What is the difference between expected value and expected utility

Expected value shows us the value that is to be expected from engaging in a lottery or risky situation where there are 2 or more possible outcomes. Likewise, Expected utility shows us the utility that is expected out of a lottery with two or more possibilities. That is why the two terms are measured differently and show us different things.

The rest of this post will describe how to calculate expected value and expected utility and has solved examples demonstrating the importance of the difference between them.

A good rule of thumb is to read the problem, and identify all of the key information. You need to know 4 things: 1 what is the probability of outcome 1? This can either be stated explicitly in the problem, or calculated from the probability given for outcome 1.

Assume the following when considering this policy. What is the EV of each scenario? Which has the higher EV? What is the EU of each scenario? Which has the higher EU?

In this question we have two scenarios. This should make sense because the cost of treatment is smaller than the clean up cost AND the probably of having to pay the treatment cost is less than 1. In this question we have two scenarios with one having a certain outcome. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name.

Email Required, but never shown. Upcoming Events. Featured on Meta. Now live: A fully responsive profile. The unofficial elections nomination post. Related 1. Hot Network Questions. Question feed. Assuming the game can continue as long as the coin toss results in heads and, in particular, that the casino has unlimited resources, in theory, the sum is limitless.

Thus the expected win for repeated play is an infinite amount of money. Bernoulli solved the St. Petersburg Paradox by distinguishing between the expected value and expected utility, as the latter uses weighted utility multiplied by probabilities instead of using weighted outcomes. Expected utility is also related to the concept of marginal utility. The expected utility of a reward or wealth decreases when a person is rich or has sufficient wealth.

In such cases, a person may choose the safer option as opposed to a riskier one. Logically, the lottery holder has a chance of profiting from the transaction. Now consider the same offer made to a very wealthy person, possibly a millionaire. Likely, the millionaire will not sell the ticket because they hope to make another million from it.

A paper by economist Matthew Rabin argued that the expected utility theory is implausible over modest stakes. This means that the expected utility theory fails when the incremental marginal utility amounts are insignificant. Decisions involving expected utility are decisions involving uncertain outcomes.

An individual calculates the probability of expected outcomes in such events and weighs them against the expected utility before making a decision. For example, purchasing a lottery ticket represents two possible outcomes for the buyer. They could end up losing the amount they invested in buying the ticket, or they could end up making a smart profit by winning either a portion of the entire lottery. Assigning probability values to the costs involved in this case, the nominal purchase price of a lottery ticket , it is not difficult to see that the expected utility to be gained from purchasing a lottery ticket is greater than not buying it.

Expected utility is also used to evaluate situations without immediate payback, such as purchasing insurance. When one weighs the expected utility to be gained from making payments in an insurance product possible tax breaks and guaranteed income at the end of a predetermined period versus the expected utility of retaining the investment amount and spending it on other opportunities and products, insurance seems like a better option.

UC Berkeley. Tools for Fundamental Analysis. Expected utility refers to the utility of an entity or aggregate economy over a future period of time, given unknowable circumstances. It is used to evaluate decision-making under uncertainty.

It was first posited by Daniel Bernoulli who used it solve the St. Petersburg Paradox. Expected value theory. People often have to choose between options when the outcome of some option is uncertain.

The expected value is the sum of the value of each potential outcome multiplied by the probability of that outcome occurring. In the case of the drug, there are only two outcomes: success and failure. In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values.

By calculating expected values , investors can choose the scenario most likely to give the desired outcome. This Expected Value Calculator calculates the expected value of a number or set of numbers based on the probability of that number or numbers occurring.

The formula for expected value for a set of numbers is the value of each number multiplied by the probability of each value occurring. To calculate the marginal utility of something, just divide the change in total utility by the change in the number of goods consumed.

In other words, divide the difference in total utility by the difference in units to find marginal utility. The expected utility theory deals with the analysis of situations where individuals must make a decision without knowing which outcomes may result from that decision, this is, decision making under uncertainty. The decision made will also depend on the agent's risk aversion and the utility of other agents. Utility theory.