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Base Rate Fallacy
What Is the Base Rate Fallacy?
In Critical Thinking, the Base Rate Fallacy is failing to factor in an earlier base rate or statistic.
Easy Definition of Base Rate Fallacy
Don't think "99% accurate" means a 1% failure rate. There's far more to think about before you can work out the failure rate. This idea is linked to the Base Rate Fallacy.
Academic Definition of Base Rate Fallacy
The Base Rate Fallacy is an error in reasoning that occurs when someone reaches a conclusion that fails to account for an earlier premise – usually a base rate, a probability or some other statistic.
(Help! I'm still confused. Look at the examples below and then read the definitions above again. Hopefully, they will become clearer.)
An Example of Base Rate Fallacy
The vaccines are useless because more vaccinated are dying than non-vaccinated
In July 2021, Public Health England (PHE) announced that more than 60% of the COVID deaths in the first half of 2021 were of vaccinated people. In other words, more vaccinated people were dying of COVID than non-vaccinated people.This statistic was quickly seized upon by the "anti-vaxxers" (those opposed to the coronavirus vaccine), who presented it as clear evidence that the vaccines did not work.
However, the "anti-vaxxers" were guilty of committing the base-rate fallacy.
The clearest way to think about this is to imagine a scenario when 99% of people are vaccinated and 1% of people aren't. Even though the vaccine dramatically reduces deaths, it is now easy to understand why there would be more deaths among the vaccinated than the non-vaccinated. Put simply, if 99% of people have a small chance of dying, then that is likely to produce more deaths than 1% of people with a greater chance of dying.
In July 2021, the situation was slightly more complicated than that though. The vast majority of the vulnerable (predominantly those over 80) were vaccinated while the majority of the less vulnerable (those under 30) were not. Even though the vaccine cut the risk of death by over 96%, the vaccinated vulnerable were still the most vulnerable, and they outnumbered the non-vaccinated. This last point is key. If literally everybody were vaccinated, then 100% of deaths would be of vaccinated people. Conversely, if literally no one were vaccinated, then 100% of deaths would be of non-vaccinated people. So, more deaths among the vaccinated speaks more about how many people have been vaccinated than it does about the efficacy of the vaccines.
Put another way, and possibly counter-intuitively for some, the efficacy of the vaccine cannot be calculated by comparing all the vaccinated with all the non-vaccinated. It could only be calculated by comparing an infected vaccinated group with an infected non-vaccinated group of equal size and equal vulnerability. In July 2021, those conditions were far from present.
In summary, the fact that more vaccinated people died than non-vaccinated told us nothing about the efficacy of the vaccines. The fact that the national COVID death rate dropped dramatically following the vaccination of the vulnerable told us everything about the efficacy of the vaccines. The "anti-vaxxers" were guilty of committing the Base-rate Fallacy because they did not account for the ratio of the vaccinated versus the non-vaccinated or the vulnerabilities of each group. They didn't factor these base facts into their conclusion.
Read about Confirmation Bias and COVID-19
Read about Availability Bias and COVID-19
Another Example of Base Rate Fallacy
This machine is useless because it's only 99% accurate
Imagine you have a machine that can detect whether coins are real or fake.Your machine is pretty good at this. When it checks a coin, it only gets it wrong 1% of the time. 99% of the time it makes the right decision.
Of course, there are two types of error the machine can make:
- It can say that a false coin is real (a false positive).
- It can say that a real coin is false (a false negative).
If you ran the machine until it spurted out a coin it believed to be a fake, what would be the chance of that coin actually being a fake? If you said 99%, that's almost certainly wrong. It could be much lower. The truth is you just don't know. Here's why:
Imagine your machine checked 10,010 coins, 10 of which were fake.

If you originally thought 99%, your answer was derived through fallacious reasoning because an earlier premise (the tiny probability of the coins being fake in the first place, i.e., the base rate) was not taken into account.
A Practical Application for Base Rate Fallacy
Know what those cameras will do for you

For example, if your shop buys a "99% accurate" face-detection camera to spot known shoplifters, your store detectives might find themselves following hundreds of people around the store who have no intention of shoplifting. The usefulness of such a system depends as much on the proportion of shoplifters in our society as it does on the accuracy of the system.
What about cameras to spot terrorists? What proportion of the population are terrorists? Minuscule. There would be thousands of false arrests if face-detection cameras that weren't 100% accurate were deployed at places like airports. Of course, this doesn't mean the cameras wouldn't be useful. It just means complementary procedures would need to be introduced. And that would be useful to know before spending millions on equipping an airport with such a capability.
Another Practical Application for Base Rate Fallacy
Give them 33% and tell them it's 50%

For example, when you buy six cans of Coke labelled "50% extra free," only two of the cans are free, not three. (It's because the original pack had four cans, and 50% of the original amount is two cans.)
If you thought three of the cans were free, then you failed to account for an earlier premise (i.e., there were four cans originally), and you committed the Base Rate Fallacy.
Summary of Base Rate Fallacy
If you think someone has taken a fact at face value without factoring in a key supporting premise (like a probability or a base rate), tell them they have committed the Base Rate Fallacy.- Do you disagree with something on this page?
- Did you spot a typo?
- Do you know a bias or fallacy that we've missed?