Probability, Heuristics, and Biases Flashcards
Probability Theory
accepted as a normative theory of probability judgements
Axiomatic Theory
starts with some axioms and definitions and develops propositions
Bayesian Updating Process:
- 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
System 1 of brain:
- Quick & automatic
- effortless & involuntary
- effortlessly generating impressions & feelings that are sources for beliefs & choices of system 2
System 2:
- involves effort
- conscious
- has beliefs from system 1, makes choices
- decides what to think about and do
- responsible for concentration on a problem
System 1 & System 2 together
- 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);
Which system can make systematic mistakes (biases)
System 1 - it may use heuristics to estimate probabilities or make decisions
Heuristics
Rule of Thumb e.g. choose the 2nd cheapest bottle of wine
Representativeness heuristic
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
The Gambler’s Fallacy
belief that after long sequence of red, “black is now due”, failure to understand independence of events
Insensitivity to Sample Size
with a smaller sample size, extreme outcomes are more likely.
Conjunction Fallacy:
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)
Disjunction Fallacy:
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
When updating beliefs, Bayes rule requires us to take into account what 3 things?
the base rate, the evidence, and the conditional probabilities
what is base rate neglect?
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
Anchoring and adjustment heuristic
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)
Availability Heuristic
makes you assess the probability of an event based on how easily it comes to mind
- assess probability based on accessibility
Affect heuristic
Assigns probability to consequences based on how you feel about them; feel good - higher probability; feel bad - lower probability
Availability Heuristic Pro
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
Availability Heuristic Con
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
Availability Heuristic Biases arise due to:
- 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
When does System 2 overwrite the intuitive response of system 1?
- 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
What is the goal of Bayesian updating? Explain in one sentence.
Normative rule of how to update probabilistic beliefs in the face of new evidence
Let H stand for hypothesis and E for evidence. Which probability are we looking for when applying Bayesian updating? Explain in one sentence.
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)
