Representativeness Heuristic

Representativeness Heuristic

Representativeness (Kahneman & Tversky, 1972) is the cognitive tendency to judge probabilities by how much an event resembles a stereotype or pattern, rather than by the underlying base rates. In financial settings it generates over-extrapolation: a short streak of same-direction returns is taken as evidence that the underlying process is trending, even when the streak is consistent with random-walk noise. Representativeness is the cognitive root of three closely related biases which differ in whether the generating process is known or uncertain but share the same underlying logic:

• The Law of Small Numbers (Tversky & Kahneman, 1972) states that people believe that even small samples should reflect the properties of the population that generated them.
  • A small sample of fair-coin flips that contains $7$ heads and $3$ tails is therefore taken as evidence that something is wrong with the coin, when in fact a fair coin produces samples that look unbalanced about $35\%$ of the time.
• The Gambler’s Fallacy states that when the generating process is known (e.g., a fair coin), the law of small numbers predicts that future flips will “correct” any imbalance – after $5$ heads in a row, the next flip is expected to be tails.
  • Field evidence: Chen, Moskowitz & Shue (2016) document analogous patterns in asylum-court decisions, loan-application reviews, and baseball umpire calls.
• Hot-Hand Bias is the belief that when the generating process is uncertain (a basketball player whose true skill is unknown), the law of small numbers predicts that a streak signals the underlying state. After several made shots, observers conclude the player is “hot.”
  • Gilovich, Vallone & Tversky (1985) found no statistical evidence for an actual hot hand in NBA shooting data, rather the streaks that subjects perceive are consistent with i.i.d. shooting.

In behavioral asset pricing, representativeness is the cognitive content of Regime $2$ in the Barberis-Shleifer-Vishny (1998) model — after a long string of same-direction earnings shocks, the investor’s posterior shifts toward the trending regime and she over-reacts. Together with conservatism (the under-reaction half), it produces the joint pattern of $1$–$12$ month momentum and $13$–$36$ month reversal. Representativeness is also the leading cognitive root of the modern extrapolative-beliefs literature, which formalizes “putting too much weight on recent observations” as a single recency-weighted average.

Intuition

Bayes’ rule combines a prior (the base rate) with a likelihood (the new evidence) to produce a posterior. Representativeness short-circuits this calculation: instead of multiplying, the agent asks “does the evidence look like the kind of thing that would come from hypothesis $H$?” and answers based on resemblance. The base rate drops out, because a description that resembles a stereotype feels probable regardless of how rare members of that stereotype are in the population.

In financial markets, the same shortcut produces over-extrapolation. Three quarters of strong earnings growth resemble a high-growth firm, even though three quarters is far too short a sample to distinguish a high-growth firm from a mean-reverting one. Investors take the resemblance at face value, conclude the firm is on a trend, and bid up the price further than the news warrants. The same pattern at the market level produces excess volatility, predictability from price ratios, and the value premium.

The unifying thread across the law of small numbers, gambler’s fallacy, and hot-hand bias is the same: people expect short samples to behave like long-run averages. When the underlying process is known to be i.i.d., this expectation produces the gambler’s fallacy (“the coin owes me a tail”). When the process might or might not be i.i.d., it produces the hot-hand bias (“the player must be hot”). The two look like opposite predictions — one expects reversal, the other expects continuation — but they share a single cognitive root.

Properties

(Cognitive Root of Base-Rate Neglect) Representativeness operationalizes $d<1$.

When an agent judges $\mathrm{Pr}(\text{Jack is an engineer}\mid \text{description})$ by how well the description resembles the engineer stereotype, she ignores the base rate $p(\text{engineer})$ in the population. In the Rabin (1998) parametric template
$\frac{\pi (A\mid S)}{\pi (B\mid S)}={\left(\frac{p(S\mid A)}{p(S\mid B)}\right)}^c{\left(\frac{p(A)}{p(B)}\right)}^d,$
this is the case $d<1$ — the prior odds are under-weighted. Kahneman & Tversky (1973) document this directly: a group given a $0.7$ engineer base rate and a group given a $0.3$ base rate produce nearly identical posteriors (around $0.5$) when given an engineer-like description, indicating that the description swamps the base rate. Representativeness is the cognitive story; base-rate neglect is the parametric form of the same bias.

(Law of Small Numbers) Short samples are expected to reflect long-run averages.

Tversky & Kahneman (1971) document that even trained statisticians, when asked to judge the probability of various sample compositions, treat small samples as if they should look like the population. A sequence of $6$ coin flips like $\text{HHHHHH}$ is judged less likely than $\text{HHTHTT}$, even though both have probability $1/64$. The bias arises because the second sequence resembles a typical fair-coin sample while the first does not.

(Gambler’s Fallacy when Process is Known) Streaks predict reversal.

When the data-generating process is known to be i.i.d. — a fair coin, a roulette wheel, a fixed-probability lottery — the law of small numbers predicts that the next observation will “correct” any imbalance. People place fewer bets on lottery numbers that won the previous week (Chen, Moskowitz & Shue, 2016) and asylum judges who granted asylum in the previous case are less likely to grant in the next case, even after controlling for case characteristics. The bias has measurable real-world consequences in domains where decisions are sequential and outcomes appear random.

(Hot-Hand Bias when Process is Uncertain) Streaks predict continuation.

When the data-generating process might not be i.i.d. — a basketball player whose true skill could vary day to day — the law of small numbers predicts that a streak signals the underlying state has shifted. After $4$ made shots in a row, observers conclude the player is “hot” and bet on continuation. Gilovich, Vallone & Tversky (1985) studied $9$ Philadelphia 76ers and found no positive autocorrelation in shot outcomes, with conditional shooting percentages after streaks essentially equal to or slightly below unconditional percentages. The hot hand subjects perceive is a cognitive illusion. Whether the same “hot hand” appears in financial markets, where investors observe a streak of strong returns and infer the firm is trending, is the central application of representativeness in behavioral asset pricing.

(BSV Regime $2$) Representativeness is the trending regime in the Barberis-Shleifer-Vishny model.

In BSV (1998), the representative investor entertains two hypotheses about the earnings process: a mean-reverting regime (conservatism) and a trending regime (representativeness). After a long string of same-direction earnings shocks, the trending regime gains posterior weight and the investor begins to extrapolate, pushing prices past fundamentals. The over-reaction half of momentum-and-reversal therefore follows directly from representativeness — a streak resembles a trend, and the trend hypothesis takes over.

Examples

The engineer-vs-lawyer problem

“Jack is a $45$-year-old man. He is married and has four children. He is generally conservative, careful, and ambitious. He shows no interest in political and social issues and spends most of his free time on his many hobbies which include home carpentry, sailing, and mathematical puzzles.” A group told that Jack was randomly drawn from a pool of $70$ engineers and $30$ lawyers gives a posterior of about $0.55$ that Jack is an engineer. A group told the pool was $30$ engineers and $70$ lawyers gives about $0.50$. The Bayesian posteriors should differ by a factor of roughly $5$ — the descriptions are identical, so the base rate is the only thing changing. Representativeness explains the near-equality: subjects judge the resemblance of the description to the engineer stereotype and ignore the base rate.

The Gilovich-Vallone-Tversky shooting study

Gilovich, Vallone & Tversky (1985) collected shot-by-shot data for $9$ Philadelphia 76ers across an entire season. For each player they computed the conditional probability of making a shot given the outcome of the previous one, two, or three shots. If a hot hand exists, $\mathrm{Pr}(\text{hit}\mid \text{previous hit})>\mathrm{Pr}(\text{hit}\mid \text{previous miss})$. The data showed the opposite or no effect for $8$ of the $9$ players, with the mean correlation between consecutive shots being $-0.04$. Yet $91\%$ of basketball fans surveyed believed in a hot hand. The authors interpret the gap as a vivid case of representativeness: short streaks resemble what people expect from a “hot” player, and the resemblance is mistaken for evidence.

The conjunction fallacy (Linda)

“Linda is $31$, 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 anti-nuclear demonstrations. Which is more probable: (a) Linda is a bank teller, or (b) Linda is a bank teller and is active in the feminist movement?” About $85\%$ of subjects answer (b), even though $\mathrm{Pr}(A\cap B)\le \mathrm{Pr}(A)$ by the laws of probability. The combined description resembles the stereotype Linda fits, so it feels more probable. Representativeness produces a violation of the most basic axiom of probability theory in roughly $4$ out of $5$ educated adults.

See Also

• 8.6. Belief-Based Biases — parent hub.
• 8.6.1. Conservatism — sibling: the under-reaction bias that pairs with representativeness in BSV.
• 8.6.3. Base-Rate Neglect — sibling: the parametric form of representativeness ($d<1$).
• 8.6.7. Extrapolative Beliefs — sibling: the modern formalization of “weight on recent observations” as a recency-weighted average.
• 8.9.1. Barberis-Shleifer-Vishny Model — the asset-pricing model where representativeness is Regime $2$.
• 8.8. Momentum — the empirical pattern that representativeness-driven over-extrapolation helps explain.