Expected utility theory is an economic concept that plays a fundamental role in understanding decision making under uncertainty. It involves calculating the expected utility that an entity or aggregate economy is likely to achieve in different circumstances. This theory, often attributed to Daniel Bernoulli, uses the weighted average of all possible outcomes based on their probabilities to determine the expected utility.
Expected utility theory helps explain why individuals may make certain decisions, such as purchasing insurance for situations without immediate payback. By considering the utility and probability of outcomes, individuals can make informed choices and optimize their decision outcomes.
Key Takeaways:
- Expected utility theory is an economic concept used to analyze decision making under uncertainty.
- It calculates the expected utility an entity or aggregate economy is expected to reach in different circumstances.
- Weighted average of all possible outcomes based on their probabilities is used in the calculation.
- The theory helps explain why individuals may make certain decisions, such as purchasing insurance.
- By considering the utility and probability of outcomes, individuals can make informed choices and optimize their decision outcomes.
What is Expected Utility?
Expected utility refers to the utility of an entity or aggregate economy over a future period of time, given uncertain circumstances. This theory is used to analyze decision making under uncertainty, where individuals must make choices without knowing the outcomes that may result from their decisions.
To understand expected utility, it is important to know that utility represents the satisfaction or value that individuals derive from different outcomes. It is a subjective measure that varies from person to person. Expected utility takes into account the probabilities of different outcomes and weighs them based on their likelihood. By calculating the weighted average of all possible outcomes, individuals can estimate the expected utility of a particular decision.
The decision an individual makes will depend on various factors, including their risk aversion, the utility of other agents involved, and the highest expected utility. Risk aversion refers to an individual’s preference for avoiding or minimizing risks. Some individuals may be more risk-averse, preferring a more certain outcome with lower expected utility. Others may be more risk-seeking, willing to take on greater uncertainty for a potentially higher expected utility.
Expected utility theory is not only applicable to financial decisions but also to situations without immediate payback, such as purchasing insurance. When evaluating the purchase of insurance, individuals weigh the expected utility of making payments against the expected utility of not having insurance. They make a decision based on their preferences and the trade-off between potential losses and peace of mind.
It is worth noting that expected utility theory assumes that individuals are rational decision makers who always act in their best interest. While this may not always be the case in real-world scenarios, the theory serves as a valuable framework for understanding decision making under uncertainty.
In the next section, we will delve into the history of the expected utility concept and how it has evolved over time.
History of the Expected Utility Concept
The concept of expected utility was first introduced by Daniel Bernoulli in relation to solving the St. Petersburg Paradox. The St. Petersburg Paradox is a game of chance in which a coin is tossed at each play. Bernoulli distinguished between the expected value and expected utility, as the latter uses weighted utility multiplied by probabilities instead of using weighted outcomes. This distinction helped resolve the paradox and paved the way for the development of expected utility theory.
“The probability of gaining each particular sum is to be multiplied by the sum itself for each particular sum, and the products added together; which will give the expectation sought” – Daniel Bernoulli
By incorporating the concept of expected utility, Bernoulli provided a more accurate representation of decision making under uncertainty. This advancement in economic theory laid the foundation for further research in the field, helping economists and decision theorists understand how individuals evaluate and make choices in situations with uncertain outcomes.
Key Figures in the Development of Expected Utility Theory
| Figure | Contribution |
|---|---|
| Daniel Bernoulli | Introduced the concept of expected utility and applied it to solve the St. Petersburg Paradox |
| Frank Ramsey | Developed Ramsey’s Representation Theorem, connecting subjective probability and utility |
| Leonard Jimmie Savage | Contributed to the subjective expected utility representation and representation theorem |
The contributions of Bernoulli, Ramsey, and Savage have played a crucial role in establishing expected utility theory as a fundamental framework for analyzing decision making. Their work has provided valuable insights into the rational behavior of individuals when faced with uncertain outcomes and has paved the way for further advancements in the field.
Understanding Expected Utility
The concept of expected utility is derived from the expected utility hypothesis, which forms the basis of decision-making under uncertainty. According to this hypothesis, the expected utility of an entity or an aggregate economy is determined by taking the weighted average of all possible levels of utility.
Expected utility theory is employed to analyze decision-making situations where individuals must make choices without having complete knowledge of the outcomes. It provides a framework that helps individuals calculate the expected utility of different options and select the one that maximizes their overall satisfaction.
The decision-making process guided by expected utility theory involves assessing the probability of each possible outcome and multiplying it by the utility associated with that outcome. The sum of these products represents the expected utility.
Importantly, the decision-making process is influenced by an individual’s risk aversion and the perceived utility of other agents. Risk-averse individuals may prioritize options with more certain outcomes, even if the expected utility is lower, while those with higher levels of risk tolerance may be inclined to choose options with higher expected utility but greater variability in outcomes.
Decision Making under Uncertainty
Expected utility theory is particularly useful in understanding decision making under uncertainty. In such situations, individuals must make choices without complete information about the probabilities and potential outcomes. By estimating the expected utility, individuals can evaluate the potential payoffs and determine the best course of action.
For instance, imagine a person is considering investing in a new business venture. They may evaluate the expected utility by weighing the potential profits against the probability of success. If the expected utility outweighs the alternative options, the individual may decide to pursue the investment.
Expected utility theory provides a rational framework for decision making under uncertainty. It allows individuals to systematically consider the potential outcomes and their associated utilities, assisting them in making informed choices.
An important assumption underlying expected utility theory is that individuals are rational decision makers who aim to maximize their expected utility. However, it’s worth noting that human decision making may deviate from the rational choice model due to various cognitive biases and heuristics.
The Role of Expected Utility in Decision Making
Expected utility theory plays a fundamental role in various fields, including economics, finance, and psychology. In economics, it helps economists and policymakers understand individual and collective decision-making processes, contributing to the development of economic models.
Moreover, expected utility theory enlightens ethical debates by providing a framework for decision making involving moral trade-offs. It enables the evaluation of the consequences of different choices based on their expected utilities, allowing for a systematic analysis of ethical dilemmas.
Within the discipline of psychology, the theory aids in studying human decision making under uncertainty, enabling researchers to explore the cognitive processes and biases that influence choices. By understanding how individuals weigh probabilities and utilities, psychologists can gain insights into human behavior.
| Fields | Applications of Expected Utility Theory |
|---|---|
| Economics | Analysis of individual and collective decision making, informing public policy decisions |
| Ethics | Evaluating the consequences of actions involving moral trade-offs |
| Psychology | Understanding cognitive processes that influence decision making under uncertainty |
The image above visually represents the concept of expected utility, showcasing the interplay between probabilities and utilities in decision making. It serves as a visual aid in understanding how expected utility theory operates.
Expected utility theory provides a valuable framework for decision making under uncertainty. By considering the probabilities and utilities associated with various outcomes, individuals can make informed choices that optimize their expected utility. Understanding this theory facilitates a deeper comprehension of human behavior in decision-making scenarios.
Expected Utility vs. Marginal Utility
Expected utility theory is closely related to the concept of marginal utility. Marginal utility refers to the additional utility gained from consuming one more unit of a good or service. On the other hand, expected utility measures the utility an individual or economy is expected to achieve under uncertain circumstances. These two concepts play a significant role in decision making, as they influence the choices individuals make.
When it comes to wealth or rewards, the expected utility decreases as a person becomes richer or already has sufficient wealth. This means that individuals may choose safer options over riskier ones, especially if they have already reached a certain level of wealth. This phenomenon can be attributed to risk aversion and the diminishing marginal utility of wealth.
Risk attitudes also shape decision making. Individuals with high levels of risk aversion tend to favor safer options with a guaranteed outcome, even if the potential gains are smaller. Conversely, individuals with low risk aversion or a higher tolerance for risk may opt for riskier options with potentially higher gains.
Expected utility theory helps explain these decision-making patterns by considering the perceived utility of different outcomes and individuals’ risk attitudes. By assessing the potential utility and associated risks, individuals can make informed choices that align with their preferences and risk tolerance.
| Concept | Definition | Explanation |
|---|---|---|
| Expected Utility | The utility an individual or economy is expected to achieve under uncertain circumstances. | Calculating the weighted average of all possible outcomes based on their probabilities. |
| Marginal Utility | The additional utility gained from consuming one more unit of a good or service. | The change in total utility resulting from a change in consumption. |
| Risk Attitude | An individual’s willingness to take on risk in pursuit of potential rewards. | Can influence the choices individuals make and their tolerance for uncertain outcomes. |
Example of Expected Utility
Decisions involving expected utility are those that involve uncertain outcomes. To make such decisions, individuals calculate the probability of expected outcomes and weigh them against the expected utility before making a choice. For example, when purchasing a lottery ticket, the expected utility is compared to the price of the ticket. If the expected utility outweighs the cost, the individual may choose to buy the ticket. Similarly, when evaluating the purchase of insurance, individuals weigh the expected utility of making payments against the expected utility of not having insurance and make a decision based on their preferences.
Here is a practical example to illustrate the concept of expected utility:
| Decision | Probability of Outcome | Utility of Outcome (on a scale of 1-10) | Expected Utility |
|---|---|---|---|
| Purchasing a lottery ticket | 1 in 1000 chance of winning $1 million | 10 | 0.001 * 10 = 0.01 |
| Not purchasing a lottery ticket | No chance of winning | 0 | 0 |
In this example, an individual weighs the expected utility of purchasing a lottery ticket against not purchasing one. The probability of winning the lottery is 1 in 1000, and the utility of winning $1 million is rated at 10. Multiplying the probability and utility gives an expected utility of 0.01. However, the expected utility for not purchasing a lottery ticket is 0 because there is no chance of winning. Based on these calculations, the individual may decide to purchase the lottery ticket if the expected utility outweighs the cost of the ticket.
Justification of Expected Utility Theory
The expected utility theory, a fundamental concept in economics, has been developed and justified by prominent economists and statisticians, including Daniel Bernoulli, Frank Ramsey, and Leonard Jimmie Savage.
One of the key contributors to expected utility theory is Daniel Bernoulli, who first introduced the concept of expected utility in his work on the St. Petersburg Paradox. Bernoulli’s formulation explained the diminishing marginal utility of wealth and emphasized the importance of expected utility in decision making.
Frank Ramsey further expanded on Bernoulli’s work by introducing the Ramsey’s Representation Theorem. This theorem established a connection between subjective probability and utility, providing a mathematical framework for decision making under uncertainty.
Leonard Jimmie Savage made significant contributions to the refinement of expected utility theory. He developed the subjective expected utility representation and representation theorem, further solidifying the theory’s foundations.
“The expected utility theory has been indispensable in the field of decision making under uncertainty, thanks to the foundational contributions of Bernoulli, Ramsey, and Savage.”
These economists’ groundbreaking contributions to expected utility theory have provided justifications for its use as a robust framework for decision making under uncertainty. Their work has paved the way for further developments in the field and highlighted the significance of expected utility in understanding and analyzing human behavior.
Summary:
In summary, the justification of expected utility theory lies in the insights and advancements brought by economists such as Daniel Bernoulli, Frank Ramsey, and Leonard Jimmie Savage. Their work has shed light on the importance of expected utility in decision making and established a solid foundation for the theory. Expected utility theory continues to be a valuable tool for analyzing decision making under uncertainty.
Objections to Expected Utility Theory
Although expected utility theory is widely used in economic modeling, it has faced objections and violations in psychological experiments. These violations have prompted psychologists and economic theorists to develop alternative theories that provide insights into decision making beyond the assumptions of expected utility theory.
One alternative theory is prospect theory, which was proposed by Daniel Kahneman and Amos Tversky. Prospect theory suggests that individuals evaluate and weight potential gains and losses differently, leading to deviations from expected utility theory. It incorporates concepts such as loss aversion and reference points to explain decision-making behavior that is inconsistent with the expected utility framework.
Another alternative theory is rank-dependent expected utility, which introduces the idea that individuals do not evaluate outcomes in isolation but instead compare them to a reference point or a set of ranked outcomes. This theory acknowledges that people may not always make decisions based solely on expected utility but also consider the relative rank or position of the outcomes.
Cumulative prospect theory, proposed by Daniel Kahneman and Amos Tversky, extends prospect theory by accounting for how individuals perceive and make decisions about multiple uncertain events or prospects. It takes into consideration the mental processes involved in assessing and combining multiple probabilities and outcomes.
Bounded rationality is another alternative approach to decision making that challenges the assumptions of expected utility theory. Bounded rationality acknowledges that decision makers have limited cognitive abilities, access to information, and time constraints, which may lead to decisions that deviate from the rational expectations of expected utility theory.
These alternative theories offer different perspectives on decision making under uncertainty and provide explanations for violations of expected utility theory. They highlight the complexity of human decision making and the need to consider factors beyond the traditional framework of expected utility.
Applications of Expected Utility Theory
Expected utility theory, a fundamental concept in economics, finds application in diverse fields such as economics, ethics, and epistemology.
Economics
In economics, expected utility theory plays a crucial role in analyzing individual and aggregate decision making. It provides a framework for understanding how individuals weigh potential outcomes and make choices. By considering the expected utility and probability of different courses of action, economists can study the decision-making process and predict economic behavior. Furthermore, expected utility theory informs public policy decisions by evaluating the expected utility of different policy options and determining their potential impact on society.
Ethics
In the realm of ethics, expected utility theory enables the analysis of decision making involving moral trade-offs. By considering the consequences of different choices, the theory allows for ethical evaluations and moral decision making based on expected utilities. It helps individuals and policymakers evaluate the outcomes and impacts of various actions, promoting ethical decision-making frameworks.
Epistemology
Expected utility theory also has practical applications in epistemology, the study of knowledge and belief. It offers a tool to assess the rationality of beliefs and decision making based on available evidence. By weighing the expected utilities of different beliefs, individuals can make rational decisions about what to believe. This application of expected utility theory provides insights into human behavior and the process of acquiring knowledge.
“Expected utility theory provides a foundation for understanding decision making in the fields of economics, ethics, and epistemology. It allows us to assess, evaluate, and optimize our choices based on expected outcomes and their associated utilities.”
The applications of expected utility theory across economics, ethics, and epistemology demonstrate its practical relevance and impact on understanding human behavior and decision making.
| Field | Application of Expected Utility Theory |
|---|---|
| Economics | Analyzing individual and aggregate decision making |
| Ethics | Assessing decision making involving moral trade-offs |
| Epistemology | Evaluating the rationality of beliefs and decision making |
The von Neumann-Morgenstern Utility Theorem
The von Neumann-Morgenstern utility theorem is a foundational concept in decision theory and economics that provides a mathematical framework for rational decision making based on utility. This theorem establishes four axioms that define a rational decision maker and ensure logical consistency in preference ordering. These axioms are:
- Completeness: The decision maker is capable of comparing and ranking all possible outcomes and alternatives.
- Transitivity: If alternative A is preferred to alternative B, and alternative B is preferred to alternative C, then alternative A is preferred to alternative C.
- Independence of irrelevant alternatives: The preference between two alternatives should not change if a third alternative is added that is irrelevant to the original decision.
- Continuity: Preferences are continuous, meaning that small changes in the probability or outcome of an alternative should result in small changes in preference.
By establishing these axioms, the von Neumann-Morgenstern utility theorem provides a rigorous framework for modeling individual and collective decision making. It helps economists and decision theorists analyze and understand how individuals make rational choices based on their utility and preferences.
The importance of the von Neumann-Morgenstern utility theorem lies in its ability to capture the complexities of rational decision making. It allows for the formal representation and analysis of decision problems involving uncertainty and helps economists and policymakers gain insights into human behavior. By applying the theorem’s axioms, researchers can evaluate the rationality of decision makers and derive meaningful conclusions about their choices.
The von Neumann-Morgenstern utility theorem has been extensively used and studied in various fields of economics, including game theory, finance, and public policy. It provides a solid foundation for understanding rational decision making under uncertainty and is indispensable in the study of economic behavior.
Criticisms and Extensions of Expected Utility Theory
Despite the usefulness of expected utility theory in analyzing decision making under uncertainty, it has faced criticisms and limitations that have prompted the development of alternative theories. Researchers have identified violations of expected utility theory in various decision-making scenarios, leading to the emergence of prospect theory as an extension.
Prospect theory incorporates elements such as loss aversion and reference points to explain deviations from expected utility theory. It recognizes that individuals may not always make decisions based solely on expected utility. Loss aversion suggests that individuals tend to weigh potential losses more heavily than potential gains, influencing their decision-making processes. Reference points, on the other hand, provide individuals with a framework for evaluating outcomes by comparing them to a specific reference point.
These extensions and alternative theories provide valuable insights into decision making under uncertainty and expand our understanding beyond the traditional framework of expected utility theory.
Prospect Theory vs. Expected Utility Theory
Prospect theory deviates from expected utility theory by recognizing that individuals do not always make decisions based solely on expected utility. Loss aversion and reference points play significant roles in shaping decision making under uncertainty.
| Expected Utility Theory | Prospect Theory |
|---|---|
| Based on expected utility calculations | Consider loss aversion and reference points |
| Assumes rational decision making | Accounts for irrational behaviors and biases |
| Does not account for the framing effect | Recognizes the influence of framing on decision making |
| Does not consider psychological factors | Takes into account behavioral and psychological factors |
This table highlights the key differences between expected utility theory and prospect theory. Prospect theory offers a more comprehensive framework for understanding decision making by incorporating behavioral and psychological factors.
An image illustrating the concept of prospect theory, which extends beyond the traditional framework of expected utility theory. It visually represents the different aspects and factors involved in decision making under uncertainty.
The concept of prospect theory revolutionized the field of economics and decision theory, providing insights into human behavior and challenging the assumption of strict rationality. By considering alternative theories such as prospect theory, researchers can gain a more nuanced understanding of decision making under uncertainty, expanding our knowledge beyond the traditional concepts of expected utility theory.
Conclusion
Expected utility theory is a fundamental concept in economics that plays a crucial role in decision making under uncertain circumstances. By providing a framework for assessing the utility and probability of different outcomes, this theory helps individuals make informed choices and optimize their decision outcomes. Despite its limitations and the emergence of alternative theories, expected utility theory remains a valuable tool for analyzing decision making in various fields.
Through expected utility theory, economists and decision makers are able to understand why individuals may choose certain actions, such as purchasing insurance or evaluating risky investments. By calculating the expected utility of different choices, individuals can weigh the potential benefits against the risks and make decisions that align with their preferences and risk attitudes.
While expected utility theory may not fully capture the complexities of human decision making, it has paved the way for advancements in understanding and modeling choices. The theory’s historical roots in the work of Daniel Bernoulli and subsequent developments by economists like Ramsey and Savage provide a solid foundation for analyzing decision making under uncertainty. By incorporating insights from psychology and other disciplines, researchers continue to improve and expand upon expected utility theory, ensuring that it remains a relevant and valuable tool in the study of decision making.