Causes Trump Statistics (Base Rate Neglect)
People tend to ignore base rates and rely on specific, vivid information (like witness testimony) when making probabilistic judgments, leading to errors in Bayesian reasoning.
THE IDEA
Causes Trump Statistics
Consider the following scenario and note your intuitive answer to the question.
A cab was involved in a hit-and-run accident at night.
Two cab companies, the Green and the Blue, operate in the city.
You are given the following data:
• 85% of the cabs in the city are Green and 15% are Blue.
• A witness identified the cab as Blue. The court tested the reliability of the witness under the circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colors 80% of the time and failed 20% of the time.
What is the probability that the cab involved in the accident was Blue rather than Green?
This is a standard problem of Bayesian inference. There are two items of information: a base rate and the imperfectly reliable testimony of a witness. In the absence of a witness, the probability of the guilty cab being Blue is 15%, which is the base rate of that outcome. If the two cab companies had been equally large, the base rate would be uninformative and you would consider only the reliability of the witness, concluding that the probability is 80%. The two sources of information can be combined by Bayes’s rule. The correct answer is 41%. However, you can probably guess what people do when faced with this problem: they ignore the base rate and go with the witness. The most common answer is 80%.
This illustrates the cognitive bias where causes (a plausible story) trump statistics (base rates). Even when statistical information is available, people often neglect it in favor of more concrete or causal evidence.
When to use it
Evaluating medical test results in light of disease prevalence.
Assessing eyewitness testimony in legal settings with known prior probabilities.
Making hiring decisions when base rates of success in a role are known.
Interpreting financial predictions or economic forecasts with historical data.
FROM THEORY TO EVERYDAY LIFE
In practice
Cab Problem
In a hit-and-run accident, 85% of cabs are Green and 15% are Blue. A witness identifies the cab as Blue with 80% accuracy. Most people answer 80% probability that it was Blue, but the correct Bayesian probability is 41%.
Medical Diagnosis
A disease affects 1 in 1000 people. A hypothetical test has 95% sensitivity and the same specificity. If a person tests positive, it is tempting to assign a 95% probability of disease, ignoring prevalence. With these assumptions, the probability is only about 2%.
A MOMENT TO REFLECT
Put it to work.
When have you ignored base rates in favor of a vivid story? How did that affect your decision?
How can you incorporate base rates into everyday judgments, such as assessing risks or probabilities?
Why does our intuition often favor causal explanations over statistical data?
CONTINUE THE CONVERSATION
Source texts
- Thinking, Fast and Slow (Daniel Kahneman)