How to Discipline Intuition
Bayesian reasoning provides rules for combining prior beliefs (base rates) with evidence diagnosticity to discipline intuition. It emphasizes that base rates matter and intuitive impressions of evidence are often exaggerated.
THE IDEA
HOW TO DISCIPLINE INTUITION
Your probability that it will rain tomorrow is your subjective degree of belief, but you should not let yourself believe whatever comes to your mind. To be useful, your beliefs should be constrained by the logic of probability. So if you believe that there is a 40% chance that it will rain sometime tomorrow, you must also believe that there is a 60% chance it will not rain tomorrow, and you must not believe that there is a 50% chance that it will rain tomorrow morning. And if you believe that there is a 30% chance that candidate X will be elected president, and an 80% chance that he will be reelected if he wins the first time, then you must believe that the chances that he will be elected twice in a row are 24%.
The relevant “rules” for cases such as the Tom W problem are provided by Bayesian statistics. This influential modern approach to statistics is named after an English minister of the eighteenth century, the Reverend Thomas Bayes, who is credited with the first major contribution to a large problem: the logic of how people should change their mind in the light of evidence. Bayes’s rule specifies how prior beliefs (here, base rates) should be combined with the diagnosticity of the evidence, the degree to which it favors the hypothesis over the alternative. For example, if you believe that 3% of graduate students are enrolled in computer science (the base rate), and you also believe that the description of Tom W is 4 times more likely for a graduate student in that field than in other fields, then Bayes’s rule says you must believe that the probability that Tom W is a computer scientist is now 11%. If the base rate had been 80%, the new degree of belief would be 94.1%. And so on.
There are two ideas to keep in mind about Bayesian reasoning and how we tend to mess it up. The first is that base rates matter, even in the presence of evidence about the case at hand. This is often not intuitively obvious. The second is that intuitive impressions of the diagnosticity of evidence are often exaggerated. The combination of WYSIATI and associative coherence tends to make us believe in the stories we spin for ourselves. The essential keys to disciplined Bayesian reasoning can be simply summarized:
• Anchor your judgment of the probability of an outcome on a plausible base rate.
• Question the diagnosticity of your evidence.
Both ideas are straightforward. It came as a shock to me when I realized that I was never taught how to implement them, and that even now I find it unnatural to do so.
When to use it
Evaluating the probability of a job candidate's success by considering both base rates of success in the industry and the candidate's specific qualifications.
Interpreting medical test results by combining the base rate of the disease with the test's accuracy.
Forecasting election outcomes by adjusting prior probabilities with new polling data.
Assessing the likelihood of a student belonging to a specific major based on base rates and descriptive information.
FROM THEORY TO EVERYDAY LIFE
In practice
Rain probability
If you believe there is a 40% chance of rain tomorrow, consistency requires you believe there is a 60% chance it will not rain.
Tom W problem
Given a 3% base rate of computer science students and a description 4 times more likely for CS than other fields, Bayesian reasoning gives an 11% probability that Tom W is a computer scientist.
Political reelection
If a candidate has a 30% chance of being elected and an 80% chance of reelection if elected, the probability of two consecutive terms is 24%.
A MOMENT TO REFLECT
Put it to work.
How can you ensure you are anchoring your judgment on a plausible base rate when evaluating evidence?
Why do people often exaggerate the diagnosticity of evidence, and how can you counteract this?
In what situations have you neglected base rates, and how could Bayesian reasoning improve your decision?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- Thinking, Fast and Slow (Daniel Kahneman)