# Difference between revisions of "Expected utility"

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{{wikilink|Expected utility hypothesis}} | {{wikilink|Expected utility hypothesis}} | ||

− | '''Expected utility''' is the [[expected value]] of a [[utility function]]. | + | '''Expected utility''' is the [[expected value]] in terms of the [[utility]] produced by an action. Each possible consequence of the action is assigned a utility by a [[utility function]] and weighed by the probability of that outcome occurring. The sum of these weighed utilities is defined to be the action's expected utility. |

Von Neumann and Morgenstern proved the [http://web.archive.org/web/20070221104329/http://www.econ.hku.hk/~wsuen/uncertainty/eu.pdf expected utility theorem], which says that when a rational agent chooses between different "gambles" (probability distributions over outcomes), the utility of such a gamble can always be seen as the expected utility of the gamble's outcome. | Von Neumann and Morgenstern proved the [http://web.archive.org/web/20070221104329/http://www.econ.hku.hk/~wsuen/uncertainty/eu.pdf expected utility theorem], which says that when a rational agent chooses between different "gambles" (probability distributions over outcomes), the utility of such a gamble can always be seen as the expected utility of the gamble's outcome. | ||

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==Blog posts== | ==Blog posts== | ||

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*[http://lesswrong.com/lw/1cv/extreme_risks_when_not_to_use_expected_utility/ Extreme risks: when not to use expected utility] | *[http://lesswrong.com/lw/1cv/extreme_risks_when_not_to_use_expected_utility/ Extreme risks: when not to use expected utility] | ||

*[http://lesswrong.com/lw/1d5/expected_utility_without_the_independence_axiom/ Expected utility without the independence axiom] | *[http://lesswrong.com/lw/1d5/expected_utility_without_the_independence_axiom/ Expected utility without the independence axiom] | ||

*[http://lesswrong.com/lw/1dr/money_pumping_the_axiomatic_approach/ Money pumping: the axiomatic approach] | *[http://lesswrong.com/lw/1dr/money_pumping_the_axiomatic_approach/ Money pumping: the axiomatic approach] | ||

*[http://lesswrong.com/lw/1ga/in_conclusion_in_the_land_beyond_money_pumps_lie/ In conclusion: in the land beyond money pumps lie extreme events] | *[http://lesswrong.com/lw/1ga/in_conclusion_in_the_land_beyond_money_pumps_lie/ In conclusion: in the land beyond money pumps lie extreme events] | ||

− | + | *[http://lesswrong.com/lw/244/vnm_expected_utility_theory_uses_abuses_and/ VNM expected utility theory: uses, abuses, and interpretation] | |

==See also== | ==See also== | ||

## Revision as of 08:14, 13 July 2012

**Expected utility** is the expected value in terms of the utility produced by an action. Each possible consequence of the action is assigned a utility by a utility function and weighed by the probability of that outcome occurring. The sum of these weighed utilities is defined to be the action's expected utility.

Von Neumann and Morgenstern proved the expected utility theorem, which says that when a rational agent chooses between different "gambles" (probability distributions over outcomes), the utility of such a gamble can always be seen as the expected utility of the gamble's outcome.

Humans, of course, are a different story.

## Blog posts

- Extreme risks: when not to use expected utility
- Expected utility without the independence axiom
- Money pumping: the axiomatic approach
- In conclusion: in the land beyond money pumps lie extreme events
- VNM expected utility theory: uses, abuses, and interpretation