Decision Making with Decision Trees

Reading Time: 11 minutes

After reading this post you will know:

• How to use Decision Trees for good decision making
• When to apply them
• Underlying concepts from Psychology and Decision Science

Decision Trees are easy! The basic steps are:

1. draw a tree with many different branches on a big sheet of paper
2. at the end of each branch, instead of a leaf, you write down the name of a cake, chocolate, or ice cream (basically anything that could be categorized as dessert)
3. pin the tree onto a vertical surface (preferably something which is allowed to be “modified”)
4. shoot an arrow at the tree
5. eat the dessert which is closest to the arrow (personally speaking I prefer euclidean distance, but it is only a matter of taste)
6. repeat step 4 and 5 as often as needs be

And while you are full of sugar – dopamin, serotonin, and all the other (bio-)chemicals soaring through your body – we talk about: Decision Trees!

Let us start with the one question, close to every teacher tries to avoid: Why do you need it? The answer is straight forward: Because it allows you to make informed decisions, when need be, and all the other times, you can go with your gut.

To support my point, let us have a look at the common use case of taking a job in a new city:

You are a data and decision scientist (what a peculiar coincidence), who has worked for a medium sized company, for the last two years (the first job as a fresh graduate). Your contract is ending and you do not wish to extend, because you believe it is time for a change. Moving is not a problem, as long as it is not a new continent (your mother would otherwise set hell loose). With that in mind, you applied at different companies. Everything went well and you picked a position at a well-known company in a capital. Doubts are creeping into your mind, because you have never lived in a big city and worked for such a well-known company before. You decide to create a Decision Tree in order to make sure you properly thought about your decision. The tree looks as the following:

The Decision Tree consists out of six parts, which are stated at the top of the image. Each square belongs to one part of the tree and is only a potential example. The red arrows indicate the flow of the Decision Tree.
Simplified it could be stated that information is gathered to make a decision, which has potential outcomes. These outcomes have likelihoods (upper and lower boundaries included) of how possible a certain outcome could be. One outcome, whether it was explicitly stated or is a combination of potential outcomes, will happen. After the actual outcome occurred, new information is possible, which can be used to understand, among other things, how well the decision making process was executed.

We will now discuss each part, beginning with:

Stuff you knew before the Decision

This part of the Decision Tree combines all your believes and information you can gather, to make an informed decision.

And here we already encounter our first problem. Believing, unfortunately, is not a fact. I still believe that my chocolate diet allows me to loose weight. Somehow my scale disagrees… This discrepancy can be explained with the Inside and Outside View.

The Inside View is how we perceive the world. You could say our individual bubble. Thanks to this, we can filter for information that we perceive as important (high quality dessert) and ignore the rest (anything else). Unfortunately (there is always a but), it is also the root of some biases:

• Confirmation Bias: Seeking and/or only believing information which confirms your believe.
• Disconfirmation Bias: Being more critical towards information that contradicts our beliefs.
• Overconfidence: Believing that we are smarter, better, and more skilled than we actually are. (Yeah exactly, that explains that one guy…)
• Availability Heuristic: The easier we can come up with an example (or the lack thereof) the more we believe that it is prevalent and frequent (or vice versa).
• Recency Bias: Believing that recent events are more dominant than they actually are.

The Outside View, on the other hand, allows us to gather information outside of our bubble and adapt our perspective of a topic (there is also high quality cake!). This can be done by asking people for their opinion (beware the Framing Effect!) and information.

This leads us to point number 2: information. Here we want hard data. “How much is the average cost of living in the new city?”, “What is the climate like?”, “How much do you get paid? Are there other benefits?”, etc.
To know if some information is still missing you can always ask yourself the following three questions:

• What can I find out that will make my decision more educated?
• How can I get this information?
• Is it enough information?

For question 1 and 2 you can simply let your inner cyber-stalker loose. Just imagine the new city is your ex and the job is the new one. This should do the trick… Well, maybe the example is a bit too much. Nonetheless, it is stupendously (and dangerously!) easy to gather a lot of information.

Question number 3 is a bit more tricky. You must understand that information gathering has its price. This can be time, maybe money, and even social status (even all three if they catch you stalking). This means that you should gather as much data as needed, to make a high quality decision. Unfortunately, to that moment, there is no such thing as perfect information. Only imperfect information, because we cannot look into the future (when do they finally invent this?!).

If you are unsure, whether you are good to go, or if you should continue gathering data, the following graph might help:

In Image 2 the first question would be: “Is there information that would change my mind?”. This allows you to think again about all the aspects, which are important to you. This might include the well-being of the company, a political climate, and the health-care system of the country. The second question is whether you can afford to gather the information, or not. If you can, get it! Otherwise, just decide. Again: at this stage, there is no such thing as perfect information.

To end this segment, there are two ways to make information gathering easier:

• Start with the Outside View
• Journaling

Start with the Outside View by jumping into the role of one of your family members, friends, coworkers, etc. This allows you to already perceive the decision in a new light and you can think about questions they might ask, as well as answers. Which would make you even doubly prepared!

Journaling allows you to keep track of the information you already gathered and when. By doing so, you can even figure out what additional information you should gather to improve the quality of the decision.

When you are done gathering information, it is time to make your decision:

Decision

The overall goal of decisions should be to “…lead you to a future with the most favorable range of outcomes” [Annie Duke]. To do so, you must know what your own preferences are. Do you prefer an international career? Can you only live in a rural area? Do you hate knowing your neighbor’s cousin’s third pet’s name? etc. Because you sometimes cannot know preferences beforehand (e.g. teaching: some love it, some very much don’t), it is advisable to try things out, before you decide. I know that this leads us straight back to step one, but trust me, trying something out, before investing e.g. years, saves you a lot of resources.

After knowing your preferences, making a decision might be easy (-ish). Sometimes there is literally only one option left, and sometimes you need two thought experiments, to help you out:

• The Only-Option Test
• Opportunity Cost

The first experiment – The Only-Option Test – asks you the question, if you would be cool, if the only option you have, would be that one option. If you do that for every option you have, you usually rather quickly figure out, which one you prefer.

Experiment two – Opportunity Cost – adds the concept or scarcity. By choosing one option, all the other benefits of the other options vanish. By combining both experiments, you should get an understanding of what options you prefer, over the others.

After narrowing down your options, the next step is to determine potential outcomes:

Potential Outcomes

Potential Outcomes is the step in the Decision Tree process that makes you think about all the potential outcomes (you don’t say), your decision could have. In our example we have potential outcomes such as “liking the city live”, “the job being okay”, and “flourishing social life”. To help you come up with potential outcomes, you can think about two things: Payoffs and Risks.

Payoffs are the “things” we gain or lose from an outcome. This can be money, happiness, time, social currency, self-improvement, goodwill, health, etc. Unlike preferences, which depend on your personal goals and desires, payoffs do not depend on the decision maker. The decision maker should pick the option with the best payoffs according to his/her taste.

Risks are the drawbacks that could come with a decision. Always think about risks in relation to the payoffs! If your gains are phenomenal and the risk is gigantic, it could be wiser to take an option with fewer upsides, and little to no downsides (only an example – the relation of up- and downsides comes in all the colors!).

Writing down potential outcomes may not sound like the most fun activity and the reason why you nonetheless should do it would be preparation. You are mentally prepared if things do not go the way you imagined them to; Additionally, you know the pitfalls (e.g. your willpower being drained) and can prepare for them. This is called Precommitment Contract and it allows you to prepare your environment, to achieve your goal (e.g. putting your phone in a time lock depository safe).

Similarly to anything, there is such a thing as too much. Due to uncertainty, you never know which outcome actually occurs and therefore, it is best to note down a good variation of potential outcomes. What we then can do is guessing the likelihood of the potential outcomes. This leads us straight to the next part of the post:

Likelihoods

Determining the likelihood of a potential outcome is guessing. This can potentially be very daunting, because of some biases, mentioned in the part “Stuff you knew before you mad the decision”. A potential approach towards guessing would be to use information you have, to determine a range, in which the event could occur (upper and lower boundary). For example: How many citizens does Geneva have? Do NOT google! We can do this! Let us simply think. Geneva is a European city in Switzerland, close to the French boarder. It is not a capitol, surrounded by the alps and next to a lake. This means that it cannot be too big, because there is little to no room to grow. We could now guess that the number of citizens should be at least 100.000 and the absolute most 500.000. The actual number is approx. 200.000, which means that it was a good guess.

If you hate guessing (as a Data Scientist I kinda do…), the good news are that you sometimes can avoid it, by searing for publicly available data. For example, study. The drop out quota is a (somehow) good indicator of letting you know, how many students decided to quit a certain study, at a certain college. Of course there are different reasons why someone quits; However, if the quota suspiciously differs in relation to other colleges (e.g. over years the quota rose, in contrast to other colleges) you know that something is going on and that the likelihood of you dropping out, is higher than somewhere else.

You may now wonder why you should use percentages? Mauboussin et a. wrote a paper about that and because an article is more entertaining, here the HBR article.

Now comes the time to make your decision. If you are unsure, revisit Image 2 and tweak your Decision Tree. In the case of our example, the decision has already been made, which lead us straight to the:

Outcome

There are two things that determine your life: The quality of your decisions and luck.

The former is discussed in this post. The latter is the ugly truth. There is another bias, which allows us to explain, why humans tend to underestimate luck: Illusion of Control. In a nutshell: humans believe that they have control over outcomes, which simply cannot (or only scarcely) be controlled by the individual.

And because we are already talking about biases, here another another bias: Resulting. I will use a quote for this one (because I have not so far and I already feel the withdrawal symptoms):

“A mental shortcut, in which we use the quality of an outcome to figure out the quality of a decision.”

How to Decide – Annie Duke

Resulting is applied when we look at an outcome and then determine whether the decision was good or bad. This leads to two problems: an outcome does not equal the quality of the decision (further discussed here) and that a certain action leads to a certain result. Because of luck, a bad decision can also create a good outcome. Making the same decision again, could then lead to a bad outcome. This is also one of the reasons why likelihood is such an important part of the decision tree. To make yourself clear that we are working with probabilities. Anything can happen and some more likely than others.

Resulting is similar to the next bias, which will be discussed in the following part of the post:

Stuff you know after the Decision

The final bias is the Hindsight Bias. This bias is the reason why people say to you: “I knew it from the beginning.”. This bias makes us believe that we saw it coming all along. Unfortunately (or thankfully), this is commonly not the case, because perfect information is usually only available, AFTER the outcome occurred.

To avoid this bias you can use Knowledge Tracker. Do you remember the task Journaling? It is exactly for that reason. But why should you do that? Keeping track of your knowledge before and after an outcome helps you to learn form your decisions and makes you a better decision maker. This not only includes the bad outcomes, but also the good ones. By writing down factors that lead to a certain outcome, you fine-tune your approach and learn to also include aspects, which you probably never thought about (cakes with alcohol).

In our example the outcome is good. With time everything worked out. But when can you use the Decision Tree? Because let us be honest: It is a lot of work…

When to apply the Decision Tree

I will make this part as quick as possible, because the post got bigger than expected. The following image (Image 3) is a “road map” which allows you to determine if you should use a Decision Tree (SLOW DOWN!) or not. If some special vocabulary is used (to be perfectly hones: quite a lot) the explanation is stated below the image. Have fun 😉

Happiness Test: How long does the decision impact your life? The shorter the impact, the faster you should go: Dinner passes, a job change fails.

Freeroll: If the potential downside of a decision is close to non-existent, it is called a freeroll.

Sheep in Wolf’s clothing aka Hidden Freeroll: If two potential decisions are so close to each other that the difference becomes insignificant. Example: Visiting Munich or Zurich.

Quit-to-itiveness: What are the costs of quitting? Is continuing worth more than quitting?

Decision Stack: Can the decision be broken down into smaller decision and can these smaller decisions be executed in serial?

Conclusion

Congratulations on making it to the end of this post! I hope you enjoyed it as much as I enjoyed writing this post. Before we are done I prepared a quick recap (and you thought we are done here *haha*):

Image 4 should show you that decision making depends on imperfect information and luck. You use the imperfect information to make the best decision currently possible. Fortuna will then play her part (though you can somewhat influence her) and then comes the outcome. The big objective is that you make decisions which give you the best odds for your future. To do so, you can/should use the Decision Tree for important decisions (Image 3) and for the rest you can go with your gut.

The End 😉

If you liked this post, didn’t like it, and/or have a book recommendation, please leave a comment, subscribe to the blog, and share this post. I am always happy to learn new things and improve myself.

DISCLAIMER: The visualizations presented in this graph do NOT represent quantitative data. They are merely used for argumentation purposes and therefore are not scientifically sound! For more information & a good laugh, have a look at the book Calling Bullshit by Bergstrom & West, Chapter 7: Data Visualization.

ADDITIONAL DISCLAIMER: In this post I heavily use materials from the book “How to Decide” by Annie Duke.