“Do I contradict myself? Very well then I contradict myself. I am large, I contain multitudes”
While this is an amusing way to avoid admitting defeat in a debate, there’s deep wisdom behind this famous Walt Whitman quote.
We live in a world where each fleeting moment is determined by an infinitely complex set of factors. The easiest way to exist in this environment – and one most people choose in my experience – is to float through life on autopilot. It takes far less energy to hold a set of beliefs, consume information that further validates those beliefs, and disregard information that runs counter to them.
But the world is unpredictable and we’re never working with perfect information. If each moment is the outcome of a complex web of factors, then to thrive in this environment we need a way to ascribe value to the likelihood of outcomes. Probabilistic thinking is the solution to this problem. It does a few important things that lead to more effective, dynamic, and unbiased decision-making:
- It keeps us open to new information
- Leads to stronger conviction
- Forces us to reckon with asymmetry & fat-tails
Before we get to each of these, it’s important to acknowledge that the software our brains run today evolved from a time when the primary goal was survival. Our brain still does an excellent job of communicating these survival instincts, but it also lets us down if we don’t actively think about the world in probabilities. Let’s unpack some of the motivations for using this approach given our increasingly complex existence…
It keeps us open to new information. This is one of the most consistent alpha-generators that everyone has access to. Most people find it extremely difficult to be receptive to new information, particularly when it deviates from what they believe to be true. The benefit of probabilistic thinking here is that we’re never wed to one single truth – we can have a lot of confidence something may be true, but there are no absolutes. You rarely hear the words “never”, “always”, “guaranteed” from a probabilistic thinker. The implications of this are that these types of thinkers are always searching for more information, either to validate their existing view or more often to find evidence opposing it. This is rooted in Bayesian thinking: I won’t go in-depth on this topic but the TLDR is that we should take into account what we already know when presented with new information. This sounds obvious, but consider the headline:
“Shark attack fatalities more than tripled in 2020”
You’re a regular beachgoer and without Bayesian thinking you may become legitimately fearful you will be the next victim. But the Bayesian approach frames this in the context of existing information. You know shark attacks are infrequent, and that since this is the case, a small change in the aggregate number could lead to a meaningful change on a percentage basis. The prior information is important. Sure enough, with just a bit of research you learn that there were 13 fatal shark attacks in 2020 compared to the average of 4. It’s easy to conclude that your risk of becoming a shark attack fatality remains infinitesimal. On the contrary, let’s consider the following:
“Sea levels have risen 6.5 inches since 1950”
Our application of prior knowledge would lead us to a different conclusion in this case. On its face, 6.5 inches over ~70 years may or may not seem like a lot. However, when you look at the steady climb in sea levels over that period you realize it appears to be a long-term trend that is concerning. Further still, you can see the pace of sea level change seems to be accelerating; sure enough, nearly half of that 6.5 total inches has come in the last 20 years. It’s important to caveat that all your prior knowledge is also framed in probabilistic terms, not binary ones. So, any new information you encounter either serves to increase the likelihood your priors were true (i.e. supporting evidence) or reduce it (i.e. information that challenges your priors). The idea is to develop your thinking such that you are always challenging and validating what you believe – in some cases your priors will be replaced completely. In fact, for me the most clarity occurs right as I am changing my mind or admitting I was wrong. In those cases, I have built this knowledge base and belief system about something so there’s significant emotional stress when I detach from it; admitting those priors were wrong means there’s compelling evidence which leads me to my most enlightened state.
Seeking out alternative perspectives is uncomfortable for most, but it’s energizing for probabilistic thinkers for the reasons described. The beliefs we hold are not binary, so information that challenges our priors is not viewed in an adversarial way, it’s actually encouraged. This stands in complete contrast to how most people think – when confronted with information that opposes their view of the world, the kneejerk reaction is to ignore it, dismiss it or undermine it. This is why I say being open to new information is a consistent alpha-generator – just engaging with information in this way already puts you well ahead of the masses.
Leads to stronger conviction. One of the benefits of training your brain to work this way is it can strengthen your resolve during difficult times. Let’s say you became aware of Bitcoin relatively early in 2013 – remember, you’re always open to new ideas and information – and learned a bit about it. You may have concluded that it’s interesting in some respects and that people were using it to buy things on the internet. Your curiosity ended there. Fast-forward two years and it’s now 2015. This Bitcoin thing is still around and there seems to be more activity within its community. You have some prior knowledge of it but now you learn a bit more about it. The idea of a peer-to-peer payment system is intriguing to you, and you consider what factors might make it intriguing to a lot more people. Maybe you buy some Bitcoin because you believe there is at least a 5% chance it becomes some type of alternative store of value over time. You conclude that if themes like decentralization, digital payments or trust structures become more important topics over the next few years, the likelihood Bitcoin becomes more important will increase.
Fast-forward to 2017-18: Bitcoin has become more mainstream; it’s seen a tremendous rise & fall in value. It’s down more than 70% from its highs, and yet society has only lost further trust in big tech companies. Decentralization is now in the cultural zeitgeist, and the United States continues to maintain historically loose monetary policy. Taken within this context, it’s much easier to assume the likelihood Bitcoin solidifies itself as a store of value has only gone up – why would you sell now? In fact, if you believe it’s more likely than ever the conditions have improved for Bitcoin, you conclude it makes sense to own more of it.
On the contrary, for folks who don’t use this approach the bear market during that time was a nightmare because they lacked conviction. Why did they own this internet money thing? Were they just getting duped? Better to sell on the way down than wait for it to go to zero! This was of course the wrong approach in hindsight but using probabilistic thinking would have given them a much better chance of thriving during those difficult times. Similarly, this method of thinking also forces us to make assumptions to the upside: what factors do I believe would lead to a 100x explosion of adoption? Forcing yourself to make these considerations means that if/when you see signs of these coming to fruition, it’s much easier to be early to megatrends.
Forces us to reckon with asymmetry & fat-tails. Let’s first take the fat-tail portion of this. We’re all familiar with the “normal distribution” curve seen below:
The normal distribution curve is fantastic because we can quickly identify our parameters and determine the probability of different outcomes. The problem is our world doesn’t really operate within a “normal distribution” curve. Our world often functions more like the below:
The dark blue line in the above is a better representation of our world today. Notice the tails of the curve are much fatter – what does this mean? It means that the chance of very extreme events happening (in either direction) is much higher than we’d expect from a normal distribution. Any one extreme event is still unlikely, but the number of extreme events is far higher and thus the probability one of them occurs is also much greater. Crazy and unpredictable things will happen, and by definition, we have no way to discern when or what those things will be.
Similarly, when we use probabilistic thinking, it forces us to reckon with asymmetries, most notably asymmetrical returns & information. Going back to our crypto example for a moment, during the depths of 2018 we may have looked at our Bitcoin position and considered: what is the probability this is all a scam and if so, my position is worth 0? Maybe we said it’s 10% or 15% for example. Then we consider: what is the probability this isn’t a scam and is just a lull in an otherwise long-term trend? The upside if it was just a dip in a longer-term trend was far greater than the downside if it was a scam. So even if we did consider the possibility it was worth zero, that wouldn’t have precluded us from continuing to own – or stack more of – it given the asymmetric upside.
In a similar way, we are always considering how relevant each piece of new information we receive is. There’s always a totem pole of information flow – somebody must be the first to hear of new useful news. Everyone else is lower & lower on the information totem pole. It’s critical to understand where you are within this structure.
All new information is not useful to all people, so it’s important to consider the source of the information, how relevant it is, what the motivation for this information flowing to you is and a bunch of different game-theory questions. This is information asymmetry. Probabilistic thinkers appreciate new information but always contextualize it. Over time they come to trust some channels of information more than others and are constantly using new information to refine the probabilities of outcomes. There is an art to training your brain to work this way. It leads to better intuition, trendspotting, pattern recognition and a host of other benefits over time.
Successfully adopting a probabilistic thinking mindsight takes time but is extremely valuable. Identifying what information matters, assigning value to the likelihood of different outcomes, appreciating fat-tails and most importantly challenging our own views is an ongoing cycle. Our world is extremely complex and it’s impossible to know with complete certainty what will happen next. Probabilistic thinking though gives us the best chance to consistently outperform and be prepared for the unpredictable.
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