Saturday, July 09, 2022
Welcome back people! This is the second last post in our Mental Model series, if you have read all the previous posts, CONGRATULATIONS! You are in the final stages of changing the way you take decisions. If you haven’t read the previous posts, what’s stopping you? Procrastination? Go check them out here.
Probabilistic thinking is essentially trying to estimate the outcome of a decision using some tools of maths and logic. It is one of the best tools we have to improve the accuracy of our decisions. Let us do what we are good at - understand through an example.
Let me ask you a question. Are you going to clear the exam you have been preparing for since the last year?
Why we need the concept of probability is worth thinking about. Things either are or are not, right? I will either clear the exam or won’t clear it. I won’t clear 70% of the exam, right? Clearing 70% of the exam doesn’t make any sense. Now, the problem here is, we just, don’t know until we live out the day. I won’t know if I’ll clear the exam until I give the exam and match my answers with the answer key (maybe I’ll still have to wait for the cutoff to come). This doesn’t help us at all in the present. The future is far from determined and we navigate it by understanding the likelihood of events that could impact us.
Our lack of perfect information about the world gives rise to probability and its usefulness. There are three important impacts of probability which we need to understand so we can integrate them into our thinking.
Bayesian Thinking: Given that we have limited but useful information about the world, and are constantly encountering new information, we should probably take into account what we already know when we learn something new. In layman terms, bayesian thinking allows us to use all relevant prior information in making decisions.
For example - Consider the headline “Crypto scams have doubled in 2022”. Without bayesian thinking, anyone who would read this headline would be afraid to invest in crypto because your chances of being a victim of the fraud is higher than it was last year, thus, miss out on wealth generation in the longer term (personal view). A bayesian approach will have you put this information into the context of what you already know. You know the crypto scams have been generally declining in the last few years because of the regulation. The crypto space is safer than it earlier was. Let’s say your chances of being a victim was 1 in 10,000 i.e. 0.01%. If the scams have doubled, your chances of being a victim are 2 in 10,000 which is 0.2%. Is it something to worry about?
It is important to note that the prior knowledge themselves are probability estimates. You are not assigning a binary structure, therefore any new information that challenges a prior simply means that the probability of the prior be reduced.
Fat-tailed curves: To understand fat-tailed curves, one needs to understand the normal distribution curve, also known as the bell curve. It is a simple curve that captures the relative frequency of many things. If you were to plot the height and weight graph of the students in your class, the result would look like a bell curve.
Fat-tail curve is almost similar to the bell curve, the only difference being in the tails. In a bell curve the extremes are predictable (as shown in the diagram above, extremes have a probability of 13.6%, 2.1%, 0.1%). In a fat tailed curve there is no real cap on extreme events. In layman terms, in a bell curve type of situation, like displaying height or weight, there are outliers on the spectrum of possibility. But the spectrum is well defined. You’ll never meet a person who is 20 times the size of an average man. But a fat tail curve doesn’t behave the same way. For example wealth, you can find many people whose net worth is 20 times that of an average man.
Asymmetries: How many times have you left your home “on time“ and reached the destination earlier? Almost never? How many times have you left your home “on time” and reached the destination late? Almost always? This is what asymmetry is all about. Considering the metaprobability - probability of the probability. Far more probability estimates are wrong on the “over-optimistic” side than the “under-optimistic” side.
We can never know the future with exact precision. Probabilistic thinking is a useful tool to evaluate how the world will most likely so we strategise accordingly.
See you next Saturday, until then have a great weekend :)
Cheers!
A FEW THINGS KEEPING ME AWAKE
Article: Toys, Secrets & Cycles by Chris Dixon
Podcast: The Knowledge Podcast - Kunal Shah
Song I am listening to: Deewana Hai Dekho by Alga Yagnik
Thought of the week: "Problems which involve human nature are impossible to solve. Just get over them!"
MEME OF THE WEEK
SARCASTIC REFLECTION
Here are the last three posts if you were too occupied to read them -