6 ideas
Under risk, all outcomes and probabilities are known, so statistical optimization works; under uncertainty, some options, consequences or probabilities are unknown, and optimizing on past data fails. Treating uncertain worlds such as markets, medicine and careers as if they were calculable risk produces an illusion of certainty and fragile decisions.
In uncertain environments with limited data, complex models overfit noise in the past, while simple rules that ignore information have lower variance and predict better out of sample. The 1/N rule, which spreads money equally across N assets, often matches or beats Markowitz mean-variance optimization because the parameters it would need to estimate are too unstable.
The same information given as a sensitivity, a false-positive rate and a base rate confuses most doctors. Innumeracy is largely a problem of representation, not a fixed cognitive defect.
A '50% risk reduction' can mean a change from 2 in 1,000 to 1 in 1,000, so relative risks inflate perceived benefits and harms while absolute risks and numbers-needed-to-treat show the real stakes. The 1995 UK pill scare reported a '100% increased' thrombosis risk, which was 1 extra case per 7,000 women, and it was followed by an estimated 13,000 additional abortions.
After September 11, many Americans avoided flying and drove instead. Gigerenzer estimates this caused about 1,600 extra road deaths in the following year, more than the number of passengers killed on the four hijacked planes. Fear of low-probability, high-casualty 'dread risks' leads people toward options that are more dangerous but feel familiar.
Doctors and managers often choose the second-best option that protects them from blame or lawsuits instead of the option that is best for the patient or the firm. Examples are ordering unnecessary scans and recommending cancer screening whose benefits they cannot quantify. The cause is an error-intolerant culture combined with statistical illiteracy, not individual malice.