Best case and worst case analysis for decision making under uncertainty
Uncertainty makes decision making hard
We face uncertainty while making decisions everyday. When we are faced with picking one of the several options, we are often perplexed because the outcomes for each option have uncertainty. In this article I will cover a simple technique that is intuitive which will work in many situations.
Best case and worst case analysis
In the picture below A-G are our options and the outcome for each option is shown. While it is difficult to estimate probability distribution of outcome for each option, we typically can estimate the best case and worst case of the outcomes. The the next section I will explain a simple technique that is very intuitive. In fact we make decisions in life using the same technique but formalizing it into my algorithm will let us document our thought process.
Algorithm
For every option compute difference of the worst case outcome of this option and best case outcome among all other options. Let us call this number delta.
Pick the option that has maximum delta. Let us call this option candidate option. This intuitively means the worst case of this option does very well compared to best case outcomes of all other outcomes.
If the delta is positive we have a dominant option and we can pick this option with absolute certainty. Our decision is optimal and many problems in real life do fall in this category.
If the delta of the candidate option is negative but is within user threshold. We can pick this option knowing that this may not be optimal but it is still acceptable. When we cannot select an option that is acceptable we have to abort this method and start looking at methods like stochastic programming.
Example
Problem:
We have $100 to invest for a month and we have to invest in only one stock of 4 stocks. Using our experience we can estimate best and worst returns for each stock. Can we find stock to invest without resorting to complex techniques?
Case 1: Which stock would you invest here?
Answer: This is easy. Our algorithm will find Stock A as dominant option.
Case 2: There is no dominant option. What would you do here?
We can pick option A if difference between best return or B and worst return of A is acceptable for us. This is to make sure we are happy even if option B gets its best return 99.9% of the time. Our algorithm would find stock A as candidate option and we have to check its delta against our acceptable threshold.
Case 2A: If the difference is 0.5% and our threshold is 1%. We select stock A knowing that we do not lose much even if stock B gets its best return.
Case 2B: If the difference is 1.5% and our threshold is 1%. We cannot pick stock A knowing that there is a possibility of stock B of getting higher returns. We have to take a gamble here or we have to build a much more complex model using stochastic programming.
Advantages compared to other complex methods
- This method requires us to quantify best and worst outcomes. We will be forced to take an objective approach instead of taking a biased approach (too conservative or too aggressive). Computing best case and worst case outcomes will force us to examine the reality closely. Example: If I sign a contract and have to cancel, I have to account for cancellation fee in the worst outcome of making that decision.
- In many real life situations there is always a dominant option. By using this approach we can convince ourselves that we have done due diligence.
- Many times complex approaches are hard to quantify. Many decision makers are able to estimate best case and worst outcomes more accurately.
- This method is easier to explain. Many of us think like this for clear cut choices. By formalizing the thought process into this method, it is easier to bring consistency to the decision and explain it to other stakeholders.
- This can be first step towards complex techniques — stochastic programming, etc. Stochastic programming is complex but with user estimates for probabilities of each outcome, it works very well for several objectives and it very powerful.
Drawbacks
- We cannot use this when our decision is not picking an option but a numerical one (amount to invest in each stock).
- We cannot use this for complex problems where we have make investment decisions every period.
- If no option is dominant and that means our heuristic option is not guaranteed to be optimal.
- If this method fails to pick an option, try stochastic programming.
Conclusion
This is a very intuitive approach especially when there is a very promising option and we are trying to rationally select it. Many of us do this intuitively many times we are comparing options. But to be more precise on important decisions, I would recommend implementing this approach formally using a spreadsheet or other tools.
