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.

Decision Tree Analysis: Choosing Between Options By Projecting Likely Outcomes

MindTools.com

Summary
Decision Trees are useful for helping decision-makers to choose between several courses of action. Their structure allows decision-makers to explore their options and investigate the possible outcomes of those options. Additionally, Decision Trees help decision-makers to form a balanced picture of the risks and rewards associated with each possible course of action. To aid in the decision making process, Decision Trees provide a framework to quantify the values of outcomes with the probabilities of achieving them.

How To Make A Decision Tree:
1.) Draw a small square to represent a decision to be made on the left hand side of a large piece of paper, half way down the page.
2.) From this box, draw lines out towards the right for each possible solution, and write a short description of the solution along the line.
3.) At the end of each line, consider the potential/likely results. If the result taking that particular decision is uncertain, draw a small circle. If this results in another decision needing to be made, draw another square. Squares represent decisions and circles represent uncertain outcomes.
4.) Starting from the new decision square, draw lines out representing the potential options that could be selected. From the circles, draw lines representing possible outcomes.
5.) Repeat steps 2-4 until all possible decisions and outcomes are illustrated.

To begin the decision making process, start by assigning a score to each possible outcome. This score is an estimate of how beneficial the result is. Next, look at each circle and estimate the probability of each outcome.

Then, calculate the value of the uncertain outcomes (multiply the value of the outcomes by their probability). Start on the right hand side of the Decision Tree and work back towards the left. Only record the result to each respective square or circle from each set of calculations.

To evaluate each decision node, write down the cost of each option on each decision line. Then subtract the cost from the outcome value previously calculated. This value represents the benefit of that decision. Once all calculations are complete, choose the option that has the largest benefit (the final decision).