## Saturday, April 4, 2009

### Decision Tree Analysis

Vanguard Software Corporation

Summary:
"Decision trees are used to select the best course of action in situations where you face uncertainty." Decision tree analysis allows the analyst to find the best solution to a problem, or come to an estimation, although he lacks some information.
As an example of such a situation, the site outlines a simple game. How much would you pay to bet on the outcome of a coin toss ? If the coin comes up heads, you win \$100. If it comes up tails, you lose. The game would look like this:

From a business perspective, you choose the option with the highest Expected Monetary Value, or EMV. The EMV of this game is \$50, due to the probabilistic value of the game, i.e. you would statistically win 50% of the time. The formula for the EMV is :

To complicate the decision, another layer is added. Suppose your friend offers you \$40 not to play the game. What should you do?

Now we have our decision tree. The square represents the decision (to play or not to play), whereas the circle represents the event, or outcome. Through decision tree analysis, you would come to the conclusion that it would be worth it for you to play, as you would statistically win at least \$50.
But what if you had to pay \$40 to play? That would look something like this:

This decision tree now takes into account your net loss or gain for playing the game. As you can see, it would still pay to play, however you can only expect to profit \$10 rather than \$50. By using decision tree analysis, we can outline all the various outcomes of a set of decisions, and then choose which decision is the most desirable.

Comment: This site is for decision tree software, DecisionPro, which calculates decisions automatically using various formulas for economic data. Although the example was developed for the business model of decision tree analysis, the same principles can be applied to intelligence analysis in order to "reduce uncertainty for the decision maker."

#### 1 comment:

1. I agree that conceptually the same process can be used for intel analysis but I think there are a number of devils in those details...

For example, how do DTs work when you dont have monetary data? Money is easy to value but other options might not be so easy to categorize. Even if we can categorize them, how would we weight them?