Now that you have values associated with each possible outcome
and probabilities associated with each branch of the tree, it's
possible to calculate the expected values associated with
each possible decision. The expected value of a decision is the
weighted average of all outcomes associated with that decision,
where the weights are the probabilities associated with each step in
the decision tree.
So for example, if we were to intervene by establishing a captive
breeding program, the diagram tells us that
This compares with a 0.53 expected probability of extinction if
reserves are simply expanded.
- There is an 80% chance that the captive breeding program will
succeed, in which case there's zero chance of extinction in 30
- There is a 20% chance that the captive breeding program will
fail, in which case there's a 95% chance of extinction in 30 years.
- The expected probability of extinction is
If we take the probability of extinction as our loss function, we're
done. We simply choose the alternative that has the lowest probability
of extinction, namely captive breeding, which has .