Episode #018 - Probability and Judgment: Why We Get Risk Wrong

Here is a medical test scenario. A disease affects one in a thousand people. There is a test that is ninety-nine percent accurate. You take the test. It comes back positive. What is the probability that you actually have the disease?

Most people say: ninety-nine percent.

The actual answer is just under nine percent.

If that number seems impossible — if you want to go back and check the problem — that reaction is exactly what this episode is about. Our intuitions about probability are not just slightly off. They are systematically, predictably, and consequentially wrong in ways that affect our medical decisions, our legal judgments, our financial choices, and our assessment of risk in nearly every domain of life.

Shawn and Claire cover what probability actually is, why we get it so reliably wrong, and what a more calibrated relationship to uncertainty would look like. They walk through Bayes' theorem and why the prior probability you hold before seeing evidence matters as much as the accuracy of the test itself. They cover the gambler's fallacy, base rate neglect, the availability heuristic as a distorter of risk perception, and the prosecutor's fallacy — the confusion between the probability of evidence given innocence and the probability of innocence given evidence, a distinction that has sent innocent people to prison.

The episode also takes on Pascal's Wager — the seventeenth-century argument that you should bet on God's existence because the expected value of doing so is infinite — and explains both why it is philosophically interesting and where it breaks down.

The deeper question throughout is what honest belief looks like. Calibration — holding beliefs at the confidence level the evidence actually supports — is one of the most demanding intellectual virtues there is. This episode is about why it matters and why it is so hard.

Shawn and Claire together. No prior mathematics required.

SHOW NOTES

Primary Sources

• Bayes, T., & Price, R. (1763). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London, 53, 370–418.
• Pascal, B. (1995). Pensées (A. J. Krailsheimer, Trans., rev. ed.). Penguin Classics. (Original work published 1670)
• Kahneman, D. (2011). Thinking, Fast and Slow. Farrar, Straus and Giroux.

Works Referenced in This Episode

• Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185(4157), 1124–1131.
• Gigerenzer, G. (2002). Calculated Risks: How to Know When Numbers Deceive You. Simon & Schuster.
• Thompson, W. C., & Schumann, E. L. (1987). Interpretation of statistical evidence in criminal trials: The prosecutor's fallacy and the defense attorney's fallacy. Law and Human Behavior, 11(3), 167–187.

Accessible Starting Points

• McGrayne, S. B. (2011). The Theory That Would Not Die. Yale University Press.
• Silver, N. (2012). The Signal and the Noise. Penguin Press.
• Mlodinow, L. (2008). The Drunkard's Walk. Pantheon.

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