19 highlights
-
Our lack of perfect information about the world gives rise to all of probability theory, and its usefulness.
-
The probabilistic machinery in our mindsâthe cut-to-the-quick heuristics made so famous by the psychologists Daniel Kahneman and Amos Tverskyâwas evolved by the human species in a time before computers, factories, traffic, middle managers, and the stock market.
-
Bayes was an English minister in the first half of the 18th century, whose most famous work, âAn Essay Toward Solving a Problem in the Doctrine of Chancesâ was brought to the attention of the Royal Society by his friend Richard Price in 1763âtwo years after his death.
-
The core of Bayesian thinking (or Bayesian updating, as it can be called) is this: 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.
-
It is important to remember that priors themselves are probability estimates. For each bit of prior knowledge, you are not putting it in a binary structure, saying it is true or not. Youâre assigning it a probability of being true. Therefore, you canât let your priors get in the way of processing new knowledge.
-
Any new information you encounter that challenges a prior simply means that the probability of that prior being true may be reduced.
-
The bell curve is great because itâs easy to understand and easy to use. Its technical name is ânormal distribution.â If we know we are in a bell curve situation, we can quickly identify our parameters and plan for the most likely outcomes.
-
The difference is in the tails. In a bell curve the extremes are predictable. There can only be so much deviation from the mean. In a fat-tailed curve there is no real cap on extreme events.
-
Think of it this way. In a bell curve type of situation, like displaying the distribution of height or weight in a human population, there are outliers on the spectrum of possibility, but the outliers have a fairly well defined scope. Youâll never meet a man who is ten times the size of an average man. But in a curve with fat tails, like wealth, the central tendency does not work the same way. You may regularly meet people who are ten, 100, or 10,000 times wealthier than the average person. That is a very different type of world.
-
The problem is in the fat tails: The risk of terror violence is more like wealth, while stair-slipping deaths are more like height and weight. In the next ten years, how many events are possible? How fat is the tail?
-
The important thing is not to sit down and imagine every possible scenario in the tail (by definition, it is impossible) but to deal with fat-tailed domains in the correct way: by positioning ourselves to survive or even benefit from the wildly unpredictable future, by being the only ones thinking correctly and planning for a world we donât fully understand.
-
Finally, you need to think about something we might call âmetaprobabilityâ âthe probability that your probability estimates themselves are any good.
-
If you look at nicely polished stock pitches made by professional investors, nearly every time an idea is presented, the investor looks their audience in the eye and states they think theyâre going to achieve a rate of return of 20% to 40% per annum, if not higher. Yet exceedingly few of them ever attain that mark, and itâs not because they donât have any winners. Itâs because they get so many so wrong. They consistently overestimate their confidence in their probabilistic estimates. (For reference, the general stock market has returned no more than 7% to 8% per annum in the United States over a long period, before fees.)
-
Another common asymmetry is peopleâs ability to estimate the effect of traffic on travel time. How often do you leave âon timeâ and arrive 20% early? Almost never? How often do you leave âon timeâ and arrive 20% late? All the time? Exactly.
-
Far more probability estimates are wrong on the âover-optimisticâ side than the âunder-optimisticâ side.
-
Successful spies are very good at probabilistic thinking. High-stakes survival situations tend to make us evaluate our environment with as little bias as possible.
-
Probabilistic thinking can only get you in the ballpark. It doesnât guarantee 100% success.
-
Successfully thinking in shades of probability means roughly identifying what matters, coming up with a sense of the odds, doing a check on our assumptions, and then making a decision.
-
Probabilistic thinking is an extremely useful tool to evaluate how the world will most likely look so that we can effectively strategize.