Lecture 9: Subjective Probabilities, Heuristics and Biases

Question 1

Subjective Probability

Answer 1

• A numerical specification of an individual’s belief that an uncertain event will occur. (e.g. probability that product is successful)
• Probabilities are subjective by nature: Two different people might assign different probabilities to an event
• Subjective probabilities must be determined by asking an expert

Question 2

Probability elicitation methods

Answer 2

1. Direct method:
   - used when the expert has probability and statistics knowledge
   - directly ask for data points on the cumulative distribution function (CDF)
2. Indirect method:
   - does not require the expert to know statistics
   - elicit/derive probabilities by asking the expert to compare the event of interest to a lottery formed by using a random device

Question 3

Direct Method (Steps)

Answer 3

1. Determine the range of possible outcomes

2. Determine some points of the cumulative distribution function

Question 4

Indirect Method

Answer 4

If there are difficulties in handling and interpreting probabilities use the indirect method.

Example:
Compare two scenarios (1) draw a card from a deck and receive 100€ if its the right card and (2) receive 100€ if the DAX is over 8000 in one year

-> can also use coins, urns or a dice

Question 5

Availability Bias

Answer 5

• The easier (or faster) we remember an example of an event, the more likely we believe it is. (e.g. ..ing word vs ..n.. word)
• This heuristic is often suitable but sometimes the availability of an event has nothing to do with its probability
• Example: Which is a more common cause of death, homicide or diabetes -> most people say homicide because it is more often reported in newspapers

Question 6

Hindsight Bias

Answer 6

• When some event occurred, people think in retrospect that they have evaluated the event to be more likely (ex-ante) than they really did.
• Particularly strong when small probabilities are involved
• Example: Respondents were asked to assign probabilities to scenario regarding Nixon’s diplomatic initiatives before he visited Russia and China in 1972. After the visit the respondents recalled their own predictions and assigned higher (lower) probabilities if the event occurred (did not occur)

Question 7

Representativeness Heuristic

Answer 7

• The probability that some object belongs to some category is evaluated to be higher if the object looks representative for the category.
• Representativeness heuristic is used as rule of thumb but it can lead to several cognitive biases (e.g. base rate neglect, reversing conditional probabilities, conjunction fallacy)
• Example: Likelihood of the sequence H,T,T,G,HT,H is estimated to be more likely than T,T,T,T,T,H (coin)

Question 8

Base rate neglect

Answer 8

• People tend to give too little weight to the base rate (e.g. prior probability in the context of Bayes’ theorem).
• Example: pool of 70% lawyer and 30% engineers;
  Description of a person that is neutral regarding profession -> Respondents estimated the probability that it is a lawyer to be 50% (ignored base rates)

Question 9

Reversing conditional probabilities (Confusion of the inverse)

Answer 9

• People tend to confuse conditional probabilities and misinterpret the direction of the conditioning for a conditional probability.
• Example: 94% of the CEOs that were asked had a dog or cat as child (p(Pet|CEO) = 0,94) -> Respondents asserted that cat/ dog ownership helped them to get CEO (p(CEO|Pet) = 0,94) -> p(CEO) is being excluded

Question 10

Conjunction fallacy

Answer 10

• A compound (and thereby more specific) event is evaluated to be more likely than a single general one
• Example: Respondents were asked which is more probable: Linda has a philosophy major and was an activist and (1) is a bank teller or (2) is a bank teller and active in the feminist movement -> Respondents say (2) despite it is dominated by (1)

Question 11

Anchoring and adjustment

Answer 11

Making evaluations often turns out to be a two-step-procedure:

1. Anchoring: A near-at-hand first guess serves as a anchor point
2. Adjustment: further thinking causes adjustment of the original guess

Bias: Adjustment is often insufficient and the anchor exerts too much influence, which causes the estimates to stay too close to the anchor.

Example: 1 x 2 x 3 x 4 x 5 x 6 x 7 vs. 7 x 6 x 5 x 4 x 3 x 2 x 1 -> median is a lot higher for second one -> people compute a few steps and then estimate

Question 12

Overconfidence Bias

Answer 12

• The tendency of a person to place too much confidence in his own abilities, knowledge or the quality of his forecast.
• When people take a guess about something that they are not certain of they tend to overestimate the probability they are correct (the stronger the more complicated the task)
• Example: Give a answer and say how confident you are in percent -> number is way to high

Question 13

Bias in probability estimates

Answer 13

• Systematic error and biases in dealing with probabilities

1. Incomplete or inappropriate data: Availability Bias, Hindsight Bias
2. Incorrect adjustment/processing of probabilities: Representativeness Heuristic, Base rate neglect, Reversing conditional probability, Conjunction fallacy
3. Insufficient critique of one’s own judgement: Anchoring and adjustment, Overconfidence