Minimax Regret Analysis
We have explained how to Model Uncertainty in the Rational Will Decision Matrix. Also, we have learned how to capture global events and create a decision matrix.
Now, we will model a decision matrix for the purpose of Minimax Regret analysis.
What is the Minimax Regret Criterion?
The minimax regret criterion is the criteria that minimize the maximum regret. It is a kind of analysis that evaluates the maximum regret you will have by choosing an option and calculate the best options that will make you regret minimum.
Let's model the decision problem of "Take the job offer at hand" or "go to school" as described in the tutorial to capture global events and create a decision matrix.
Lets recap that, you got a job offer that will pay you 90K/year. But, you are ambitious that, if you go to school and complete a diploma, you will get a better job that will pay you 120K/year. But, you are also afraid that a recession may come and that can make you jobless for a long time. You think the probability of coming recession is 50%.
Your alternatives are :
1. Go to School and complete diploma
2. Take the job offer at hand.
Your uncertainties are:
1. The recession may come.
2. The recession won't come.
And your objective
To Maximize Salary.
Start the Decision Matrix and create an objective "Maximize Salary" as a Number type. We have demonstrated how to model objective in the Getting Started to Decision Matrix tutorial.
Model the option "Take job offer at hand" as shown below. Notice the Global event button. Click that button to make the events global ("applicable to all options")
Select the option "Go to School". You will see the same global events are created for that option as well because you checked the global event button.
Model the "Go to School" option as shown below.
Now, you are done modeling the situation. Let's analyze the result.
Minimax Regret Analysis
So far, we have analyzed results based on Maximizing Expected Utility criteria. You can change that criteria to be MiniMax Regret. In the ribbon, check the "Methods" tab and check the "Minimax Regret" radio button.
Once you do that, you will see the Maximum Regret chart shows up in the Result section.
The chart shows that your maximum regret amount can be for -90,000$ opportunity loss if you go to the school and if the recession comes. But if you take the job and if the recession does not come, you will still have some regret. In that case, your regret will be for the -30,000$ opportunity loss. Looking into this figure, we can come to the conclusion that, if you take the job offer at hand, your maximum regret will be minimum. So, based on the criteria of "Minimax Regret", it will be the right choice to take the job offer at hand.
Viewing the Regret Matrix
Finally, you may like to see the Regret Matrix. From the ribbon's View tab, click the "Regret Matrix View" button.
Once you click that button, you will see the Regret matrix as shown below.