Bayesian Thinking – Introducing Probability Theory’s Most Important and Least Understood Concept

As humans, we tend to ignore general information at focus on specific, recent, individuating details. Perhaps it’s a quirk of evolution: faced with a snarling tiger, we’re more likely to focus on the look in its eyes rather than the dappled sunlight shining down through the trees.

Unfortunately, this tendency can cause huge problems when it comes to decision making, risk assessment, and investment strategies. Rather than integrating all of the information available to us and making a strategic decision, we tend to focus on the immediate. This means that underlying factors – the prevalence of a disease, the risk of disaster, and long-term trends in the stock market – are ignored.

This mistake goes by many names – the Base Rate Fallacy and Bayesian Thinking are the most common – and is one of the most common but least understood mistakes out there. In this article we’ll look at how it occurs, give a couple of examples of it in action, and how you can avoid it.

Thinking Fast and Thinking Slow 💨

The Base Rate Fallacy has recently come to greater public prominence through the work of American-Israeli psychologist Daniel Kahneman in his book Thinking, Fast and Slow. Kahneman’s example of the principle at work is one of the simplest. He writes:

“An individual has been described by a neighbor as follows: ‘Steve is very shy and withdrawn, invariably helpful but with little interest in people or in the world of reality. A meek and tidy soul, he has a need for order and structure, and a passion for detail.’ Is Steve more likely to be a librarian or a farmer?”

Most people, when asked this question, will immediately answer that Steve is more likely to be a librarian. His personal qualities are those we expect of a librarian, after all. And yet this answer would be wrong, because there are more than 20 times as many male farmers in the US than librarians. 

The reason why so many people get this question wrong is because we tend to focus on recent, personal details rather than general facts, even if they are obvious. Think again for a second about this question, and it’s immediately clear that someone chosen at random from the populace will be more likely to be a farmer, because there are simply more farmers. 

In other words, all of the personal details about Steve have little (or no) bearing on the question, but merely serve to mislead us. By far the most important piece of information needed to answer this question is: what percentage of males are farmers? This percentage, in this particular example, would be the “base rate”. 

Going Further – Examples ✅

Once you learn to recognize the base rate fallacy, you’ll start to see it everywhere. In fact, it might even change the way you look at the world. Let’s take a look at a few examples, and you’ll see what I mean.

Epidemiology 

One of the most common areas in which the base rate fallacy raises its ugly head is in epidemiology. We can see the reason for this by taking a basic example.

Say that the rate of a particular disease is ten times higher among blondes than it is among people with any other hair color. Then say that Pat is diagnosed with the disease, and that is all we know about this person. We don’t know anything else: not Pat’s hair color, or even if they are male or female. What is the likelihood that Pat is blonde?

A person affected by the base rate fallacy will tend to hugely overestimate the probability that Pat is blonde. Some might even say that the probability of them being blonde is 90%. This makes a kind of sense, but it’s totally wrong. 

The actual answer to this question depends far more on what percentage of people are blonde. This is the “base rate” in the current example, and is much more important than any other information we have. 

Let’s do the math. Let’s say we have a group of 100 people, and that they are representative of the population of the world. Worldwide, about 2% of people are blonde, so 2 of our group of 100 will be blonde. Let’s also say that the disease affects 5% of the general population, and so it affects ten times as many blondes – that’s 50%. So, 1 of our 2 blondes will have the disease, and (roughly) 5 of the remaining 98 people will have it. Now we can see the true picture: we have 6 people with the disease, one of whom is blonde. 

That makes the probability of a person with the disease being blonde 1 in 6, or about 17%. 

Most people won’t give this answer, of course. Because we like people (and perhaps because we like blondes) we tend to focus on the human details in a story, and not the base rate. 

Mass Surveillance

Diseases that only affect blonde people might seem a little obscure, so let’s look at a real world example of the base rate fallacy, and one that is having real life effects on the citizens of Europe.

Back in 2016, the European Union passed the Passenger Name Records (PNR) directive. This legislation allowed the EU to collect information on citizens in order to detect, prevent, and investigate terrorism. Unfortunately, the amount of data collected has quickly overwhelmed national authorities, inconvenienced many people, and led to a very small number of interventions. 

This is because systems like this need an impossibly high level of accuracy in order to work effectively, and most people won’t see that immediately because of the base rate fallacy. Let’s simplify the numbers a little to see why. 

Say a city with a population of 1 million starts a surveillance system like this. Say that the system is 99% accurate – pretty good, by most people’s standards. Or so you would think. But let’s ask a simple question: if someone is identified as a terrorist by this system, what is the chance that they are actually a terrorist?

If you’ve been through the previous example, you might see where this is going. The answer is not 99%. In fact, it’s closer to 1%.

This is because most people won’t take into account the error rate of the system, or will completely underestimate its effects. An accuracy rate of 99% means this – that (1) when a terrorist is detected, the system will register it as a hit 99% of the time, and fail to do so 1% of the time and (2) that when a non-terrorist is detected, the system will not flag them 99% of the time, but register the person as a hit 1% of the time.

Let’s say, further, that the actual number of terrorists in the city is 0.01%. This means that once all 1 million citizens have been tested, the number of true positives registered by the city’s surveillance numbers 99, with the number of false positives at 9,999. 10,098 people have been flagged by the system, of whom just 99 – less than 1% — are actually terrorists. 

The Consequences 👮

In the two examples above, it might not seem like that much “harm” has been done to those involved (except, of course, for all the people who were misidentified as terrorists). But the base rate fallacy can have detrimental effects on many aspects of our economy and daily lives.

One of the clearest examples of this is the impact of the fallacy on investment decisions. When making investment decisions, investors generally have access to two different types of information. One type is general information on the movement of a stock over the long-term: the base rate. The second type is more specific information, such as how many basis points the market has shifted, what percentage a company is off in its corporate earnings, or how many times a company has changed management.

This short-term, event-specific information is definitely important for some people, and is often critical for professional traders or short-sellers. Unfortunately, it is often given far more weight than it should be by more “traditional” investors looking to predict the long-term performance of a stock. A company could have a solid financial position, consistent growth rates, and managers with proven track records, but one bad quarter, or a rumor about financial irregularities, can turn many people off. 

In the financial world, in fact, the effects of the base rate fallacy are so well known, and so common, that many analysts spend their careers trying to predict when investors will make this kind of mistake. This field is known as “behavioral finance”, and seeks to replace the dated idea that individuals always make “rational” decisions by taking into account the many ways in which they don’t, with the base rate fallacy being a major example of this.

A Final Word

The base rate fallacy goes by many names, and appears almost everywhere that humans make decisions. At the most basic level, it is the tendency for humans to give undue weight to recent, personal, imminent information rather than looking at longer-term trends. 

Once you’ve learned to recognize this fallacy, you’ll probably start seeing it everywhere, and perhaps even in your own decisions.