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
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