## Thursday, April 2, 2009

### Decision Trees

Edwin Greenlaw Sapp
CIA Historical Review Program
22 September 1993

Summary
The decision tree is a prototype for the preponderance of logic diagrams. It is a linear means of representing the alternatives, objectives, and consequences of a series of decisions. The decision tree, essentially, is an algorithm for the analysis of complex sequential decision problems.

Decision trees can be used to depict a series of true-false sequences (a deterministic way) or to display subjective likelihoods and their relationships (a probabilistic use). The technique is simple:
1. Identify the strategies available, and the possible states of nature (chance events) that might occur.
2. Draw the tree skeleton.
3. If probabilities are being expressed, enter the economic or statistical data and associated (subjective) probabilities.
4. Finally, analyze the tree to determine the best course of action.

For a rudimentary example, suppose you would prefer to hold a party on your patio, but there is a 40 percent chance of rain and the party cannot be moved once the decision has been made. You have only two strategies: outside and inside. The chance event is rain or no rain. The tree would look like this (no lines were included):

Now assess the subjective value of the ultimate alternatives: there are four, so on an ascending scale, outside-no rain-comfort would rate "4," while outside-rain-disaster is last and least.

You also have a quantified probability to add into the chance event: 60-40 against rain. When you have multiplied the subjective value by the probability of the alternative, the completed tree looks like this:

There is, then, a slight quantified edge (2.8 vs. 2.4) to holding the party outdoors. You, as decision maker, have been told something subjective by me as an analyst. By means of a simple graphic device, you not only know where I have been subjective, but what impact that subjectivity has had on the recommended outcome. In short, you have no misunderstanding about my reasoning and weighting processes.

There are few cut and dried means of assuring the inclusion of all alternatives, and the best advice seems to be to build a likely model and then study the results, seeking the impact of certain alternatives and the relationship among alternative courses of action. If it is possible to assign appropriate probabilities to the various branches, the result is both a decision-making tool and an effective vehicle for the communication of analysis.

Author's Note: This summary only includes the information from the article that is most applicable to our discussion of decision trees.