# Rank dependent expected utility theory

Rank-dependent expected utility theory is a decision-making model that modifies the traditional expected utility theory by incorporating the decision-makers attitude towards the probability of outcomes, emphasizing the rank or order of outcomes in their preferences.
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Updated: Jun 14, 2024

## 3 key takeaways

• Rank-dependent expected utility theory adjusts traditional expected utility by weighting probabilities according to their rank, reflecting individuals’ risk attitudes more accurately.
• This theory accounts for the tendency of people to overweigh small probabilities and underweigh large probabilities.
• It provides a more realistic description of decision-making under risk and uncertainty compared to traditional expected utility theory.

## What is rank-dependent expected utility theory?

Rank-dependent expected utility (RDEU) theory is an extension of the traditional expected utility theory, which was developed to address some of the inconsistencies observed in real-world decision-making under risk and uncertainty.

The traditional expected utility theory assumes that people evaluate risky options by calculating a weighted sum of the utilities of possible outcomes, with probabilities as weights.

However, RDEU theory modifies this approach by incorporating a probability weighting function, which reflects how individuals perceive and weigh probabilities differently based on their rank or order.

### Importance of rank-dependent expected utility theory

RDEU theory is important because it provides a more accurate and realistic model of how people make decisions under risk. It captures the psychological behavior of individuals who tend to overweigh unlikely events and under weigh highly probable events.

This adjustment makes the theory better suited for explaining real-world phenomena, such as why people buy insurance for rare events or play lotteries with very low chances of winning.

### Components of rank-dependent expected utility theory

The RDEU theory involves several key components:

• Utility function: This represents the decision-maker’s preferences over different outcomes, similar to traditional expected utility theory.
• Probability weighting function: This function transforms the actual probabilities into decision weights, reflecting how the decision-maker perceives the likelihood of different outcomes.
• Ranking of outcomes: Outcomes are ranked in order of preference, and the decision weights are assigned based on this ranking.

### How rank-dependent expected utility theory works

In RDEU theory, the decision weights are derived from a probability weighting function that distorts the actual probabilities. The overall value of a risky prospect is then calculated by summing the weighted utilities of the possible outcomes, where the weights depend on the rank of the outcomes and the transformed probabilities.

## Example of rank-dependent expected utility theory in practice

Consider a simple gamble with two possible outcomes:

1. Winning \$100 with a probability of 0.1
2. Winning nothing with a probability of 0.9

In traditional expected utility theory, the expected utility (EU) would be calculated as: EU = (0.1 * U(\$100)) + (0.9 * U(\$0))

Where U(\$100) and U(\$0) are the utilities of the respective outcomes.

In RDEU theory, we first apply a probability weighting function to the probabilities. Suppose the weighting function is w(p), where w(0.1) might be 0.2 (overweighting the small probability) and w(0.9) might be 0.8 (underweighting the large probability). The rank-dependent expected utility (RDEU) would then be calculated as RDEU = (w(0.1) * U(\$100)) + (w(0.9) * U(\$0))

Assuming U(\$100) is 1 and U(\$0) is 0, we get: RDEU = (0.2 * 1) + (0.8 * 0) = 0.2

### Impact of rank-dependent expected utility theory

RDEU theory has several significant implications:

• Behavioral insights: It provides deeper insights into human behavior under risk, explaining phenomena like the overvaluation of low-probability events and undervaluation of high-probability events.
• Policy and economics: This theory can inform policies and economic models by accounting for how people actually perceive and respond to risk, leading to better-designed insurance products, investment strategies, and public policies.
• Financial decision-making: Investors and financial analysts can use RDEU theory to better understand market behavior and develop strategies that align with actual risk perceptions.

### Challenges and limitations

While RDEU theory offers a more realistic model of decision-making under risk, it also presents challenges:

• Complexity: The inclusion of a probability weighting function complicates the model, making it more difficult to apply in practice.
• Parameter estimation: Accurately estimating the probability weighting function and utility function for individuals can be challenging.
• Empirical validation: While RDEU theory explains many observed behaviors, it still requires robust empirical validation across different contexts and populations.

Understanding rank-dependent expected utility theory is essential for analyzing decision-making under risk and uncertainty.

By incorporating probability weighting and the rank of outcomes, RDEU theory offers a more accurate and nuanced view of how individuals evaluate risky prospects. This enhances our understanding of economic behavior and informs better decision-making strategies.

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Arti is a specialized AI Financial Assistant at Invezz, created to support the editorial team. He leverages both AI and the Invezz.com knowledge base, understands over 100,000... read more.