How can you build a decision tree
Say you’re considering treatment options for a medical problem. The problem is elective now, so you can either manage it conservatively until it worsens irreversibly or you can choose one of two surgical options.
How would you decide?
💡The path to genius avoids stupid. So first: what’s a bad way to decide? Going with pros and cons is a poor choice. Link to why I think so in comments.
A good way to approach your medical dilemma would be to build a decision tree. For every decision option, a number of different outcomes are possible. Some you look forward to, some not. Some more likely, others less so. A decision tree helps you gather these variables into an expected total value for each option and then compare the relative values among all.
Approach the decision in the following order:
1️⃣Take an option (say, conservative management) and list all reasonably potential outcomes for it.
2️⃣List payoff for each outcome based on your preference. Decide preference by splitting 10 bucks among all outcomes, in unit increments of 1 (shown as potential outcomes in the image below). Which means all payoffs should add up to 10. This also limits your list of outcomes to a reasonable number.
3️⃣List probability of occurrence of the outcomes. Express probability in percentage, not words (unlikely, rarely, often, etc.) because people understand them differently and you may want the opinion of your spouse or family on this decision.
Tip: Total probability may not always add up to 100% because you are listing all reasonable outcomes but not every outcome possible.
4️⃣Get expected value for each outcome by multiplying payoff and probability. Add up all expected values to get the total value for the decision option. Remember the maximum total value is 10 so if you get a bigger number, something’s off in your math.
5️⃣Repeat steps 1–4 for the next option (surgery option 1).
6️⃣Compare the values for all options and pick the best one.
Knowing how something works means knowing when it doesn’t work. A decision tree has its limitations. Real-life (that includes business!) problems are not always clear cut. In one or more of payoff, probability, and preference.
If you’re mulling over greenlighting a budget for a new product, your choice of outcomes may depend on estimates of the market demand, which can cover a big gradient. Plus what your competitors are planning to do. So you can’t really say how likely something is.
Or say you’re looking for a spouse. After nine years of being married, I wouldn’t know the list of reasonably possible outcomes.
That said, decision trees work well when you have time and when you don’t have to think of second-/third-/fourth-order consequences. For trickier problems, which I will define in upcoming posts, there are other ways to decide.
