Expected Value Decision

The Expected Value Decision is used to chose the best of many Actions in a stochastic environment, the expected value decision choses the action determined by the maximum expected payoff and the lowest expected cost

Optimal Action

While expected value decision chooses the best actions in any given action set, it may not necessarily be the most Optimal Action
The most optimal action will only be chosen when it is in the set of all available actions

Example

Consider the a decision where someone is trying to go to work but there is a chance of raining
The available actions are:

  • Stay at Home
  • Go to work without umbrella
  • Go to work with an umbrella

For this scenario, the umbrella is large and cumbersome

The probabilities for rain are:

  • Rain:
  • No Rain:

And us the Decision Matrix can be given by

Stay at Home Go Without Umbrella Go With Umbrella
Rain Get Fired
Get Wet
Stay Dry
No Rain Get Fired
Gain Aura
Lose Aura

Given this there should never be a reason to stay at home since it will always result in a net loss

The Expected Value of the rest of the action/outcome pairs can be calculated

Stay at Home Go Without Umbrella Go With Umbrella
Rain
No Rain
Expected Payoff

According to the expected payoff table, going without an umbrella is the best possible action in this scenario with an expected payoff of