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Willful Ignorance: The Mismeasure of Uncertainty by Herbert Weisberg

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CHAPTER 9 PROBABILITY AND REALITY

Uncertainty entails two different aspects, or dimensions. We can be uncertain either because we harbor positive doubt about something or because we interpret the situation to be ambiguous. Probability in the broadest sense relates to our uncertainty generally. However, in the face of substantial ambiguity, quantifying our full uncertainty may be difficult or impossible. Since Bernoulli's day, there have been just a few serious attempts to develop a calculus of uncertainty that accounts for potential ambiguity.

Several noted economists, starting with Keynes and Frank Knight, have called attention to the limitations of standard probabilistic models to deal with the uncertainties of economic systems. In the 1960s, Daniel Ellsberg (yes, that Daniel Ellsberg, for those of us old enough to remember the Pentagon Papers affair) raised a stir by describing a “paradox” that challenged standard economic theory. The accepted wisdom among economists was that individuals and companies were rational in the sense of attempting to optimize expected values, as defined by mathematical probability theory. Ellsberg argued that the ambiguity pertaining to a situation ought to be taken into account in decision-making.1

The latest in this tradition of highlighting the limits of probabilistic models is Nassim Nicholas Taleb, whose jeremiads have indeed proved prophetic in light of the financial collapse that began in 2007.2 Taleb credits the iconoclastic genius Benoit ...

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