Every decision is a math problem

This summer I was fortunate enough to spend a month in Peru traveling with my partner Emily and a few of our friends. While staying in Lima, we took a day trip out to the Huacachina sand dunes. The tour included a dune buggy ride through the desert and sandboards for each customer to sled down the sandy slopes. However, for those seeking an additional thrill, sand skis were available to rent for an additional $10. Ally, a friend that was traveling on the trip, determined that she was going to rent the skis and asked if I would like to join her.

I’m sure most of you know exactly what you would decide to do in my shoes. However, in this blog post I’m not concerned with what we decide to do, but instead how we decide. And to be upfront, I have absolutely no understanding of how most people make decisions. But I do know how I do, with math.

To me, every decision is a math problem, or more specifically, an expected value function. Expected value functions are simply the value of an event multiplied by its probability. For example, imagine you spin a wheel with the numbers 1–5 on it, all with an equal probability. If you land on the number 1, you win $100. If you land on any other number you win nothing. The expected value of spinning the wheel then is simply 0.2 * $100, or $20.

This expected value function is simple because both the probability and the value are easy to quantify. However, in most of our decisions in life, we are not dealing with such simple inputs. So what about more complicated life decisions such as choosing our careers, our partners, or whether or not to rent sand skis? How do we assign values and probabilities?

To estimate the value of any life experience we can attempt to quantify the amount of joy or suffering it brings us. Economists and moral philosophers call these quantified units, utils. Imagine a utils scale ranging from negative 100 to positive 100. Things that bring us the absolute most joy a human can experience are worth 100 utils. Things that bring us the absolute most suffering a human can experience are worth -100 utils. A completely neutral experience is worth 0. With utils, we can attempt to quantify any experience, including the expected value of renting sand skis.

In making my decision, I made the following estimations.

• There is a 2% chance that I will suffer an extreme injury, such as a broken leg and that an extreme injury would bring me -50 utils.
• There was a 9% chance at a minor injury, such as scrapes and bruises, and that these injuries would bring me -10 utils.
• There was a 90% chance of no injuries and that an injury free experience would bring me 5 utils.

Now, the expected value of renting skis can be calculated with the following math:

Expected value = (0.02 * -50) + (0.09 * -10) + (0.9 * 5)

Expected value = 2.6

Because the expected value was greater than 0, this meant that I could expect a positive experience. I decided to rent the skis. However, after I rented the skis and got to the top of the slopes, my math changed and I thought there was a much higher risk of injury. I skied down one small slope, and called it quits.

Of course, my simple expected value function did not capture all of the real life inputs. I did not factor in the opportunity cost of spending $10 on the skis or the negative utility I gained from having to carry the skis around for our trek through the desert. Even further, my simple equation only captured my joys and sufferings, but our decisions also impact other people. My friends would clearly have had some of their trip spoiled if I had to be rushed to the hospital.

But just because our expected value functions will likely never be perfect, does not mean that they are not useful. Using math in my decision making process has improved my life and made me a better person. I feel very confident about most of my decisions. I think very concretely about the impact I have on the world and those around me. And I’ve found like minded folks in the Effective Altruist community.

This isn’t to say that I crunch the numbers for every single decision in my life. The vast majority of decisions are obvious enough that I can make them instantaneously. If someone offered me $5 to let Mike Tyson punch me in the face as hard as he could, I would not waste my time with calculations. But it can be a useful mechanism when making difficult or extremely important decisions. For example, 80,000 Hours, is a non-profit that conducts research on which careers have the largest positive social impact and provides career advice based on that research. Determining how we will spend our lengthy working careers is a major life decision and once we determine our values and skillset, we can make the decision more informed by using math. This applies to other major life decisions as well.

What’s the alternative?

I know that the vast majority of people have never created an expected value function to make a decision. But then how do they/you make decisions? While I think I’m generally an empathetic person, I’ve always struggled to understand why other people make the choices they make. If you are reading this I encourage you to comment, text me, email me, or reach out in any capacity to let me know a little bit more about your decision making process.