Probability, Heuristics, and Biases

Question 1

Probability Theory

Answer 1

accepted as a normative theory of probability judgements

Question 2

Axiomatic Theory

Answer 2

starts with some axioms and definitions and develops propositions

Question 3

Bayesian Updating Process:

Answer 3

• start with hypothesis based on some prior belief that the hypothesis is true
• observe some evidence
• know the probability that we would observe such evidence were the hypothesis actually true
• update our belief that the hypothesis is true based on the evidence
• the updated belief is called posterior belief

Question 4

System 1 of brain:

Answer 4

• Quick & automatic
• effortless & involuntary
• effortlessly generating impressions & feelings that are sources for beliefs & choices of system 2

Question 5

System 2:

Answer 5

• involves effort
• conscious
• has beliefs from system 1, makes choices
• decides what to think about and do
• responsible for concentration on a problem

Question 6

System 1 & System 2 together

Answer 6

• active when awake
• system 1 - automatic,
• system 2 - low effort mode
• system 1 generates input for system 2 (impressions, intuitions, intentions, feelings)
• when system 1 cannot find an answer it calls on system 2
• division of labour between the two systems is highly efficient, but system 1 can make systematic mistakes (biases);

Question 7

Which system can make systematic mistakes (biases)

Answer 7

System 1 - it may use heuristics to estimate probabilities or make decisions

Question 8

Heuristics

Answer 8

Rule of Thumb e.g. choose the 2nd cheapest bottle of wine

Question 9

Representativeness heuristic

Answer 9

estimate the probability that an outcome was a result of a given process based on how representative you think the outcome is of that process

Question 10

The Gambler’s Fallacy

Answer 10

belief that after long sequence of red, “black is now due”, failure to understand independence of events

Question 11

Insensitivity to Sample Size

Answer 11

with a smaller sample size, extreme outcomes are more likely.

Question 12

Conjunction Fallacy:

Answer 12

A and B is a conjunction
overestimating the probability of a conjunction
- people mistakenly believe that the probability of two events happening together is greater than the probability of one of those events happening alone (either A or B).
overall probability in conjunctive event lower than in any elementary event
This violates a basic rule of probability.
The rule is:
Pr (A + B) </ Pr (A) and
Pr (A + B) </ Pr (B)

Question 13

Disjunction Fallacy:

Answer 13

A or B is a disjunction
underestimate probability of disjunction
Probability of an elementary event serves as an anchor; insufficient adjustment from anchor
- people mistakenly judge the probability of a disjunction to be less likely than one of its components occurring.
Overall probability in disjunctive event is higher than in any elementary event
This violates a basic rule of probability.
The rule is:
Pr (A or B) >/ Pr(A) and Pr (A or B) >/ Pr (B) (The probability of the union of the two events (A or B) is at least as likely as the occurrence of just event (A) alone).
Why is this important?
- Used in risk assessment such as insurance or in disaster planning (prob that at least one catastrophic event will happen in a given period, e.g., probability that there will be flooding or an earthquake or a storm

Question 14

When updating beliefs, Bayes rule requires us to take into account what 3 things?

Answer 14

the base rate, the evidence, and the conditional probabilities

Question 15

what is base rate neglect?

Answer 15

Base rate neglect refers to estimating a too high posterior by not correctly taking the base rate, the evidence, and the conditional probabilities into account
- could be explained using the availability heuristic: some information may be more available than other information
- relevant in medical diagnosis e.g. mammograms

Question 16

Anchoring and adjustment heuristic

Answer 16

pick an initial estimate and adjust up or down to come up with final answer; insufficient adjustment leads to answers that are affected by anchors (even when anchors are irrelevant)

Question 17

Availability Heuristic

Answer 17

makes you assess the probability of an event based on how easily it comes to mind
- assess probability based on accessibility

Question 18

Affect heuristic

Answer 18

Assigns probability to consequences based on how you feel about them; feel good - higher probability; feel bad - lower probability

Question 19

Availability Heuristic Pro

Answer 19

Pro: Allows people to make quick and efficient decisions based on information they have recalled
Instances of large classes recalled faster than instances of small classes

Question 20

Availability Heuristic Con

Answer 20

Con: Biases can arise because availability can be affected by factors other than probability
- it can lead to irrational fears, and over and underestimation of risk

Question 21

Availability Heuristic Biases arise due to:

Answer 21

• Retrievability - salience and familiarity makes instances more retrievable (e.g. I know a woman astronaut so I overestimate proportion of astronauts who are women)
• Effectiveness of a search net - Biased search procedures (e.g., frequency of word door versus love)
• Imaginability - (e.g. calculate risk of expedition by imagining contingencies)
• Illusory correlation - strengthened for events which frequently co-occur

Question 22

When does System 2 overwrite the intuitive response of system 1?

Answer 22

• sometimes not correcting may be due to not noticing
• making statistical nature of problem salient being aware of System 1 think may help for some
• But: System 1 decision serves as anchor, corrective adjustment may be insufficient
• Impacted by various factors, e.g., time pressure, multi-tasking, good mood, contrary to biological clock

Question 23

What is the goal of Bayesian updating? Explain in one sentence.

Answer 23

Normative rule of how to update probabilistic beliefs in the face of new evidence

Question 24

Let H stand for hypothesis and E for evidence. Which probability are we looking for when applying Bayesian updating? Explain in one sentence.

Answer 24

Prior probability Pr(H) is your probabilistic belief that H is true before you get any evidence.
When we are updating beliefs we are looking for the posterior probability that H is true given the evidence E, i.e. for Pr(H|E)

Question 25

Write Bayes formula, be careful to define each term

Answer 25

Pr (H|E) = Pr (E|H) X Pr (H) / Pr (E|H) x Pr(H) + Pr (E| not H) x Pr (not H)
Pr (not H) - prior probability that hypothesis is not true
Pr (E|H) - probability of observing the evidence conditional on the hypothesis being true
Pr (E| not H) - probability of observing the evidence on the hypothesis being true
Pr (E) - total probability of observing the evidence

Question 26

What does the base rate fallacy refer to? How can it be explained?

Answer 26

Base rate fallacy is the tendency to estimate a too high probability by not taking the base rate into account i.e., by ignoring a very low base rate (PRIOR).
The probability Pr(E|H) serves as an anchor and an individual who fails to estimate the probability Pr (H|E) fails to adjust their beliefs downwards from the anchor and to take the base rate into account

Question 27

Give an example where the base rate fallacy may be relevant?

Answer 27

Medical screening, military reconnaissance

Question 28

What is the Rule of total probability?

Answer 28

it is the denominator of Bayes Rule
- Pr(E) = Pr(E|H) x Pr(H) + Pr(E| not H) x Pr (not H)

Question 29

What can be explained by the use of representativeness heuristic?

Answer 29

The Gambler’s Fallacy

Question 30

What are adjustment and anchoring heuristic biases?

Answer 30

• Insufficient adjustment
• Overestimating probability of conjunctive events
• Underestimating probability of disjunctive events

Question 31

When does System 2 overwrite the intuitive response of system 1?

Answer 31

• not correcting may be due to not noticing
• making statistical nature of problem salient & being aware of the existence of System 1 thinking may help for some
• But: System 1 decision serves as anchor; corrective adjustment may be insufficient
• Impacted by various factors, e.g.: time pressure, multi-tasking, good mood, contrary to biological clock

Question 32

What is the role of System 1 and the role of System 2 in Kahneman and Tversky’s Dual System Theory?

Answer 32

System 1: Quick & automatic; no effort & no sense of voluntary control; effortlessly generating impressions & feelings that are source for beliefs & choices of System 2
System 2: Mental activities that involve effect; conscious, reasoning, has beliefs; make choices; decides what to think about and what to do; responsible for concentration on a problem

Question 33

Why do people use heuristics?

Answer 33

Heuristics are helpful as they help us make quick decisions
The decision are “correct” much of the time

Question 34

How do heuristics work?

Answer 34

• Generic heuristic process of attribute substitution
• Essence of attribute substitution
• person using heuristic may be answering a different question than the one they are being asked
  Example: instead of question “How likely is this airplane crash?”, the individual may be answering the question, “How easily can I imagine this airplane crashing?”