# Utility hypothesis

### From Nemo

In economics, game theory, and decision theory the expected utility hypothesis is a theory of utility in which "betting preferences" of people with regard to uncertain outcomes (gambles) are represented by a function of the payouts (whether in money or other Export goods), the probabilities of occurrence, risk aversion, and the different utility of the same payout to people with different assets or personal preferences. This theory has proved useful to explain some popular choices that seem to contradict the expected value criterion (which takes into account only the sizes of the payouts and the probabilities of occurrence), such as occur in the contexts of gambling and insurance. Daniel Bernoulli initiated this theory in 1738. Until the mid twentieth century, the standard term for the expected utility was the moral expectation, contrasted with "mathematical expectation" for the expected value.

The von Neumannâ€“Morgenstern utility theorem provides necessary and sufficient "rationality" axioms under which the expected utility hypothesis holds.

## **Expected value and choice under risk**

In the presence of risky outcomes, a decision maker could use the expected value criterion as a rule of choice: higher expected value investments are simply the preferred ones. For example, suppose there is a gamble in which the probability of getting a $100 payment is 1 in 80 and the alternative, and far more likely, outcome, is getting nothing. Then the expected value of this gamble is $1.25. Given the choice between this gamble and a guaranteed payment of $1, by this simple expected value theory people would choose the $100-or-nothing gamble. However, under expected utility theory, some people would be risk averse enough to prefer the sure thing, even though it has a lower expected value, while other less risk averse people would still choose the riskier, higher-mean gamble.

## **References:**

1.http://en.wikipedia.org/wiki/Expected_utility

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- http://www.sbg.ac.nz/study-school-business
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