Today I am going to discuss the art of making a good decision. Especially when you need to consider alternatives which have both monetary and non-monetary impact. Just like last week, this article is inspired by the book “How Not to Be Wrong” by Jordan Ellenberg (link to Goodreads).
When my spouse and I need to travel back to Europe, we have same debate – how early we should be at the airport so that we don’t miss our flight. When flying there, I am always rooting for getting there as late as possible. And she wants us to be at the airport four hours before the flight. When we are flying back, our roles flip. What can I say … too many relatives, too many responsibilities, less relax time.
But how can you decide? Is there a mental model for solving this situation?
What is the expected value (of a decision)?
Let’s say that you have a friend who really wants to make a $1000 bet with you (the details are not important, but you can imagine anything you what). You calculate that you have a 20% chance to win $1000, the expected value of the bet is $200 (20% x $1000 + 80% x $0 = $10). This is not the expected dollar value you are going to get in the end (you will either get $1000 or $0), but it sort of an average value of the two options. Another example is 10% to win $1500. The expected value in the second bet is 10% x $1500 = $150. So the first bet is better than the second bet – the expected value is bigger.
What if you cannot quantify the outcome (of a decision)?
Let’s start digging into the airport example by introducing a new term – util. This is a very personal value, but for me arriving at the airport 1 hour in advance costs me 1 util. Let’s assume that for my spouse the value is the same. On the other hand, missing the plane will cost me 6 utils, but it will cost my wife 12 utils (i.e., she will regret it two times more than me). Let’s assume that if we arrive 3 hours in advance, we only have 5% chance to miss the plane. but if we arrive 2 hours in advance, we have 20% chance to miss the plane.
For me the decision looks like this: 1) Option A – 2 hours in advance (2 utils + 20% x 6 utils = 3.2 utils expected value); 2) Option B – 3 hours in advance (3 utils + 5% x 6 utils = 3.3 utils). Bur for my wife the trade-offs are different: 1) 2 hours in advance (2 utils + 20% x 12 utils = 4.4 utils); 2) 3 hours in advance (3 utils + 5% x 12 utils = 3.6 utils). So while I don’t really care between Option A and B (3.2 utils vs. 3.3 utils), the difference for my spouse is huge (4.4 utils vs 3.6 utils).
What if you mix the two?
Finally, let’s further complicate the example. We need to take a cab to the airport. If we want to get there 3 hours in advance, we would pay $30 (e.g., because it is rush hour). But if get there 2 hours in advance, we would only pay $20. Again, these numbers are completely made up.
To calculate the expected value of the sum of two things, you sum the expected value of the first thing with the value of the second thing. Let’s say that I value 10$ as 1 util (in other words I value my time as 10$ per hour).
This is my equation: Option 1, 2 hours in advance = 2 utils (from the cab) + 3.2 utils (from getting there 2 hours early) = 5.2 utils; Option 2, 2 hours in advance = 3 utils (from the cab) + 3.3 utils = 6.3. Clearly, I favour Option 1.
This is my spouse’s equation: Option 1 = 2 utils + 4.4 = 6.4; Option 2 = 3 utils + 3.6 = 6.6. The gap is narrower this time, but Option 2 is still more valuable to my spouse.
What decision will you make?
In my case, I have outsourced the decision-making to my spouse. So we get there 3 (and sometimes more) hours in advance.
The one action that I would recommend to you is to keep in mind all this the next time you need to make an important decision (not about airplanes and travel, but maybe about your next job). Define all the trade-offs, lay them down on the table, and think critically about their expected value.
What are the next steps?
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