10 Base Rate Fallacy Examples

Base rate fallacies occur when statistically relevant information is ignored or overlooked in favor of information that is less relevant.

Key components include:

• The base rate refers to the statistical likelihood of an event occurring (e.g. 1% chance).
• Due to irrelevant or complicating factors, a person over-inflates the likelihood that it would have happened (we may falsely assume there was a 50% chance of it occurring).
• This over-inflated idea of likelihood is attributed to the base rate fallacy, which is a mental heuristic that has overlooked statistical probability and focused instead on irrelevant data.

Base rate fallacies happen when an individual misjudges the likelihood of an event unfolding because they do not take into account other pertinent and relevant base rate information.

Phrased differently, base rate fallacies happen when one ignores statistical information in favor of using inaccurate information that one believes to be relevant, in order to make a judgment. This behavior typically results from irrational beliefs that stats don’t apply to a scenario, when in fact they do.

Below, I will explore several examples of base rate fallacies to better understand the phenomenon.

Base Rate Fallacy Examples

• Driving Close to Home is More Dangerous: Over half of the car accidents reported in 2002 happened within 8kms from the driver’s home. Therefore, we tend to overinflate the sense of danger when close to home. In fact, the reason most crashes occur close to home is because we spend most of our time driving near our house. At any one time, we’re no more likely to crash just because we’re near home.
• Gender stereotypes: We will often rely on gender as a stronger indicator of a person’s profession than other factors. For example, 25% of doctors may be women. But when we see a female in a hospital, we might assume she’s the nurse 95% of the time. We have overinflated the probability based on stereotypes.
• Gambler’s Fallacy: The gambler’s fallacy is a type of base rate fallacy. It occurs when a coin lands on heads 5 times in a row, so we overinflate the probability that it will be heads the 6^th time we toss the coin. In reality, it’s only got a 50% chance of landing on heads.
• Fundamental Attribution Error: The fundamental attribution error is a mental shortcut that involves explaining another person’s behavior in terms of their personality rather than statistical likelihood (see below: Tom’s Major).
• The Monty Hall Problem: Imagine a gameshow host (his name was Monty Hall!) offers you three doors. Two have goats behind them, one a free car. You choose Door 1. Monty Hall then opens Door 2, revealing a goat. He gives you the choice to stick with Door 1 or switch to Door 3 for your ultimate choice. Should you switch? Common sense says you’ve got a 50/50 chance of success. But some mathematicians disagree. Statistically, the 1/3 probability of Door 2 having the car has moved to Door 3, giving it 2/3 probability of being the correct door now. You should definitely switch your choice!
• Living on a Prayer: An investor is given two options of companies to invest in which vary in projected risk and return. Operating under the assumption and bias of the common phrase “no risk, no reward” they may opt for investing in the riskier company without looking into its history to understand if it’s the best decision. They’re making decisions based on a mantra rather than the base rate statistic.
• Personalizing Statistics: If you’re told 10% of the population has a disease, you’re likely to shrug and assume it isn’t you. If you’re in a room with 10 people and told 1 person in the room has the disease, you’re more likely to worry it’s you. The base rate is the same, but the way it’s presented has changed your perspective.
• Overinflated Ego: When hearing that only 6% of applicants are accepted into a particular school, one believes their child will be accepted because they personally believe their child is “brilliant.”
• Population stereotypes: Most people know that Scotland has a high number of red heads. So, if we line 10 people up in a room and say one of them is from Scotland, most people will select the red head. They’re neglecting to realize that only 13% of Scots are red headed, so your chances are quite low that the Scot in the room has red hair.

Some Examples Explained

1. Tom W.’s Major

Kahneman and Tversky conducted a study to determine whether individuals would make conclusions based on base rate evidence provided, or fall victim to base rate fallacy due to favoring less relevant information in their decision-making.

In this study, the researchers went to a school where 80% of students were studying to be librarians and 20% were studying to be engineers.

They then provided students with a sketch of Tom W. Participants were told that Tom was a student at the school. He was an orderly, detail-oriented, competent, and self-centered individual. They were then asked to guess whether he was an engineering or a library student.

On the one hand, students know that 80% of students at the school are going to become librarians. That’s the base rate.

But they’ve got other information that acts as a red herring: Tom seems to fit a stereotype of an engineer.

Despite this base rate information showing that he’s 80% likely to be a librarian, students decided instead to lean into the engineer stereotype. Ninety-five percent of participants guessed that Tom W was an engineer.

This highlights how individuals tend to ignore relevant statistics when making decisions, and lean on biases instead.

Related Concept: Statistical Bias in Research

2. Car Accidents

It was reported in 2002 that over half of car accidents took place between one’s home and an  8kms distance.

This stat may have been dismissed as inaccurate. People might think, “That would only be a few minutes of driving, how could an accident happen in that short time?”

However, looking into the statistics further before making a judgment would have revealed the reasoning: most car trips are not far from home, car trips often happen every day (going to and from school, work, socializing) which provides more opportunities for accidents to happen.

A base rate fallacy exists in this scenario, then, due to one misjudging the likelihood of several car accidents happening close to home because they did not take into account other relevant information and instead relied on mental shortcuts to come to a conclusion (i.e., that automobile accidents only happen on long trips).

3. Coin Toss

People often ignore what they intuitively understand to be true when it comes to probabilities.

Consider a scenario where two people are making judgements on how many times a coin will be flipped and land on heads (H) vs. tails (T) for ten flips. It would be likely that one would argue there is a higher chance of variability of the flips (THHTHTTHTH) rather than be heads every single flip for the ten flips (HHHHHHHHHH).

In reality, however, this assumption poses a base rate fallacy. That is, both scenarios have a 50% chance of happening (50% heads, 50% tails) and to assume one scenario would be more likely to happen is not based on statistics or reality.

This can also be interpreted as a form of framing bias.

4. The Monty Hall Problem

The Monty Hall Problem is named after a conundrum made famous by gameshow host Monty Hall.

In the gameshow, Monty Hall gives a contestant 3 doors to choose from. Two doors have a goat behind them. One has a car. He asks you to choose a door. At this stage, you have 1/3 chance of winning the car:

• Door 1: 1/3 Chance
• Door 2: 1/3 Chance
• Door 3: 1/3 Chance

The contestant selects Door 1. So, Monty Hall opens Door 2, revealing there is a goat there. He then gives the contestant a choice: switch choices, or stick with Door 1?

• Door 1: 1/3 Chance
• Door 2: 1/3 Chance
• Door 3: 1/3 Chance

The common sense solution is to say it doesn’t matter. You’ve now got a 50/50 chance of success. The goat is either behind Door 1 or Door 3.

But this isn’t true.

Monty Hall was always going to reveal one goat door to you in Step 2 of his challenge.

So, in reality, your chances aren’t 50/50. Your chance remains 1/3 for the door you first selected. The 1/3 chance from the revealed door transfers to the last remaining door, like this:

Option 1:

• Door 1 Goat – You Select Door 1
• Door 2 Goat – Monte Reveals Door 2
• Door 3 Car

Option 2:

• Door 1 Goat – You Select Door 1
• Door 2 Car
• Door 3 Goat – Monte Reveals Door 3

Option 3:

• Door 1 Car – You Select Door 1
• Door 2 Goat
• Door 3 Goat – Monte Reveals Door 3

In choosing to always reveal the door that is not a winning door, Monte is changing the odds. There is now a 2/3 probability that the car is behind the remaining door. You definitely should switch choices now!

5. Job Stereotypes

Base rate fallacies often occur when we make stereotypes about people’s professions. Consider the following.

Suppose you were asked to categorize an individual as a type of profession and were given the following information: this individual is a woman, she enjoys social activism and debates, and she was selected to be part of this study from a pool made up of 95% nurses.

If you were then asked whether you thought she was a politician or a nurse, it is likely that you would conclude she was a nurse. This is because, rather than utilizing the data at hand, biases that exist (women are nurturing and perpetuated as caretakers) would inform your decision instead.

Conclusion

Base rate fallacies are a form of cognitive bias that results in individuals making illogical decisions. From the examples, above it is clear to see how one can fall prey to acting on a base rate fallacy.

Without seeking relevant statistics or probabilities prior to making a judgment or decision, it may also result in perpetuating biases and stereotypes. To improve upon the likelihood of misjudging, consulting experts, and researching base rates prior to solidifying a conclusion is beneficial.

Being aware that base rate fallacy can happen and trying to mitigate the degree to which it happens, is also a great starting point.