Roughly 60-65% of the general population are predominantly visual thinkers, i.e., they tend to think spatially and in pictures more so than in words and symbols. This proportion is even higher — around 90% — among scientists and engineers. It’s no wonder then that people use a wide variety of graphical and diagrammatic representations to help them understand and communicate complex ideas.

One visual representation that has proven particularly useful to decision makers is the influence diagram. This diagram shows at a glance the major elements of a decision problem — the specific decisions that must be made, the objective(s) being pursued, and the uncertainties and events beyond our control that are involved — and the relationships and dependencies between all these elements.

Consider for example the following decision problem: Joe Smith’s old clunker breaks down, and he is facing a $2000 repair bill to get it back on the road. Since the car is ready for the junkyard anyway, Joe decides to buy a new car instead. Now, Joe lives in California, and would normally like to buy a nice sporty convertible. But there is a good chance that his company is going to promote him and transfer him to their new office in Minnesota. If this happens, Joe would rather have a sport utility vehicle with 4-wheel drive. In addition to wanting a car that is weather-appropriate, Joe is also concerned about style, comfort, mileage, cost, and reliability.

The influence diagram for this decision situation would be as follows:

The symbols (boxes, diamonds, etc.) are called “nodes”. Rectangles are decision nodes (in this example, “What car to buy?”); rounded boxes are intermediate consequence nodes; diamonds are consequence nodes; and ovals are called chance nodes, which represent uncertainty or uncertain events (in this example, the chance of being transferred to Minnesota).

The lines with arrows are called “arcs”. The arcs show influence; if an arc points from node X to node Y, it indicates that node X has some relevance to node Y and/or sequentially comes first. A node is influenced by all the arcs coming into it, and has influence on the node(s) to which its own arc(s) point. In the above example, the final consequence “Overall satisfaction” is determined by the aggregate of the intermediate consequences “Style”, “Comfort”, etc. Note that the decision “What car to buy?” is not influenced directly by the chance of relocating to Minnesota since Joe will be making this decision before he knows if he will be transferred. If Joe was able to defer his car purchase decision until he finds out whether he will be transferred, there would be an arc from the “Transfer to Minnesota” node to the decision node “What car to buy?”.

The influence diagram is useful because it allows us to get our mental arms around the entire decision context. It lets us see which elements influence other elements, helps us determine where additional information might be useful, and enables us to better analyze the decision options. Perhaps more importantly, the process of constructing an influence diagram forces us to consider all of the elements and their relationships, and to make sure we haven’t missed anything.

In future posts I’ll go into more detail on the influence diagram and its close relative, the decision tree, and I’ll also get into how to actually perform the decision analysis.