# Influence diagrams

Influence Diagrams (IDs) make it easier to express and communicate complex uncertainties. They are a natural way to develop and understand a big picture and complement probability trees (and attack trees) - a framework facilitating calculations with probabilities and the development of insight into the solution of a problem.

Some of the same symbols are used as in a diagram of effects but their meaning is entirely different:

• An oval represents an uncertainty. It is labeled with a descriptor (variable) to identify the set of events or quantity about which we are uncertain or question to which we would like to find an answer.
• A double oval represents an uncertainty that will cease to be an uncertainty once we know how all uncertainties that are relevant to it turn out.
• A rectangle represents a decision. It is labeled with a descriptor (variable) to identify the set of events or quantities among which the decision-maker node is choosing. If a decision node appears the diagram becomes a decision tree.
• An octagon represents a value node. It is labeled with a descriptor of the value measure, the quantity the decision-maker node uses in making decisions.
• A double octagon represents a value node that has ceased to be an uncertainty once it has been expressed in the nodes that are relevant to it. It is the criterion to be used when making the decision.
• An arrow represents relevance. A previously used word, “influences” is discouraged as it suggest causality. The basic arrow represents flow of knowledge. When a decision-maker is involved, it implies a chronology:
• Uncertainty node to uncertainty node: The outcome of the node at the base of the arrow is provided when probabilities are assigned for the node at the head of the arrow, meaning the probabilities at the node at the head of the arrow are conditional on the resolution of the uncertainty at the base of the arrow.
• Decision node to uncertainty node: The alternative chosen at the base of the arrow is provided when probabilities are assigned for the head of the arrow, meaning the probabilities at the node at the head of the arrow are conditional on the alternative chosen at the base of the arrow.
• Uncertainty node to decision node: The outcome of the uncertainty at the base of the arrow is known when the decision is made, meaning the uncertainty is resolved 'before' the decision is made.
• Decision node to decision node: The alternative chosen at the base of the arrow is known and remembered when the decision is made at the head of the arrow, meaning the decision at the base of the arrow is made 'before' the decision at the head of the arrow.
1. Determine the key uncertainty you would like resolved.
2. Is there another uncertainty that would be helpful for resolving the key uncertainty? If so, make another oval, label it with this uncertainty, and draw an arrow from it to the key uncertainty.
3. Repeat step 2 until all important uncertainties relevant for the key uncertainty are in the diagram.
4. Are there uncertainties that would help resolve the uncertainties found in step 2 and 3? If so, add to diagram. This recursion ends when adding uncertainties are no longer helpful for understanding the problem.
5. Will any of the uncertainties be completely resolved (determined) if you have all of the information? Draw another oval around those to mark them as deterministic node.
• No loops: following the arrows, there can be no path that leads back to where we started or have been before (no more circular reasoning and then claiming it is logical).
• Single decision-maker: only one octagon in the diagram.
• No forgetting previous decisions: each decision is connected to every other decision by an arrow.
• No forgetting previously known information: if there is an arrow from an uncertainty node to a decision node, there must be arrows from that uncertainty node to all subsequent decision nodes.