A tutorial on how to capture a decision problem using an influence diagram.
You have a problem and you need to take an action. So, you have a decision problem. Before thinking about analyzing all the details, it is the best idea to capture the problem before you forget all the key elements of the context. Please note that Influence diagram is not meant to find a solution to the problem or analyzing which decision to take. We have other modeling tools for that, like a "Decision Tree". Rather, it encapsulates the big picture of the scenario, so that you understand what you are dealing with. Or what are the variables that affect you?
Why is it important to capture the big picture at the beginning? There is a saying that a problem well stated is a problem half-solved. Therefore, you need to define the problem first.
Moreover, once you start digging into the detail, you may get overwhelmed with lots of analysis steps and other information. In many cases, when a good influence diagram is created, the solution of the problem can be obvious to you by looking into the diagram, without further analysis.
A Sample problem :
"Should I take the job offer at hand?"
Say, you have just graduated from a very good university. You are confident in your skill. Now you received a job offer, which does not pay a good salary. You are thinking, should I turn down this offer and wait for another better offer? If you do so, there can be a possibility that you are waiting for a long time without any job. That will mean, you have no income until that time. If you do not have enough money to support yourself, it can be a very difficult situation for you. Worst case, the financial crisis can drive you to break down psychologically. But if you get a good offer, you will have more money in your bank, and you will be happier. Now, it is a difficult decision for you to take. What should you do?
We will capture this whole scenario in a representable diagram so that you can do a proper analysis.
Revisiting the concepts of the Decision elements:
|A 'decision' is a variable that represents 'what you can do'.|
|A 'chance' is a variable that represents 'what you cannot do' or what can be uncertain outcomes, that you do not have control.|
|An 'objective' is a variable that represents 'a matter that you care about'. For example, in our decision problem, it can be the "ultimate money flow in your bank".|
|A 'deterministic' is a variable that represents, 'what can be determined from other variables'. So, it is a calculated value, a value that is derived from other variables.|
|An 'influence' means a variable can change the state of another variable. It is represented by an arrow connecting 2 elements. For example, an uncertain outcome can depend on what action you take. An uncertain outcome can affect your net utility value (objective). So, an arrow can be connected from that uncertain chance element to your objective element.|
Identifying actions that you can control (Decision Element)
First, think about what are your possible actions?
- "Take the Job Offer at hand",
- "Wait for a better job offer".
Drag and drop 2 decision element to the canvas. And double click on an element to edit the node title. Name one as "Take the job offer at hand", and another one as "Wait for a better job offer".
Identifying Uncertainties that you cannot control (Chance Element)
Now, think about what are the uncertainties? The uncertainties are
- "You may not get any job at all for a long time"
- "You may get a better offer with a higher salary".
Let's create two chance elements.
Well, there can be more uncertain variables, like "Mental Stress" "Distance from home" etc. But, just to make the learning easier, we are keeping the model simple.
Identifying things that you care about (Objective element)
Now, let's think about what utility you care about? You are trying to solve a problem, but why it is a problem? It is a problem because you have an objective in your mind. Your objective is to maximize your satisfaction with the "money inflow in your bank", right? Let's create that objective element.
Identifying things that can be determined from other matters (Deterministic element)
Now think about any other variable that affects your ultimate objective. Are there any? What about tax? Even if you get a better job with a very high salary, you may need to pay very high tax because of the higher salary bracket. At the end of the day, depending on the country you live in, the difference between the net money flow that you will get from a better salary job and the job at hand, may not be much.
So, we have identified another decision element "tax" that can affect your ultimate objective "money inflow to my bank". A tax rate is calculated based on the gross salary. So, we can say, it is a deterministic variable. Because we can determine the tax on the gross salary amount.
Let's drag and drop a 'Deterministic' element to the canvas for 'tax'.
Ok, we have encapsulated all necessary variables. Now, let's think about which variable influences what variable.
Decision - "Take the job Offer at hand" influences the chance "I may get a better offer with a higher salary". Because, if you take the job at hand, another employer may be interested in hiring you. So, you can draw an arrow from the decision to the chance as shown below:
You can easily identify which element influences another element one by one. You can also place a note explaining some facts. You can double-click on an arrow and annotate the arrow with some rich information like 'high probability', 'more tax' etc. Finally, when you are done connecting arrows and other annotations, your diagram may look like this:
When considering influence arrow, think about which factor influences another factor directly, (not indirectly). Then draw arrow from that influencing factor to the influenced factor. Say, A influences B, and B influences C then arrow relationship should be A -> B -> C. Not directly A -> C.