Chapter 4: From Cournot’s Principle to Market Efficiency
1 Glenn Shafer Introduction Cournot’s principle says that an event of small or zero probability singled out in advance will not happen. From the turn of the twentieth century through the 1950s, many mathematicians, including Chuprov, Borel, Fréchet, Lévy and Kolmogorov, saw this principle as fundamental to the application and meaning of probability.2 In their view, a probability model gains empirical content only when it rules out an event by assigning it small or zero probability. In the 1960s, when probability theory was gaining in importance in economics, and especially finance, Cournot’s principle was no longer so widely accepted. In fact, the principle had almost disappeared with those who had espoused it in the first half of the twentieth century. In this chapter, I argue that its disappearance entailed a loss of clarity in the interpretation of probability, which accounts in part for the high level of confusion in initial formulations of the efficient-markets hypothesis. The game-theoretic framework for probability (Shafer and Vovk, 2001) revives Cournot’s principle in a form directly relevant to markets. In this framework, Cournot’s principle is equivalent to saying that a strategy for placing bets without risking bankruptcy will not multiply the bettor’s capital by a large or infinite factor. It can therefore be applied directly to strategies for exploiting market prices without assuming the existence of meaningful probability distributions related to these prices. The claim that an investor cannot make a lot of money using public information is part of the efficient-markets hypothesis...
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