Conquer Big Life Decisions With Math
Decision Analysis simplified for normal people like us — the best life lesson I learned in grad school.
Overview
In this blogpost, I’m going to introduce the basics of Decision Analysis.
What I’m about to show you has related topics to the fields of data science, systems engineering and artificial intelligence.
But for today, I’ll show you a simple way of using it to make better decisions in your life. Specifically, I’ll go over:
- Why we need Decision Analysis
- How it works
- Practical everyday use
- Key Takeaways
Why we need Decision Analysis
How do we make huge decisions in our lives?
What job offer should I take? Which car should I buy? Should I marry this girl? (If you’re using DA for that last one, the answer is no).
Life is full of choices that have risks, consequences, and (often forgotten) rewards we’ll have to live with. Mastering how to make decisions —especially with your head — is paramount to maximizing your odds at success.
Success is never a guarantee, even if you make all the right choices.
The quote above is from my graduate advisor. He taught me Decision Analysis from a book called Foundations of Decision Analysis by Ronald A. Howard and Ali E. Abbas, and it’s come in handy at two pivotal moments in my life:
The first time was (1) when I dropped out of grad school to start a business. The second time was (2) figuring out what to do when COVID hit. Both were heavy-impact decisions in my life, and I’m glad I learned this skill from my advisor.
Looking back, I can objectively know with Decision Analysis that I made the right calls both times, even with high uncertainty.
But there were so many other times in my life where I wish I knew what I knew now. Some examples include which college to apply for, what major I chose, which job offers to accept… the list goes on and on.
So if you’re struggling to find guidance for a monumental decision you’re pondering, I hope you find this as helpful as I did.
How Decision Analysis works
Whenever you use decision analysis, the first thing to ask yourself is:
“Do I have time to use decision analysis?”
An obvious question, but methodically organizing information will surprisingly take more time than we think.
Also, Decision Analysis relies on a common measure of value for measuring outcomes (usually time or money). In fact, one of the shortfalls of decision analysis is that sentimental or emotional value is difficult to quantify.
That being said, I’ve never needed to use the math behind this technique (though it’s surely available). Typically, organizing the information and mapping things out on a decision tree is enough to clarify what the right decision is.
Key Concepts (with an example)
Below, I’ll walk you through some key concepts with a simple example: deciding (A) to study or (B) to cheat on a test.
Decisions — a choice to make that’s within your control.
Don’t confuse this with events and outcomes!
You can make a good decision that leads to a bad outcome (studying for a test and failing anyway). Likewise, you can make a bad decision that leads to a good outcome (cheating off a classmate and getting a perfect score).
Events — things out of your control that happen as a result of decisions or other events.
Outcomes — consequences/rewards of a decision or event, assigned with a common measure of value. Time and money are two primary examples, but school grades can work too.
Probabilities — the likelihood of an event unfolding. Probabilities of possible outcomes from an event must add up to p=1.0. These might come from historical data or from your own experience/educated guessing.
Decision path — a pathway of decisions & events that leads to specific outcomes. A decision path describes one potential reality for a chain of events and decisions.
E-values— a decision path’s score that shows how “good” a decision is. This is calculated by multiplying outcomes by probabilities, and summing them up to get the e-value of a decision.
In our example, consider the point equivalents to letter grade outcomes:
- B = 80
- F = 0
- A+ = 100
- Expulsion = -100
Calculating the e-value of cheating:
e=(0.8*100)+(0.1*0)+(0.1*-100)=70
Whereas the e-value of studying is:
e=(0.6*80)+(0.4*0)=48
Ethics aside, the best decision according to e-value is to cheat.
Remember, however, that e-value is not an outcome. Even though cheating is the best decision, you still risk the 10% chance of getting expelled. In the example, we chose to cheat and getting expelled (-100) could have been the real outcome.
For many, this outcome would be unacceptable, but that’s because e-value is risk-neutral — it doesn’t take other risk attitudes like risk-averse or risk-seeking into consideration.
Note: See “further reading” at the end for more notes on risk attitudes.
Practical Usage
In the real world, you’re probably never going to fully calculate e-values.
The most useful technique in decision analysis is organizing information into decision trees (like the example) to map out decisions and what paths they can take us on.
To do that, it’s important to be tenaciously systematic when looking at the information at-hand.
Here’s the basic checklist of the steps:
- Identify decisions — remember, these are not outcomes.
- Identify events — these are out of your control.
- List outcomes — measured in money or time.
- List probabilities — historical data or educated guesses.
- Make the decision tree — usually enough to make a decision.
- Calculate results — you probably don’t have to do this.
Again, it’s important to be systematic. Follow the steps in exactly this order. Personally, I replay the problem for steps 1–4 to make sure I don’t miss anything.
Take. Your. Time.
A note on information noise
Lastly, there will almost always be unnecessary information you’ll have to filter out.
For example, you might consider applying for your dream job despite having been told they’re not hiring. But since you’ve interned at the company before, you might formulate you have a 95% shot at getting hired.
Thinking you have a 95% chance is a mistake.
The probability you assigned to the outcome of getting hired for your dream job isn’t 95% — in reality, it’s 0% based on the current information.
You can decide to wait, but if you need a job now, applying for this company doesn’t belong on the current decision tree (though it could be relevant in later decisions).
Key Takeaways
- Separate relevant information by being systematic. Always identify (in this order) decisions, events, probabilities, outcomes, and results while filtering out noise.
- Use Decision Trees as a self-check. Making a quick decision tree usually leads to a clear choice.
- Probabilities and events are based on current data. In a lot of cases, you’ll be guessing at what your chances are. You may also be unaware of hidden events, which is why seeking advice from experts is generally a good idea.
Further reading:
If you enjoyed this introduction to decision analysis, I recommend the book Foundations of Decision Analysis. It has many useful concepts beyond the scope of this blog like risk attitudes.
As a simple example, would you prefer (A) $1000 now or (B) a 10% chance at $1M? Computing the e-values gives:
Decision A = p(1.00) x $1,000 = 1,000
Decision B = p(0.10) x $1,000,000 + p(0.9)*$0 = 100,000
As you can see, raw decision analysis with e-values suggests that the best decision is to take the 10% risk over the guaranteed $1,000. Yet I’d wager a good percentage of people would take the guaranteed deal A over deal B.
This doesn’t mean that these people are illogical — it means they’re risk-averse rather than risk-seeking or risk-neutral.
Everything I’ve taught in this post only covers risk-neutral decision making. However, risk-neutral e-values can be mapped to something called u-values (utility values) that takes risk preferences into consideration.
Alternatively, there’s a case for subjective decision making in the book Blink: The Power of Thinking without Thinking by Malcolm Gladwell. My graduate advisor also made us read this book in our decision analysis class, which gave me great insights on how both methods surprisingly compliment each other.
To read more about my personal experience with big life decisions, here’s a blogpost I wrote awhile back: How to decide to startup.
