# Three Heuristics That Distort Probability Judgment

Cite as: Gorak, R. (2026). Three Heuristics That Distort Probability Judgment. Tradicted. https://www.tradicted.com/research/tversky-heuristics-1974/
Paper: Amos Tversky and Daniel Kahneman — *Judgment under Uncertainty: Heuristics and Biases*
Published in: Science (1974)
Original: https://www.jstor.org/stable/1738360

Key finding: Anchoring caused subjects given a starting point of 10 to estimate 25 percent African countries in the UN, while those given 65 estimated 45 percent — a 20-point spread from an arbitrary number.

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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. Heuristics operate below the level you notice while trading. Recording the reasoning behind each entry in a [trading journal](/trading-journal/) gives you something to audit afterward.

## FAQ

### What is the anchoring effect and how large is it?

20 percentage points separated median estimates when arbitrary starting points differed by 55 points. Tversky and Kahneman (1974) showed subjects adjust insufficiently from initial values even when anchors are generated by a random wheel spin. Offering accuracy payoffs did not reduce the effect. In finance, initial price levels and analyst targets create the same anchoring pull on subsequent estimates.

### How does insensitivity to base rates affect probability judgment?

Bayes' rule predicts the odds ratio between 70/30 and 30/70 engineer-lawyer conditions should be 5.44; subjects produced essentially identical judgments in both. Tversky and Kahneman (1974) found that even an uninformative description caused subjects to assign probability .5 regardless of base rates of .7 or .3. Portfolio managers who weight vivid narratives over background failure rates exhibit the same pattern.

### What does the research show about overconfidence in probability estimation?

True values fell outside subjects' stated confidence intervals on about 30 percent of problems, against a calibrated rate of 2 percent. Tversky and Kahneman (1974) found this overclaiming held for both naive subjects and experienced researchers. Options traders who set implied volatility too low and risk managers who underestimate tail probabilities replicate the same interval-narrowing documented here.

### How does the availability heuristic create predictable errors in frequency estimation?

Subjects estimated 70 committees of 2 members versus 20 committees of 8, from a group of 10. The correct answer is 45 in both cases. Tversky and Kahneman (1974) showed that ease of mental construction, not actual frequency, drives these estimates. Market participants who judge the probability of a crash by how easily they recall the last one exhibit the same availability-driven distortion.

## Source

Tversky, A., & Kahneman, D. (1974). Judgment under Uncertainty: Heuristics and Biases. *Science*, 185(4157), 1124–1131.

[Read the full paper →](https://www.jstor.org/stable/1738360)