Tversky and Kahneman (1974) identified three cognitive shortcuts — representativeness, availability, and anchoring — that systematically distort probability judgment. In a series of controlled experiments published in Science, Vol. 185, No. 4157, 95 undergraduate students and trained researchers served as subjects. In an anchoring experiment, subjects given a random starting point of 10 estimated 25 percent of UN member countries were African. Those given 65 estimated 45 percent. Subjects' stated 98-percent confidence intervals were too narrow on about 30 percent of problems; the calibrated rate is 2 percent.
What the Study Found
Tversky and Kahneman (1974) set prior odds at 70/30 engineers-to-lawyers versus 30/70 in separate conditions. Both groups produced essentially identical probability judgments — a violation of Bayes' rule, which predicts an odds ratio of (.7/.3)² = 5.44. When given an uninformative description, subjects assigned probability .5 for engineer. The stated base rate was .7 or .3; both produced the same answer. High school students estimating 8×7×6×5×4×3×2×1 produced a median of 2,250; those estimating 1×2×3×4×5×6×7×8 produced a median of 512; the correct answer is 40,320. 53 of 95 students chose "about the same" in the hospital problem. The smaller hospital was correct — it deviates more from 50 percent.
Methodology
Tversky and Kahneman conducted controlled judgment experiments at the Hebrew University, Jerusalem, using undergraduate students and experienced research psychologists as subjects. The hospital problem used 95 undergraduate students. No single time period applies across the paper's experiments. Key manipulations included varying base rates, anchor values, and sample sizes. Accuracy payoffs were provided in several experiments and confirmed not to reduce anchoring or base-rate neglect.
Key Statistics
| Metric | Finding | Context |
|---|---|---|
| Anchoring: starting point 10 | Median estimate 25% | Subjects estimating % African countries in UN |
| Anchoring: starting point 65 | Median estimate 45% | Same question; arbitrary starting point differed by 55 points |
| Ascending sequence (1×2×…×8) | Median estimate 512 | Correct answer is 40,320 |
| Descending sequence (8×7×…×1) | Median estimate 2,250 | Correct answer is 40,320 |
| Bayesian odds ratio (70/30 vs. 30/70 conditions) | (.7/.3)² = 5.44 | Subjects produced essentially equal judgments across conditions |
| Uninformative description — probability of engineer | .5 regardless of base rate | Base rate stated as .7 or .3; subjects ignored it |
| Hospital problem — chose "about the same" | 53 of 95 students | Correct answer: smaller hospital shows more extreme deviation |
| Confidence interval miscalibration | ~30% of problems outside stated 98% interval | Expected rate for proper calibration is 2% |
| Second-group median odds | 3:1 | Should have retrieved 9:1 odds; anchoring pulled toward even odds |
| Events assigned probability .10 that actually occurred | 24 percent | First group — too extreme; events were far more frequent than judged |
| Committees of 2 — median estimate | 70 (correct: 45) | Imaginability bias; small committees easier to visualize |
| Committees of 8 — median estimate | 20 (correct: 45) | Imaginability bias; large committees harder to visualize |
Why This Matters
Analysts who hear an initial earnings estimate anchor to that number, even when aware of the bias. The same interval-narrowing pattern found here produces systematic underestimation of tail risk in quantitative models. Availability bias distorts perceived risk after market events: recently experienced outcomes feel more probable than base rates support. Overestimating conjunctive probabilities — each step in a plan feels likely — drives the planning fallacy in project management and portfolio construction.