=>In the Regret theory, we compare outcomes, particularly after the fact.
=>We regret a decision if an alternative outcome would have led to a higher payoff. And we rejoice if our choice led to a better outcome than other alternatives.
=>When we make a decision we also consider the emotional outcomes.
->How would I feel if I win vs. how would I feel if I lose.
=>These anticipated emotional states contaminate our subjective estimation of utility, bending the value function.
