Prune confusion with decision trees 🌳

Nearly 20 years ago, going into the winter of 2006, my wife and I had a decision to make.

We both worked at Ford Motor Company, and they were going through a tough time. To reduce payroll, they were offering a Voluntary Separation Package to salaried employees.

Volunteer to leave, and you’ll get a small severance; I think it was something like one month for each year of employment, so three months pay for us.

If Ford did not get enough volunteers, then they’d have to institute an involuntary layoff. With low tenure, I wasn’t confident we’d survive.

Should we put our names in the hat?

If we didn’t put our names in, we’d keep our jobs - but there was a risk we’d be laid off later with no severance. Not great.

If we did put our names in, we’d get a small severance, but we’d be without jobs. Not great.

My wife and I would talk about it at length, but it was too complex to keep in my head. Where would we work? Should we move? Will Ford pay our tuition (we had one more semester in our Masters programs)? How long will it take to get a job? What happens if we can’t find a job?

It wasn’t clear what option we should choose.

I needed a way to organize it and get a little mathematical so I could make an effective decision. Excel and decision trees to the rescue!

What is a decision tree?

Decision trees are a useful and visual way to organize complex decisions. They encourage you to think probabilistically (where things have a chance of occurring) instead of in black and white (where things definitely will, or definitely won’t, happen).

Let me show you what this looked like for my Ford decision - as a visual created for today’s newsletter. There was no Miro back in 2006; all of these details were done in Excel back then.

The core decision you’re trying to make is called the Root Node. In this case I’m deciding whether to quit working at Ford.

Out of the Root Node grow Branches, which are the possible choices or actions. My Branches aren’t labeled in the visual, but they’re related to the action of submitting our names into the Voluntary Separation or not.

Next are Decision Nodes, which are decisions that occur subsequent to the Root. In my case, the “decisions” are mostly on someone else. Ford was going to choose whether to accept our names or not. Ford was going to choose whether to pay our last semester tuition or not. And future companies were going to choose to hire us or not. That’s not always the case; many decisions will be ones you can make.

Finally you have Outcome Nodes, which is the final result of the decisions made along that path. In my Ford example, it was sort of a net income measure. There was severance or income coming in, then tuition payment and living expenses going out.

Thinking Probabilistically

One thing not shown in my image, and a key part of true decision trees, is adding probabilities to these various paths and actions. For example, what are the odds that any one of the first four Decision Nodes about the Voluntary Separation Package would happen? I might’ve split it up as follows:

None Accepted - 5%
One Accepted - 40%
Two Accepted - 40%
Laid Off - 15%

I would do the same for every other branch. What are the odds that Ford would pay tuition? Call it 50-50. What are the odds that we’d get a job in April versus July? Again, I might call it 50-50.

From there you can calculate Expected Values for every Decision Node.

If you look at the bottom path of getting Laid Off / Not Paid, there’s a 50-50 chance of either outcome.

To calculate the Expected Value, you multiply the outcomes by the probabilities. That means (0.5 x -11) + (0.5 x -22) = -16.5. I should expect to lose $16.5K down that path.

It’s pretty straight forward with a simple set of decisions and 50-50 probabilities, so you don’t need to (and I didn’t!) do all the calculations. It’s really helpful when things get complicated and you’ve got asymmetric probabilities.

Expected Value calculations give you insight into the upsides and downsides of your collection of decisions.

The Importance of Pruning

Since this is real life, we only want to do what is useful. That means it’s not only okay, but desirable, that you would not list out every possible permutation in your decision tree.

For example, in my Ford example, the top and bottom paths only have one Decision Node option for Tuition Status. I assumed that if Ford kept us employed they’d pay tuition, and if Ford laid us off, they would not pay tuition.

It’s unnecessary and unhelpful to distract the decision with options that are low probability or would never be chosen by you. Prune them from your map.

How are decision trees useful?

Decision Trees help in quite a few ways.

• Getting things on paper reduces perceived complexity.
• Representing things visually makes it easier to interact with.
• Forces you to think, and assign, probabilities to scenarios.
• Probabilities enable you to think about how to influence those probabilities.
• Gets some cold, hard, numbers to balance emotions.
• Creates a map for you to create new, previously unseen, options.
• Shows you the full spectrum of possible outcomes, exposing downside risk.

You are not outsourcing your decision to a decision tree, but you are getting help in arraying probabilities and outcomes across a complex set of interactions.

By arranging the probabilities and Expected Values you’re getting a really good mathematical model of how things will play out. This mathematical model is a tool that can supplement your judgement and other ways of thinking.

As for how the decision tree helped in my Ford example:

I knew it was better to have Ford pay tuition than not. I didn’t need a decision tree for that! What I did need was a decision tree to help me see the impact of that decision, especially the non-ideal option, alongside all the other decisions.

Same for the other options. It’s obviously better to not be laid off. It’s obviously better (for my bank balance) to find a job in April versus July. What’s not obvious is the mathematical outcomes of these scenarios.

For one thing, a 15% chance of being laid off is not a low chance! It also carries an expected loss of $16.5K (from our calculation earlier), and that’s something I’d like to avoid.

I could also see there were two paths that had two positive outcomes; Ford accepting one or both of our voluntary separations, with tuition being paid. Those are paths I could be relatively happy going down.

The only path outside layoffs with a double negative outcome is the one where only one of us were accepted, and tuition was unpaid.

That decision tree model was paired with my own subjective desires to give me a fuller picture.

My wife and I had already considered leaving. I had interests that I couldn’t pursue at Ford. The possibility of getting a small severance to leave would be a nice help along that path.

If I was only going based on expected value on the decision tree, then I would have chosen not to submit for severance as that had the highest number.

We chose to submit our names for the voluntary separation.

How can decision trees be misused?

Decision trees are a tool, and like any tool, it can be misused. Be conscious of these and avoid them!

Too simple - Trying to over-simplify the complexity of the real situation. You can achieve simplicity, but you lose its ability to be helpful in making a quality decision.

Too complex - Trying to cover all permutations and complexities, you create too many branches and paths. The result is something unwieldy that can’t be used to make a quality decision.

Poor, or no, probabilities - Estimating probabilities is tough, but it’s an exercise and a muscle you need to develop. Doing this poorly creates poor outcomes.

Assuming static conditions - The world is constantly moving. If your probabilities, nodes, and branches are not shifting alongside changes in reality, the decision tree won’t help.

Other Examples

The example I’ve walked you through today about quitting is just one way you can employ a decision tree, but there are many other scenarios, in work and home life, where they can be helpful!

👔 Buying a Business - Should you buy a business or not? That’s a good root node. You could map out:

• Possible changes in interest rates.
• Changes in leadership.
• Changes in the competitive landscape.
• Changes in consumer behavior.
• Getting a loan, and at different terms.

🏚️ Investing in Real Estate - The root node could be whether to purchase a particular property. You could consider:

• Ranges of post-purchase build out (e.g. low, medium, high amount of remodel)
• Options for renting it out (how long does it take, what’s your occupancy rate)
• What would happen if you just put that money in an index fund for two years instead?

🩻 Medical Decisions - Choosing a particular medical intervention is a good root node. You can think through:

• What are the risks of negative outcomes?
• What options would you have available should a negative outcome occur?
• What’s the cost of non-intervention?
• What happens if you don’t opt for post-operation rehab?
• What happens if you choose a non-surgical intervention?

📱 Product Launch - Should you launch a new product? Consider:

• Various rates of consumer adoption.
• Various rates of churn.
• Various marketing channels and strategies.
• Cost of delay (e.g. staff salaries, potential bad timing of market).

That’s just the tip of the iceberg!

Some decisions, like where to go to lunch today, may not need a decision tree (although you could still create one 🤓). But for complex decisions with lots of interplay, decision tress are helpful maps.

How did our Ford decision end up?

In case you’re curious, I thought I should wrap up the story on what happened at Ford.

The first thing to say is that a decision’s quality is not the same as a decision’s outcome. There’s something called outcome bias where you judge a decision based on the outcome; we want to avoid that.

All things considered, with a little bit of luck we got a good outcome AND had a good decision process.

Ford accepted both of our voluntary separations, paid for our final semester of school, and we got jobs relatively quickly - in the brand new state of Texas!

Call to Action

I know you’re going to have something to decide this week. Is your team trying to figure out at uncertain path? Is there something going on in your personal life that you can’t crack?

Give decision trees a shot! If you run into any trouble or just want to share what yours looks like, hit me up at kevin@catalyst.group18.co.

Enjoy!

Kevin