Summary of Key Points
This article uses everyday examples to explain the crucial application of Bayesian thinking in decision-making. We subconsciously employ Bayesian reasoning in our daily lives (such as experienced drivers adjusting their driving distances or Warren Buffett evaluating companies), but we tend to make mistakes in two specific scenarios: situations with extreme prior probabilities (highly likely or unlikely events) and those with moderate prior probabilities (random events with no clear tendency). The article outlines the following decision-making principles:
- For events with extreme prior probabilities, one should be stubbornly skeptical of new evidence; for those with moderate prior probabilities, one should be open to change based on new information. This is not a matter of personality but a rational choice.
1. Bayesian Thinking Is Everyday
Bayesian thinking isn’t about complex formulas; it’s about making judgments based on experience and then adjusting them with new information. For example:
- Warren Buffett evaluates companies by first examining thousands of successful businesses to form an idea of what a good company looks like (prior probability), and then comparing the characteristics of the company under consideration (new information) to reach a conclusion.
- An experienced driver determines a safe driving distance on the highway based on past experience (prior probability) and adjusts it according to the speed of the vehicle ahead and road conditions (new information).
We use this logic subconsciously in most of our daily decisions, but our intuition can fail when dealing with extreme or moderate probability events.
2. Extreme Probability Events: Don’t Let a Single Anomaly Overrule Your Common Sense
Extreme probability events refer to those that are either very likely to happen (e.g., the probability of a 40-year-old woman not getting cancer is 99%) or highly unlikely (e.g., the probability of getting cancer is 1%). In such cases, even if new evidence seems conclusive, it should be questioned rather than immediately dismissing your initial belief:
- Cancer Screening Pitfalls: The probability of a 40-year-old woman developing cancer is 1%, and screening tests have a 90% sensitivity (90% of positive results are correct, 9% are false positives). A single positive result indicates a 9.2% chance of actually having cancer; a second positive result only increases this to 50%. Since not getting cancer is a highly likely event, a third test is necessary.
- Individual Cases vs. Scientific Conclusions: Someone might argue that their grandfather smoked all his life without getting cancer, but since cancer is a rare event, smoking merely increases the risk, not making it a certainty. Individual cases do not undermine the scientific evidence that smoking causes cancer.
- Stock Market Scams: Only 4% of stocks hit the daily limit up, and a “predictive” indicator may perform well in these cases, but its accuracy is limited due to the low base probability.
Rule: In situations with extreme probabilities, no matter how compelling the new evidence appears, question the evidence itself first.
3. Moderate Probability Events: New Evidence Is More Reliable Than Intuition
Moderate probability events involve scenarios where all options have roughly equal chances (e.g., a new user’s gender is unknown, or a stock’s short-term performance is unpredictable). In these cases, any new information should influence your judgment:
- Recommendation Algorithms: If a new user’s gender is unknown (50% prior probability), the system may initially assume they are female after viewing content related to male celebrities. Viewing more content about pregnancy will increase this assumption, but if they later purchase male products, the system might not immediately change its assessment, as the likelihood of them being female becomes highly likely.
- Stock Market Performance: Short-term price changes are often random (moderate prior probability). Identifying reasons for price movements is usually hindsight. For example, although China State Shipbuilding Corporation’s stock rose 628% in the first half of the year, it only did so on 57% of the days. The key is to look at underlying factors (such as industry policies or company performance) rather than relying on random patterns.
Rule: In situations with moderate probabilities, any new evidence deserves attention, and you should not be misled by intuition (e.g., assuming a stock will rise after a significant drop).
4. The Strength of Evidence Matters: Different Prior Probabilities Require Different Levels of Conviction
To override a prior probability, the strength of the evidence needed is quantifiable:
- Moderate Prior Probability (50%): A small amount of new evidence can change your assumption (e.g., a new user’s gender being determined after viewing male celebrity content).
- Highly Extreme Prior Probability (99%): You need extremely convincing evidence (e.g., two positive cancer test results increase the probability to 91%; four results increase it to 99%).
- Extremely Low Prior Probability (One in a Million): You need almost conclusive evidence (e.g., flipping a coin ten times in a row and getting heads every time suggests there might be a problem with the coin or that you’re dreaming).
Core Principle: Extreme prior probabilities require substantial evidence to be overturned, while moderate prior probabilities are more sensitive to new information.
5. Stubbornness or Openness? Rationality Depends on the Probability Context
Whether you are stubborn or open to change depends on the probability context:
- Extreme Probabilities: You should be as steadfast as a rock facing strong waves (e.g., believing in the link between smoking and cancer; continuing to test for cancer after two positive results).
- Moderate Probabilities: You should be flexible like a flag in the wind (e.g., adjusting your assumptions based on new information when the user’s gender is unknown or stock performance changes).
The essence of this article is that decision-making should not rely on intuition but on understanding the underlying probabilities and the strength of the evidence. By grasping these principles, you can avoid most common mistakes in decision-making.