Review of G . Shafer and V . Vovk “ Probability and

This monograph reports a series of outstanding and entirely unexpected results by the authors, in part purely mathematical, and in part belonging to the branch of mathematical science that studies financial markets. It involves a new conception of probability, which the authors call “game-theoretic probability”, but I would prefer to call “market probability”. (Whenever a new scientific approach is created, the somewhat mystical essence of things is at stake, and this is why the name is important. My reasons for preferring “market probability” will become clear as we proceed.) At the base of this new approach lies not the assumption that some source of randomness like coin tossing exists, but only the assumption that one can bet money on the future course of events, as market speculators have done from time immemorial. There are two styles in scientific writing. One style, modern, moves the scientific novelty of the authors’ discoveries to the foreground. This style is flawed, because novelty is elusive, and in general there is nothing worse than starting a dispute over priority (the classical example—Leibniz and Newton). The other style, ancient, emphasizes continuity. In the Middle Ages it was thought to be in good taste to say first that, well, Hermes Trismegistus (a.k.a. the Egyptian god Thoth) and Albertus Magnus, as it turns out, had about the same opinions as the author about the matters under discussion. This is a very good style for a monograph, and it is the style followed by the authors of this book. Admittedly, they begin not from Hermes Trismegistus himself, but only from Pascal and Fermat, going from them to Mises and