Reports that say that something hasn’t happened are always interesting to me, because as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns—the ones we don’t know we don’t know. And if one looks throughout the history of our country and other free countries, it is the latter category that tend to be the difficult ones.
Donald Rumsfeld (U.S. Department of Defense, 12 February 2002)
Abstract
The concepts of risk and uncertainty are rather subtle, and so are their applicability to the social sciences. By reviewing the historically significant example of the St. Petersburg Paradox, this note suggests that when mathematical models of rationality and intuitions about rationality conflict, sometimes the former must be bent to fit the latter. This line of reasoning is all the more relevant when confronting the kind of uncertainty which many refer to as “ambiguity”.
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Notes
This might surprise those who have some familiarity with measure-theoretic probability. In this abstract presentation, intimately connected with Kolmogorov’s axiomatisation, probability is defined as a normalised and additive measure on a probability space. Since this is built on the \(\sigma\)-algebra generated by a given set, the additivity of the measure is taken, without much hesitation, as countable additivity. De Finetti rejected the general adequacy of this assumption, which he saw only justified by mathematical convenience, and considered to be inapplicable in many practical situations. In particular, he compared the ad hoc hypothesis of identifying the sample space with a \(\sigma\)-algebra to the Procrustean bed. The “Critical Appendix” of the second volume of [4] devotes ample space to this issue.
Ellsberg is known outside academia for his role in triggering the Watergate scandal, through the dissemination of confidential documents. Recently Edward Snowden has pointed him out as a role model.
\(r_A\) is an abbreviation for “A red marble is extracted from urn A”, and so on.
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Hosni, H. R for Risk. Lett Mat Int 5, 173–178 (2017). https://doi.org/10.1007/s40329-017-0179-z
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DOI: https://doi.org/10.1007/s40329-017-0179-z