The Fourfold Pattern

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

Mental model

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Practical application

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.

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