Cumulative Prospect Theory (CPT) stands as one of the most influential models in behavioral economics and decision theory. Developed by Daniel Kahneman and Amos Tversky in 1992, CPT extends the foundations laid by Prospect Theory, offering a more nuanced explanation of how individuals make decisions under risk and uncertainty. Unlike traditional economic theories that assume people are fully rational, CPT accounts for the psychological biases and cognitive processes that shape human decision-making. In this article, I will delve deeply into the principles of CPT, explain its components, and illustrate its applications and implications in real-world scenarios.
Table of Contents
What is Cumulative Prospect Theory?
Cumulative Prospect Theory is an advanced model that addresses the way people perceive gains and losses, which often deviates from traditional economic models. It proposes that individuals do not treat all probabilities in the same way when evaluating risky choices. Instead, they weigh probabilities in a nonlinear fashion. This theory refines the original Prospect Theory, which had two main components: the value function and the probability weighting function. CPT introduced the idea of cumulative decision-making, which accounts for the way individuals aggregate probabilities when faced with multiple potential outcomes.
The theory is rooted in two primary concepts: loss aversion and probability weighting. Loss aversion refers to the tendency for people to prefer avoiding losses over acquiring gains of the same magnitude. Probability weighting describes how individuals tend to overweight small probabilities and underweight large probabilities, leading to choices that differ from what traditional expected utility theory would predict.
Key Components of Cumulative Prospect Theory
CPT comprises several key elements that differentiate it from other decision-making models. These include:
- Value Function: In CPT, the value function is concave for gains and convex for losses. This reflects diminishing sensitivity, meaning that as the magnitude of a gain or loss increases, the perceived value of the change decreases. The value function is steeper for losses than for gains, which captures the notion of loss aversion.
- Probability Weighting Function: The probability weighting function represents how people perceive probabilities. In traditional expected utility theory, probabilities are treated linearly. However, in CPT, small probabilities are often overweighted, and large probabilities are underweighted. This helps explain behaviors like buying lottery tickets or insurance.
- Cumulative Decision Weights: CPT introduces the concept of cumulative decision weights, which modify the way probabilities are aggregated. Instead of evaluating each outcome independently, individuals combine outcomes in a cumulative manner, considering both the potential gains and losses in a way that reflects their psychological bias.
The Value Function: Gains and Losses
The value function is central to understanding CPT. The function can be split into two distinct parts: one for gains and one for losses. For gains, the function is concave, meaning that the marginal value of each additional unit of gain decreases as the total gain increases. This is a manifestation of diminishing sensitivity. For losses, the function is convex, which means that the pain from each additional loss increases as the size of the loss grows. This reflects the psychological phenomenon of loss aversion.
Loss Aversion
One of the most important insights from CPT is the concept of loss aversion. Kahneman and Tversky found that losses are psychologically more painful than equivalent gains are pleasurable. In their experiments, they showed that people tend to prefer avoiding losses rather than acquiring gains of the same magnitude. For example, the negative emotional impact of losing $100 is greater than the positive impact of winning $100.
Loss aversion can be quantified using a value function where the coefficient of losses is greater than that for gains. Typically, the coefficient for losses is about 2.5 times larger than that for gains. This implies that individuals are roughly 2.5 times more sensitive to losses than to gains.
Example of Value Function
Let’s look at an example of how the value function operates:
- Imagine a person is given two options: either gain $100 or lose $100.
- The value of gaining $100 might be 70 units of value.
- The value of losing $100 might be -175 units of value.
This illustrates loss aversion — the pain of losing $100 outweighs the pleasure of gaining $100 by a factor of approximately 2.5.
Probability Weighting: The Distortion of Probabilities
In Cumulative Prospect Theory, people do not evaluate probabilities in a straightforward manner. Rather, they apply a subjective weighting to probabilities, leading to decisions that deviate from those predicted by expected utility theory.
Overweighting Small Probabilities
One of the key insights of CPT is that people tend to overestimate small probabilities. For example, the chance of winning a lottery may be extremely small, but the subjective value placed on that small chance is disproportionately high. This helps explain why people are willing to spend money on lottery tickets despite the extremely low likelihood of winning.
Underweighting Large Probabilities
On the other hand, individuals tend to underweight high probabilities. For instance, the probability of winning a relatively small but certain reward (like a 90% chance of winning $10) may be perceived as less attractive than it actually is. People may focus more on the 10% chance of losing, even though the expected value is heavily skewed toward the larger probability.
Example of Probability Weighting
Suppose a person faces a choice between two gambles:
- Gamble 1: 50% chance of winning $100, 50% chance of winning $0.
- Gamble 2: 100% chance of winning $50.
Using CPT’s probability weighting function, the individual might overweight the small probability in Gamble 1 and underweight the certainty of Gamble 2, choosing Gamble 1 even though the expected value of Gamble 2 is higher.
Cumulative Prospect Theory in Action: A Real-World Example
Let’s take a closer look at how CPT can be applied in real-world decision-making. Consider the stock market, where investors face uncertainty regarding the future performance of their investments.
- Investor A: Investor A is risk-averse and prefers to avoid losses. Based on CPT, this individual is likely to be more sensitive to potential losses than gains. If faced with a choice between a risky investment that has a high chance of a small gain and a low chance of a large loss, Investor A may avoid the risk, even if the expected value of the risky investment is higher.
- Investor B: Investor B, on the other hand, may overweight the small probability of a large gain, despite the large probability of a small loss. As a result, this investor may be more inclined to take risks, even when the overall expected value is lower.
Example with Calculation
Let’s calculate the expected utility for both investors:
Investor A:
- Risky investment: 70% chance of gaining $100 and 30% chance of losing $100.
- For Investor A, the value of a $100 gain is 70, and the value of a $100 loss is -175.
- The expected utility is calculated as: 0.7×70+0.3×(−175)=49−52.5=−3.50.7 \times 70 + 0.3 \times (-175) = 49 – 52.5 = -3.50.7×70+0.3×(−175)=49−52.5=−3.5
Investor B:
- Risky investment: 70% chance of gaining $100 and 30% chance of losing $100.
- For Investor B, the value of a $100 gain is 70, and the value of a $100 loss is -100.
- The expected utility is: 0.7×70+0.3×(−100)=49−30=190.7 \times 70 + 0.3 \times (-100) = 49 – 30 = 190.7×70+0.3×(−100)=49−30=19
Despite the negative expected utility for Investor A, they may still avoid the risky investment, demonstrating the influence of loss aversion and probability weighting.
Implications of Cumulative Prospect Theory
Cumulative Prospect Theory has far-reaching implications across various fields. In finance, it helps explain investor behavior, especially in the context of market anomalies, such as the equity premium puzzle (where stocks yield higher returns than can be justified by traditional models). In marketing, CPT can be used to predict consumer choices, especially in the context of promotions and pricing strategies.
Furthermore, CPT plays a significant role in understanding policy decisions, risk management, and insurance markets. It explains why individuals may purchase insurance even when the expected value suggests that it is not economically rational to do so.
Conclusion
Cumulative Prospect Theory offers a powerful lens through which to understand human decision-making in uncertain environments. By incorporating psychological insights like loss aversion and probability weighting, it provides a more accurate description of how people evaluate risks and rewards compared to traditional economic models. Whether in investment decisions, consumer behavior, or policy-making, CPT has proven to be a valuable tool for understanding the complexities of human choices. I hope this exploration has helped clarify the key principles of CPT and its real-world applications.
