51.4 Influence Diagrams: a description

Influence diagrams tend to be simpler on face value than decision trees. While they do not display the level of detail found in a tree (i.e., scenarios, probabilities, and payoffs), influence diagrams portray more clearly the factors to consider in decision making, and how those factors are related. Even in complex problems, the corresponding influence diagram is almost always small enough for simple reproduction and efficient communication.

The design of an influence diagram is subject to a number of guidelines. Here are the basic ones:

• “Nodes” of different shapes represent the factors relevant to the problem. Each element of the problem — the final objective (e.g., maximizing profit), along with each decision, and random event that can affect the objective — is represented by a single node. A value node (diamond) denotes a measure of the final objective. A decision node (square) is used to indicate a decision. A chance node (circle) is used to represent an event whose value (or outcome) is currently unknown.

• Related nodes are connected by arcs. An arc ending in an arrow is drawn between two nodes to indicate that: (a) the first event precedes the second, and/or (b) the first event or action affects (or conditions) the second. An influence arc might indicate that the probabilities for one event depend on the outcome of a prior event or action. An influence arc might also indicate that an action or event makes some contribution to, or deduction from, the final objective (e.g., project cost, or profit).

In the following sections we will explain in detail how to build an influence diagram model of the investment decision described below: How to invest $1,000?

• You have $1,000 to invest, and two potential investments: an equity investment (with potentially different market returns), and a risk-free Certificate of Deposit (CD).

• You will reconsider your investment decision at the end of one year, but not earlier.

• The CD pays simple interest at a rate of 5% annually — your return would be $50.

• Your research into the equity investment has a simple probability distribution describing its year-end performance:

  1. a 30% probability that its market value will have gone up by $500;

  2. a 40% probability of a modest $100 increase in value; and

  3. a 30% probability of a substantial drop in value, -$600.

• Your investment objective is to maximize growth, and you are sufficiently wealthy that the possible loss of $600 does not pose a material threat.

   

  Notes: Assigning 30%/40%/30% probabilities to the outcomes of the risky investment in the example follows a standard method for representing a probability distribution of outcomes based on expert opinion. This particular type of discrete distribution is referred to as a Swanson’s mean, or 10/50/90, distribution. The three outcomes represent the 10th, 50th, and 90th percentile values elicited from the expert. A similar approach uses 25%/50%/25% probabilities for the three outcomes.