My question: How did Kahneman arrive at the 60% number in the last sentence ("60% of the pairs")?
From Daniel Kahneman, Thinking Fast and Slow (Chapter 19, Illusion of Understanding):
Update: from your answers, it appears that the number should have actually been 65%, so it was wrong in the book.
A very generous estimate of the correlation between the success of the firm and the quality of its CEO might be as high as .30, indicating 30% overlap. To appreciate the significance of this number, consider the following question:
Suppose you consider many pairs of firms. The two firms in each pair are generally similar, but the CEO of one of them is better than the other. How often will you find that the firm with the stronger CEO is the more successful of the two?
In a well-ordered and predictable world, the correlation would be perfect, and the stronger CEO would be found to lead the more successful firm in 100% of the pairs. If the relative success of similar firms was determined entirely by factors that the CEO does not control (call them luck, if you wish), you would find the more successful firm led by the weaker CEO 50% of the time. A correlation of .30 implies that you would find the stronger CEO leading the stronger firm in about 60% of the pairs—an improvement of a mere 10 percentage points over random guessing, hardly grist for the hero worship of CEOs we so often witness.