To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.
.
Leo
Newton
Brights
Milds

Optimal decision

From Wikipedia, the free encyclopedia

An optimal decision is a decision that leads to at least as good a known or expected outcome as all other available decision options. It is an important concept in decision theory. In order to compare the different decision outcomes, one commonly assigns a utility value to each of them. If there is uncertainty as to what the outcome will be, then under the von Neumann–Morgenstern axioms the optimal decision maximizes the expected utility (a probability–weighted average of utility over all possible outcomes of a decision).

Sometimes, the equivalent problem of minimizing the expected value of loss is considered, where loss is (–1) times utility.

"Utility" is only an arbitrary term for quantifying the desirability of a particular decision outcome and not necessarily related to "usefulness." For example, it may well be the optimal decision for someone to buy a sports car rather than a station wagon, if the outcome in terms of another criterion (e.g., effect on personal image) is more desirable, even given the higher cost and lack of versatility of the sports car.

The problem of finding the optimal decision is a mathematical optimization problem. In practice, few people verify that their decisions are optimal, but instead use heuristics to make decisions that are "good enough"—that is, they engage in satisficing.

A more formal approach may be used when the decision is important enough to motivate the time it takes to analyze it, or when it is too complex to solve with more simple intuitive approaches, such as with a large number of available decision options and a complex decision–outcome relationship.

YouTube Encyclopedic

  • 1/5
    Views:
    18 918
    126 725
    1 000
    417
    413
  • (ML 11.8) Bayesian decision theory
  • Decision Tree 1
  • Bounded Rationality
  • On Conditional Branches in Optimal Decision Trees
  • Jay Myung - "Optimal Decision Stimuli for Risky Choice Experiments..."

Transcription

Contents

Formal mathematical description

Each decision in a set of available decision options will lead to an outcome . All possible outcomes form the set . Assigning a utility to every outcome, we can define the utility of a particular decision as

We can then define an optimal decision as one that maximizes  :

Solving the problem can thus be divided into three steps:

  1. predicting the outcome for every decision
  2. assigning a utility to every outcome
  3. finding the decision that maximizes

Under uncertainty in outcome

In case it is not possible to predict with certainty what will be the outcome of a particular decision, a probabilistic approach is necessary. In its most general form, it can be expressed as follows:

Given a decision , we know the probability distribution for the possible outcomes described by the conditional probability density . Considering as a random variable (conditional on ), we can calculate the expected utility of decision as

,

where the integral is taken over the whole set (DeGroot, pp 121).

An optimal decision is then one that maximizes , just as above:

An example is the Monty Hall problem.

See also

References

  • Morris DeGroot Optimal Statistical Decisions. McGraw-Hill. New York. 1970. ISBN 0-07-016242-5.
  • James O. Berger Statistical Decision Theory and Bayesian Analysis. Second Edition. 1980. Springer Series in Statistics. ISBN 0-387-96098-8.
This page was last edited on 9 September 2018, at 17:30
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.