Representative Heuristic

Cognitive Tool box 

• We have some fundamental, automatic cognitive abilities, such as (Kahneman, 2003):

  • The ability to judge similarities between objects or events; 

  • the ability to recognize a previously experienced situation or individual; 

  • The ability of retrieve additional information about an object or situation once it has been recognized; 

  • The ability to “see” casual relationships between events 

Two heuristics, two cognitive capacities

• Availability heuristic → memory retrieval 

• Representativeness heuristic  → similarity assessment 

• Representativeness is an assessment of the degree of correspondence between a sample and a population, an instance and a category, an act and an actor or, more generally, between an outcome and a model 

Representativeness heuristic

• People rely on representativeness heuristics in which probabilities are evaluated by the degree to which A is representative of B (that is, by the degree to which A resembles B)

• E.g when A is highly representative of B, the probability that A originates from B is judged to be high 

  • When A is not similar to B, the probability that A originates from B is judged to be low 

Conjunction Fallacy

• The conjunction of two events is ranked to be more likely than one or both of the conjuncts

• The violation of the conjunction rule is called the conjunction fallacy

Conjunction fallacy: Mathematical Explanation 

• Let A = “Linda is a bank teller”

• Let B = “Linda is active in the feminist movement” 

  • The probability of A and B (the conjunction) is denoted as P(A∩B) according to the conjunction rule in probability 

    • P(A∩B) ≤ P(A)

• This means that the probability of two events (A and B) occurring together cannot be higher than the probability of either one occurring alone 

• For instance:

  • Let P(A) = 0.4 (40% chance Linda is a bank teller)

  • Let P(B) = 0.6 (60% chance Linda is active in the feminist movement)

  • then , the maximum possible value of P(A∩B) (if A and B were independent) would be:

    • P(A∩B) = P(A) x P(B) = 0.4 x 0.6 = 0.24

• The subjects ranked the outcomes by the degree to which Bill (or Linda) matched the respective stereotypes 

• The correlation between the mean ranks of probability and representativeness was .96 for Bill and .98 for Linda

“Transparent Version”

• A group of 142 undergraduates at UBC were asked to check which of two alternatives was more probable: 

  • Linda is a bank teller (B)

  • Linda is a bank teller and is active in the feminist movement (B&F)

• The order of alternative was inverted for one half of the subjects, but this manipulation had no effect 

• Overall 85% of respondents indicated that B&F was more probable than B, in a violation of the conjunction rule

“Additional explanation” version

• Another group of UBC udnergraduates was asked to indicate which of the following two arguments they found more convincing:

  • Argument #1: Linda is more likely to be a bank teller thank she is to be a feminist bank teller, because every feminist bank teller is a bank teller, but some women bank tellers are not feminists, and Linda could be one of them 

  • Argument #2: Linda is more likely to be a feminist bank teller than she is likely to be a bank teller, because she resembles an active feminist more than she resembles a bank teller 

• The majority of subjects (65%, n = 58) chose the invalid resemblance argument (Argument 2) over the valid extensional argument (Argument 1) 

Conjunction Fallacy

• Naive subject do not spontaneously treat the conjunction rule as decisive 

• Naive subjects generally endorse the conjunction rule in the abstract, but their application of this rule to the Linda problem is blocked by the compelling impression that B&F is mro representative of her than B is

Conjunction Fallacy 

• 103 physicians were given problems of the following type:

•  A 55 year old woman had pulmonary embolism (blood clots in the lung) documented angiographically 10 days after a cholecystectomy. Please rank the following in terms of the probability that they will be among the conditions experienced by the patient (use 1 for most likely and 6 for the least likely) Naturally the patient could experience more than one of these conditions 

  • Dyspnea (shortness of breath and hemiparesis (partial paralysis) 

  • Calf pain

  • Pleuritic chest pain

  • Syncope and tachycardia 

  • Hemipareisis 

  • Hemoptysis

• 91% of physicians violated the conjunction rule 

• Conjunction fallacy is robust to:

  • Transparency 

  • Additional explanation

  • Statement of extension of (whether or not) 

  • Expertise

Conjunction fallacy among children 

• In a simpler form with children participants (Agnoli, 1991) 

  • In summer at the beach, are there more women or more tanned women?

  • Does the mailman put more letters or more pieces of mail in your mailbox?

Conjunction “fallacy”?

• Gigerenzer et al → “adaptive toolbox”

• Content-blind norms

• E.g semantic ambiguity of “AND” operator (union vs intersection)

  • “We invited friends and colleagues to the party”

  • Probability vs frequency formats 

The representativeness heuristic overrides the factors that should affect judgment

• Insensitivity to prior probability of outcomes (base-rates)

• A certain town has 2 hospitals 

  • Large hospital: About 45 babies are born each day

  • Small hospital: About 15 babies are born each day

• In each hospital about 50% of babies are boys, However, the exact percentage varies from day to day some days it might be higher, and some days lower 

• Insensitivity to prior probability of outcomes (base-rates)

• Insensitivity to sample size

• Misconception of chance 

• Example: Coin Flip → HTHTTH to be more likely than HHHTTT 

Conjunction fallacy & Prejudice 

• Gervais, Shariff and Morenzayan (2011): Do you believe in atheists? Distrust is central to anti-atheist prejudice