Which is more likely?

Why the longer story felt likelier

Every feminist bank teller is a bank teller. So "bank teller and feminist" can never be more likely than "bank teller". The same goes for every round: the long statement is the short one with one more thing that has to come true.

Amos Tversky and Daniel Kahneman gave the Linda story to 142 students at the University of British Columbia in the early 1980s. 85 in 100 said the feminist bank teller was more likely. The detail fits the story, so it makes Linda easier to picture. Our gut reads "easy to picture" as "likely". Each detail adds a little colour and takes away a little chance.

The same game in a trading room

Tversky and Kahneman then asked 115 people at an international forecasting conference in 1982, most of them professional analysts. One group rated the chance that the United States and the Soviet Union would break off relations the next year. Another group rated the same break, but after a Russian invasion of Poland. The second group gave the longer story more than three times the odds: 0.47% against 0.14%.

Market forecasts are built the same way. Prices surprise, so the central bank moves, so the market falls. Each "so" makes the story easier to believe and less likely to happen. A fund pitch works the same way: the doctorate, the models and the backtest make the story vivid, but the claim is still "beats the market next year", and every reason stacked on top is one more thing that has to hold.

Sources

1. Tversky and Kahneman, "Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment", Psychological Review 90 (1983), 293–315.
2. Tversky and Kahneman, "Judgment under uncertainty: heuristics and biases", Science 185 (1974), 1124–1131.