Prospect Theory

Daniel Kahneman and Amos Tversky's Prospect Theory is a cornerstone of behavioral economics. It challenges the foundational assumptions of expected utility theory, offering a more accurate description of how people actually make decisions under risk. The theory replaces the notion that people evaluate final states of wealth with the idea that psychological reference points, probability distortions, and an asymmetric sensitivity to losses dominate choice.

The Central Flaw in Expected Utility Theory

Traditional models, like Bernoulli’s expected utility theory, assume that people evaluate the utility of final states of wealth. Kahneman and Tversky demonstrated that this is flawed. Experimental evidence shows that people assess outcomes as gains and losses relative to a reference point, typically the status quo or their current wealth, not against an absolute level of final wealth.

Key Principles of Prospect Theory

The theory is built on several cognitive features that operate largely automatically (System 1):

1. Reference Point (Reference Dependence): Outcomes are evaluated relative to a neutral reference point—such as the status quo, an expectation, or an entitlement. Outcomes above this point are perceived as gains; those below it are perceived as losses. The same absolute monetary outcome can feel like a gain or a loss solely because of a shift in the reference point.

2. Diminishing Sensitivity: The subjective difference between outcomes shrinks as they move farther from the reference point. For example, the psychological difference between $100 and $200 feels much larger than the difference between $1,100 and $1,200. This principle applies both to the value of money and to the impact of probabilities, giving rise to an S-shaped value function and a nonlinear probability weighting function.

3. Loss Aversion: The displeasure from a loss is psychologically more intense than the pleasure from an equivalent gain. The loss aversion ratio is typically between 1.5 and 2.5, meaning the pain of losing $100 is roughly 1.5 to 2.5 times as strong as the pleasure of gaining $100. This asymmetry makes the value function steeper in the domain of losses than in the domain of gains.

4. Probability Weighting: People do not treat probabilities linearly. Small probabilities (e.g., 1% or 5%) tend to be overweighted, while moderate and large probabilities are underweighted. This explains why individuals are simultaneously attracted to long-shot gambles (overweighting the small chance of a large gain) and to insurance against unlikely disasters (overweighting the small chance of a large loss). The probability weighting function captures the non-linear transformation of objective probabilities into decision weights.

The S-Shaped Value Function

The combination of diminishing sensitivity and loss aversion produces a characteristic S-shaped value function that is concave in the domain of gains (exhibiting risk aversion) and convex in the domain of losses (exhibiting risk seeking), with a steeper slope for losses than for gains. This graph has become the “flag” of Prospect Theory and explains two critical behaviors:

• Risk Aversion in Gains: People prefer a sure gain ($500 for sure) over a gamble with a higher expected value (50% chance of $1,000). The diminishing sensitivity of gains makes the certain additional gain more attractive than the uncertain possibility of a larger one.
• Risk Seeking in Losses: People prefer a gamble (90% chance to lose $1,000) over a sure loss ($900). The vivid aversion to a sure loss, amplified by loss aversion, drives them to accept risk in the hope of avoiding any loss at all.

The Importance of Framing (The Gift Experiment)

Problems 3 and 4 from the original research provide a rigorous demonstration that choices violate the standard rational model:

• Problem 3: Given $1,000, choose between a 50% chance to win an additional $1,000 or a sure $500. Most people choose the sure $500 (risk aversion in gains).
• Problem 4: Given $2,000, choose between a 50% chance to lose $1,000 or a sure loss of $500. Most people choose the gamble (risk seeking in losses).

Both problems lead to the exact same final states of wealth—a sure $1,500 versus a 50% chance of ending up with either $1,000 or $2,000. Yet preferences reverse. The initial gift shifts the reference point: in Problem 3 the options are seen as gains, in Problem 4 they are seen as losses. This demonstrates that decisions are not just about final wealth; they are shaped by the psychological experience of gains and losses relative to a reference point. Framing the same objective outcome as a gain or a loss systematically changes risk preferences, exactly as predicted by Prospect Theory.