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# Expected Utility Theory

Updated on January 29, 2024
Article byWallstreetmojo Team
Edited by
Reviewed byDheeraj Vaidya, CFA, FRM

## What Is Expected Utility Theory?

The expected utility refers to a theory summarizing the utility that one expects an aggregate economy or entity to reach irrespective of different circumstances. Individuals utilize it as a tool to analyze situations where they have to make decisions without being aware of the possible outcomes.

For eg:
Source: Expected Utility Theory (wallstreetmojo.com)

This theory advises selecting an event or action with maximum expected utility. The decision to select an action will depend on an entityâ€™s risk appetite. This concept also helps in explaining the reason for individuals taking out an insurance policy. Two applications of this theory are economics and public policy and ethics.

### Key Takeaways

• The expected utility theory refers to a decision-making tool under circumstances when an entity does not know the outcome. People use it for elucidating decisions taken under certain risk conditions.
• Individuals can calculate expected utility by summing up (probability x utility) for every outcome.
• A noteworthy advantage of this utility is that it can show how people value the various potential outcomes based on their risk attitude.
• One must note that this utility theory might be impractical in certain circumstances where the assumptions concerning transitivity, rationality, and completeness do not hold.

### Expected Utility Theory Explained

The expected utility refers to an event or actionâ€™s utility over a certain duration under any circumstance. This concept facilitates decision-making when there is uncertainty. According to this theory, people will select the event or action with the maximum expected utility, which one can obtain by summing up the products of utility and probability over every possible outcome. Individualsâ€™ decision depends on their risk aversion and other agentsâ€™ utility.

It is derived from the expected utility theory, a hypothesis stating that the weighted average of every possible utility level will best depict utility at any point in time under uncertainty.

The theory notes that moneyâ€™s utility need not necessarily be the same as the overall value of money. Moreover, as noted above, it helps explain why individuals take out an insurance policy to safeguard themselves from risks. However, in this case, the payback for individuals is not immediate. Instead, the policyholders can avail of tax benefits and obtain a specific income once a predetermined duration expires. Therefore, paying for insurance with expected utility is better than investing funds in any other product.Â

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### How To Calculate?

To calculate expected utility, individuals must multiply the agentâ€™s value of every plausible outcome of the event or action by the probability of the outcome materializing. After that, they must compute the sum of those numbers.

### Examples

Let us look at a few expected utility examples to understand the concept better.

#### Example #1

Suppose an individual named Sam purchases a lottery ticket. In this case, there are two potential outcomes â€“ he may lose the full amount spent to make the purchase, or he might make a profit if he wins the lottery partially or fully. After assigning probability values to the associated costs, which in this case, is the lottery ticketâ€™s cost price, it is easy to find that the expected utility one can obtain from buying the ticket is more than not purchasing it.

#### Example #2

Jordan Ellenberg, a mathematician at the University of Wisconsin, explored the issue of arriving at the airport too early or late. He explained that the problem comes down to the concept of expected utility.

According to him, determining when individuals must leave for the airport to catch their flight involves an exchange or a tradeoff: The earlier one shows up at the airport, the more likely the person is to catch a flight. However, if individuals show up early, they have to bear the cost of the time lost at the airport waiting for their flight. After all, one can utilize that time elsewhere for something productive.

The concept of utility helps in quantifying this. For example, suppose every hour at an airport cost 5 utils (unit of utility). On the other hand, let us say that the cost of missing a flight is 25 utils. So, simply put, missing a flight is 5 times more annoying to an individual than the total inconvenience of spending one hour at an airport. This allows one to determine the expected utility loss based on when one arrives at the airport.

### Applications

A few applications of this concept are as follows:

#### #1 – Ethics

According to the belief of utilitarians, an actâ€™s result determines if an entity took the right action. That said, it is extremely challenging to establish an actâ€™s long-term consequence. Hence, a few authors argue that one must consider the act with the maximum anticipated moral value, the right act, rather than the act leading to the best consequences.

Other experts argue that even if individuals must take an action that will result in the best outcome, this utility theory may help make decisions when the actionsâ€™ consequences become uncertain.

#### #3 – Economics And Public Policy

This utility theory has application in public policy because it elucidates that the social arrangement maximizing the overall welfare throughout society is the most accurate. The micromort concept that Ronald Howard, an American professor, introduced in the 1980s utilizes this utility concept to gauge various mortality risksâ€™ acceptability.

The use of expected utility in behavioral finance is also popular for guiding health insurance plans. Moreover, insurance sales involve utilizing this theory to compute risks with the objective of long-term financial gain while considering the chance of going bust for a limited period.

Let us look at the benefits and limitations of this type of utility.

• It can elucidate the risk attitudes, which are individualsâ€™ preferences over uncertain outcomes. In other words, the concept reflects how individuals value outcomes differently based on their risk appetite.
• The concept can offer a normative framework for the purpose of rational decision-making. This means it can specify what individuals must do to fulfill their objectives, given their beliefs and preferences.
• It can handle dynamic and complex decisions where outcomes depend on various factors and uncertain and interrelated events.

Moreover, it can help spot and rectify cognitive biases, which refer to systematic errors concerning judgment. These errors influence how individuals process and perceive information.

• Measuring and eliciting the probability and utility values required to apply this theory can be challenging. This is because individuals may not have consistent or well-defined preferences over outcomes. Or, they may fail to express their preferences in numerical terms.
• The theory can be impractical or unrealistic in a few situations where transitivity, rationality, and completeness assumptions may not hold.
• Other models or theories may modify or challenge this theory by better predicting or explaining human behavior under uncertain circumstances.

### Expected Utility vs Expected Value

Expected utility and value can be confusing, especially for individuals new to the field of economics. However, they can understand their meaning and avoid confusion by learning about their vital differences. So, let us look at them.

### Expected Utility Theory vs Prospect Theory

Many individuals unfamiliar with these two theories may be confused when understanding the concepts. People must remember that some differences help them distinguish the two theories. This table shows a comparison between the two theories.

How to maximize expected utility?

One can maximize it by increasing the probabilities. Maximizing this utility means choosing the option yielding the maximum average utility. In this case, the average utility is all utilitiesâ€™ probability-weighted sum. This theory needs individuals to be aware of every outcomeâ€™s probability.

Who created the expected utility theory?

Daniel Bernoulli was the first to posit this theory in the 18th century. In 1738, he was able to resolve the St. Petersburg Paradox (the reason why individuals were willing only to make a small payment for a high-risk gamble with infinite anticipated monetary value) using the hypothesis.

Why is expected utility theory useful?

It offers a way of ranking the events or actions based on how choice worthy they are. One must remember that the higher this utility, the better it is for one to select the event or action. Thus, choosing the act that has the highest utility is the best decision. In the event of a tie among several acts, one can select any one.

What is risk-neutral expected utility?

If the utility of an individualâ€™s anticipated value of a gamble is the same as its expected utility, it is risk-neutral.

This has been a guide to what is Expected Utility Theory. We explain how to calculate it, examples, and comparison with expected value and prospect theory. You can learn more about it from the following articles â€“