Diaconis & Skyrms, Ten Great Ideas about Chance

Ten Great Ideas about Chance by Persi Diaconis and Brian Skyrms (Princeton University Press, 2018) grew out of a course that the authors team-taught at Stanford, which had as a prerequisite one undergraduate course in probability or statistics. It is, as the authors describe it, “a history book, a probability book, and a philosophy book.” In writing about the ten great ideas—measurement, judgment, psychology, frequency, mathematics, inverse inference, unification, algorithmic randomness, physical chance, and induction—they proceed more or less chronologically within each topic, starting with Cardano and Galileo and the notion that chance can be measured.

The second idea, that judgments can be measured and that coherent judgments are probabilities, is the one most obviously relevant to finance. Here, as clearly seen in prediction markets, “the probability of A is just the expected value of a wager that pays off 1 if A and 0 if not. If you pay a price equal to P(a) for such a wager, you believe that you have traded equals for equals. For a lesser price you would prefer to buy the wager; for a greater price you would prefer not to buy it. So the balance point, where you are indifferent between buying the wager or not, measures your judgmental probability for A.” In this idealized model “an individual acts like a bookie—or perhaps like a derivatives trader—and buys and sells bets. … She buys fair or favorable bets and sells fair or disadvantageous bets, doing business with all comers. A Dutch book can be made against her if there is some finite set of transactions acceptable to her such that she suffers a net loss in every possible situation. We will say that she is coherent if she is not susceptible to a Dutch book.” Over time, given a change in evidence, she will revise her probabilities using the “unique coherent rule,” Bayesian updating. “Any other rule leaves one open to a Dutch book against the rule—a Dutch book across time, a diachronic Dutch book.” Market makers, beware the diachronic Dutch book!

Ten Great Ideas about Chance takes intrinsically difficult notions that great minds struggled with over the centuries (I personally would put induction at the top of the list) and makes them accessible to anyone with a basic grasp of probability.