Psychology of Perception of Deviations
Explores two cognitive biases: poor intuition for large deviations in Extremistan (fat-tailed distributions) compared to Mediocristan, and the framing effect where equivalent risks are perceived differently based on wording.
THE IDEA
Psychology of Perception of Deviations
Fragility of Intuitions About the Typicality of the Move
Dan Goldstein and I ran a series of experiments about the intuitions of agents concerning such conditional expectations. We posed questions of the following sort: What is the average height of humans who are taller than six feet? What is the average weight of people heavier than 250 pounds? We tried with a collection of variables from Mediocristan, including the above-mentioned height and weight, to which we added age, and we asked participants to guess variables from Extremistan, such as market capitalization (what is the average size of companies with capitalization in excess of $5 billion?) and stock performance. The results show that, clearly, we have good intuitions when it comes to Mediocristan, but horribly poor ones when it comes to Extremistan—yet economic life is almost all Extremistan. We do not have good intuition for that atypicality of large deviations. This explains both foolish risk taking and how people can underestimate opportunities.
Framing the Risks
Mathematically equivalent statements are not psychologically equivalent. Worse, even professionals are fooled and base their decisions on their perceptual errors. Our research shows that the way a risk is framed sharply influences people’s understanding of it. If you say that, on average, investors will lose all their money every thirty years, they are more likely to invest than if you tell them they have a 3.3 percent chance of losing a certain amount every year.
The same is true of airplane rides. We have asked experimental participants: “You are on vacation in a foreign country and are considering flying a local airline to see a special island. Safety statistics show that, if you fly once a year, there will be on average one crash every thousand years on this airline. If you don’t take the trip, it is unlikely you’ll visit this part of the world again. Would you take the flight?” All the respondents said they would. But when we changed the second sentence so it read, “Safety statistics show that, on average, one in a thousand flights on this airline have crashed,” only 70 percent said they would take the flight. In both cases, the chance of a crash is 1 in 1,000; the latter formulation simply sounds more risky.
When to use it
Evaluating investment opportunities in markets with extreme outliers (e.g., venture capital, hedge funds).
Designing public health messages about rare disease risks (e.g., one-time vs. annualized probabilities).
Improving risk communication in insurance or safety industries to avoid framing-induced misperceptions.
Training professionals (e.g., financial analysts, pilots) to recognize and correct for intuition failures in fat-tailed environments.
FROM THEORY TO EVERYDAY LIFE
In practice
Intuition about large deviations in Extremistan
Participants were asked to guess the average market capitalization of companies valued above $5 billion. Their intuitions were poor compared to similar questions about height or weight, revealing a systematic bias in understanding fat-tailed distributions.
Framing of airline crash risk
When told ‘one crash every thousand years’ (if flying once a year), 100% of participants would take the flight. When told ‘one in a thousand flights crash,’ only 70% would take it—even though the probability is identical.
A MOMENT TO REFLECT
Put it to work.
When you encounter a statistic about rare events (e.g., stock market crashes, startup success rates), consider whether the distribution is fat-tailed. How might your intuition be misleading?
Think of a recent decision involving risk. How was the risk framed? Would you have decided differently if the same probability were presented in a different format?
How does describing a risk as an average waiting time differ psychologically from describing the same risk per event? What assumptions are needed to compare the two?
CONTINUE THE CONVERSATION
Source texts
- The Black Swan The Impact of the Highly Improbable With a new section On Robustness and Fragility (Nassim Nicholas Taleb)