Thinking Probabilistically

In this past Monday’s post, I spoke about how I disagree with the idea that economics is about putting numbers on everything.

But a conversation I had over the weekend helped me think about how I might be wrong in this regard. If economics is about getting the most out of life, and if there are opportunity costs to everything in life – and I think both of these ideas to be central to thinking like an economics – then thinking probabilistically is a skill more of us should pick up.

Why? Because life is uncertain.

Getting the most out of life requires us to make decisions. These decisions are based on information that is almost always going to be incomplete. This is because acquiring all possible information relevant to the decision making process is an expensive, time consuming process. How do we know if have collected “enough” information? We don’t – we make at best an educated guess.

And regardless of how much information we have collected, we live in an uncertain world. Our best laid plans are likely to go awry. And so we make decisions on the basis of incomplete information, and the outcome of these decisions is uncertain.

For example: which college should I enroll in? I’ll decide this by taking a look at the college website, speak to folks within the college, speak to some of its alumni, maybe visit the college and speak to some professors. I could do this for as long as I like, and as thoroughly as I possibly can. But I will never be able to acquire all information relevant to this decision. And so my decision to enroll in a college is on the basis of incomplete information.

And say you did all the background research, and attended all the introductory seminars, and visited the college, and enrolled in it in, say, 2019. Six months into your course, the pandemic hits. Not your fault, not the college’s fault, and maybe we will never know for sure whose fault it is – but the outcome of your decision to enroll certainly wasn’t one you were expecting.

But this also applies to which chai tapri to visit after having bunked one of the lectures in the first six months. And whether to have a second cutting chai at that tapri. The point is, every single decision needs an evaluation on your part. And this evaluation is always with incomplete information, and the outcomes are always uncertain.

But can you evaluate the probability that things will work out reasonably well? What if, in 2019, you asked yourself about the chance that there would be a major pandemic that would disrupt college life completely? Well, an entirely reasonable approach would have been to take a look at the past one hundred years and ask if something along these lines had taken place. And you would have to conclude, quite reasonably, that the chance of something like this happening was one in a hundred, at best. You should therefore have bet on something like this not happening.

The point I’m making is not that you would have been wrong in this particular case – the point is the process of thinking probabilistically. I’m not saying you should whip out paper and pencil every time you decide to have chai at the tapri. But for most major decisions where probability based calculations are possible, it helps to put a probability based estimate on things working out. You will still end up making the wrong bet every now and then, and that’s fine. The point is that you know the odds (more or less) going into battle, and this helps you decide whether or not to engage in battle in the first place.

Again, I have not read Russ Roberts book just yet, but I think the point he is making in the book is that some problems are beyond the pale of this probability based approach to life. And I still stand by what I said in Monday’s post, economics ought to be about more than putting a number on most things.

But that being said, thinking probabilistically is very underrated, and I would encourage you to get started.

Two final points: my thanks to Amit Varma for a conversation about this that inspired this post. And trust me, he knows more than a thing or two about thinking probabilistically.

And second, via Samarth Bansal, a website that seems very promising in terms of helping all of us learn about statistics and probability.