Chapter 29: The Fourfold Pattern

Type: Chapter 29

Category: Psychology

Difficulty: Advanced

Reading time: 7 min

Core idea

Prospect theory produces four distinct risk attitudes, organized by two dimensions:

• Domain: gains vs. losses
• Probability: high (near-certain) vs. low (unlikely)

This fourfold pattern explains why the same person will:

• Buy insurance (risk-averse in the high-probability gain domain… wait — insurance is risk-averse in the loss domain with high probability of loss)
• Buy lottery tickets (risk-seeking in the gain domain with low probability)
• Settle legal cases (risk-averse, avoiding the certain large loss of a trial going wrong)
• Continue gambling to recover losses (risk-seeking in the loss domain)

The pattern is not incoherent. It follows systematically from two mechanisms: (1) the S-shaped value function of prospect theory (diminishing sensitivity + loss aversion), and (2) the probability weighting function — how people subjectively transform probabilities.

Why it matters

The probability weighting function

People do not treat probabilities linearly. They overweight low probabilities and underweight high ones. A 1% chance feels more than 1/100 as important as a 100% certainty; a 99% chance feels less than 99/100 as important as certainty. The probability weighting function is an inverted S-shape: steep near 0 and 1 (near-zero and near-certainty are especially salient), flat in the middle.

This weighting function interacts with the value function to produce the fourfold pattern.

The four quadrants

Domain	Probability	Risk attitude	Example behavior
Gains	High (probable gain)	Risk-averse	Accept certain gain over favorable gamble
Gains	Low (unlikely gain)	Risk-seeking	Buy lottery tickets
Losses	High (probable loss)	Risk-seeking	Reject certain loss, prefer gamble
Losses	Low (unlikely loss)	Risk-averse	Buy insurance

The upper-left quadrant (high-probability gains, risk-averse) and lower-right quadrant (low-probability losses, risk-averse) represent the “sure thing” preference — people avoid gambling when the outcome is likely favorable, and pay to avoid unlikely disasters.

The upper-right quadrant (low-probability gains, risk-seeking) and lower-left quadrant (high-probability losses, risk-seeking) represent “long shot” behavior — gambling for the small chance of a large gain, and gambling to avoid locking in certain large losses.

Settlement decisions and litigation

The fourfold pattern has direct application to legal settlements. A defendant facing a likely judgment against them (high-probability loss domain) will be risk-seeking — they prefer to gamble at trial over accepting a certain settlement. A plaintiff facing a likely large judgment (high-probability gain domain) will be risk-averse — they prefer a certain settlement. This asymmetry makes settlement difficult precisely in cases with clear liability and large damages: the plaintiff wants to settle; the defendant wants to go to trial.

Author’s argument: The fourfold pattern explains why litigants and lawyers frequently behave in ways that seem mutually disadvantageous — each is responding rationally to the prospect theory value of their own position.

Key takeaways

Key takeaways

• Fourfold pattern: prospect theory predicts four distinct risk attitudes organized by domain (gains/losses) × probability level (high/low) — not a single consistent risk attitude.
• Probability weighting: people overweight low probabilities and underweight high ones — a nonlinear transformation that interacts with the value function to produce the four quadrants.
• High-probability gains → risk-averse: prefer the certain good outcome to a gamble with equal expected value.
• Low-probability gains → risk-seeking: overweight the small chance of a large gain (lottery, long-shot investments).
• High-probability losses → risk-seeking: prefer the gamble to a certain large loss (continue gambling after losses, reject settlement).
• Low-probability losses → risk-averse: pay to eliminate small risks (insurance, extended warranties) — overweighted low probability × loss aversion.

Mental model

click to zoom

The fourfold pattern — four risk attitudes predicted by the interaction of domain and probability level.

Read it as: Risk preference is not a stable individual trait — it depends on which quadrant of the fourfold pattern the current situation activates. The same person is risk-averse in the top-left (won’t gamble a near-certain gain), risk-seeking in the top-right (buys lottery tickets), risk-seeking in the bottom-left (gambles to avoid certain loss), and risk-averse in the bottom-right (buys insurance against small risks). The pattern is systematic and predictable — but often appears contradictory to observers expecting consistent risk attitudes.

Practical application

Litigation and the fourfold pattern

When a legal case has clear liability and large damages, expect settlement to be difficult. The plaintiff (high-probability gain) is risk-averse and wants to settle. The defendant (high-probability loss) is risk-seeking and prefers to gamble at trial. Mediation must overcome the structural asymmetry by reframing each party’s position — for example, helping the defendant see a settlement as avoiding the upside of an escalating judgment (loss avoidance framing).

Applying the fourfold pattern:

• Product design: low-cost extensions and warranties exploit the low-probability loss quadrant — people pay disproportionately to eliminate small risks, even when the expected value is negative.
• Salary and bonus negotiations: employees in the gain domain (salary increase above current) are risk-averse and prefer certain smaller increases over gambles. Employees who face potential pay cuts are in the loss domain and become risk-seeking.
• Portfolio management: the fourfold pattern predicts that investors will hold losing positions too long (risk-seeking in the loss domain) and sell winners too early (risk-averse in the gain domain) — the disposition effect, one of the most-replicated findings in behavioral finance.

Example

A pharmaceutical company is evaluating two experimental drug candidates. Drug A has a 90% chance of reducing symptoms by 30% (high-probability, moderate gain). Drug B has a 10% chance of eliminating symptoms entirely but an 80% chance of no effect (low-probability, large gain). From an expected-value standpoint, Drug A is superior (0.9 × 30% = 27% vs. 0.1 × 100% = 10% expected symptom reduction).

The fourfold pattern predicts: executives in the high-probability gain domain (Drug A) should prefer the certain result. But if the company is facing a competitive crisis (loss domain), they will switch to risk-seeking and prefer Drug B’s “home run” potential even though the expected value is lower. The decision context — not just the probabilities — determines which quadrant is active and therefore which risk attitude dominates.

Related lessons

Related

Chapter 26: Prospect Theory The S-shaped value function and loss aversion that underlie the fourfold pattern. Chapter 30: Rare Events The overweighting of small probabilities — the mechanism that drives lottery-buying and insurance-buying behavior. Prospect Theory The full formal model, including the probability weighting function that produces the fourfold pattern.