Judgment and Decision Making in Information Systems Fallacies

Judgment and Decision Making in Information Systems Fallacies in Probability Judgment Yuval Shahar M. D. , Ph. D.

Probability Judgments • Both lay people and experts use various judgmental heuristics to judge the probability of uncertain events, such as: – Representativeness (similarity of an instance to a set) – Availability (ease of recall or generation of instances) – Anchoring and adjustment (starting from an initial value) • Probability judgment is mostly intuitive and, unlike formal probability models, is not extensional – It is not based on a detailed (possibly exhaustive) set of possible events – Compound probabilities are not aggregated from elementary ones

The Conjunction Fallacy in Probability Judgment (Tversky and Kahneman, 1983) • If the extension of event A includes the extension of event B, The probability of A should be equal or larger to that of B: – A B => P(A) P(B), because: – P(A) = P(A 1 A 2 … An) = P(A 1)+P(A 2)…+P(An), where each Ai is an extension (a possibility) of event A • Thus, the probability of a conjunction of events cannot be bigger than the probability of any of its components: P(A B) P(A) • In reality, people’s judgments of probabilities do not conform to this law, but are based on various heuristics

A Linguistic Conjunction Fallacy • • Given the probability estimation task: A. “In four pages of a novel (about 2000) words) how many words would you expect to find that have the form ----ing? ” § Options: (0, 1 -2, 3 -4, 5 -7, 8 -10, 11 -15, 16+) B. “How many words would you expect to find that have the form -----n-? ” The median estimates were: – A: 13. 4 (N = 52) – B: 4. 7 (N = 53), P<0. 01 Similar results for -----ly (median: 8. 8) versus -----l- (median: 4. 4) This obvious violation of the conjunction rule occurs due to increased availability (ease of retrievability) of *ing words versus *n- words

Representative Conjunctions • “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 antinuclear demonstrations. • Rank the following 8 statements by likelihood: – – – Linda is a teacher in an elementary school Linda is active in the feminist movement (F) … Linda is a bank teller (T) … Linda is a bank teller active in the feminist movement” (T&F) • F>T&F>T, 85% (N=88)

Representative Conjunctions: Test Types • Indirect tests – Two different groups judge probability of conjunction and its constituents • Direct-subtle tests – Same subjects do both judgments but the inclusion relationship is not emphasized • Direct-transparent tests – Same subjects do both judgments in a format that highlights the inclusion relationship

Conjunction Experiments: Structure • Three types of subjects: – Statistically naïve undergarduates – Statistically informed graduates – Statistically sophisticated graduates • Two types of tests – Direct (subtle) – Indirect • Questions: About Linda and about Bill

Conjunction Experiments Results • In all comparisons, the conjunction is ranked higher than its constituents • There is no difference between direct and indirect tests! • Incidence of violations in direct tests is 88% overall • There is no effect of statistical sophistication level in either test type

Transparent Tests • The questions include only two alternatives: – Linda is a bank teller (T) – Linda is a bank teller and active in the feminist movement (T&F) • Nevertheless, 85% indicate that T&F>T (N=42) • Additional experiments strengthened the conclusions while showing that there is no misunderstanding of the statements

Other Representative Conjunction Experiments • Medical diagnosis – Expertise does not help in preventing the representational conjunction errors • Predicting Wimbeldon tennis results – Borg will lose the first set and win the match (2. 2 rank, where 1 is best) – Borg will lose the first set (2. 7) • Rolling a six-sided cube with 4 green and 2 red faces – GRGRRR ranked higher then RGRRR

Causal Conjunctions • Including a possible causal explanation elevates rated likelihood of a conjunction fallacy (58% in the following case): – Mr F had one or more heart attacks and is over 55 yrs old • Assigning the attributes to two different individuals reduced error rate to 29%

The Hot Hand Fallacy in Basketball (Tversky and Gilovich 1989) • People tend to see runs of hits and misses in basketball game – that is, P(Hit|previous hit)>P(Hit|previous miss) • In reality, neither analysis of a year of NBA games nor that of two college team games showed any statistical phenomena at any aggregation level: Basketball shooting is a pure chance process like coin tossing • The problem is due to the fact that people misperceive what random sequences really are, thus creating the cognitive illusion of finding patterns where none exist; and the more one watches games, the stronger the illusion!