Your uncertainty, your probability, your decision

In 1973, in his foreword for de Finetti’s book “Theory of Probability, A critical introductory treatment”, Professor Lindley wrote that “(. . . ) every now and again delightful ideas spring to view; the idea that we shall all be Bayesian by 2020 (. . . ). But, as I said, this is a book about life” (Finetti, 1974, ix). The two strains of idea, that we should all use probability to approach uncertainty, and that research that has been done on this topic in the twentieth century has the potential to “(. . . ) affect the activities of many people and ultimately all of us” (Lindley, 2006, xiv), is also central to his current book “Understanding Uncertainty” Lindley (2006). Thirty years ago, the year 2020 may have appeared far ahead in the future, but today we can see 2020 showing up at the horizon. So, the question is, where do we stand with our understanding of probability and uncertainty? This question is one of concern for Professor Lindley, as he writes: “(. . . ) I made a discovery. There were people out there, like politicians, journalists, lawyers, and managers, who were, in my opinion, making mistakes; mistakes that could have been avoided had they known the answers to the questions pondered in my ivory tower” (Lindley, 2006, xiv). These words were not intended to be critical. Rather, they express the view that it is up to academics to communicate and “(. . . ) explain in terms that motivated, lay persons can understand, some of the discoveries made in academe, and why they are of importance and value to them, so that they might use the results in their lives” (Lindley, 2006, xiv). The author makes every effort to achieve this goal. The book is written with exceptional clarity, and the arguments are presented in a way that directly addresses the reader “(. . . ) conveniently called ‘you’ (. . . )” (Lindley, 2006, 1, 2). The “you” is a stylistic choice that places the author directly in line with other influential authors who hold the so-called subjectivistic interpretation of probability theory1. This reinforces the author’s intention to place the readers in the center of the argument: in fact, he notes “[t]his book is for you, whoever you are” (Lindley, 2006, 2). This intention stems directly from one of the book’smainmessages: that probability is inevitable. The book is not primarily about the calculus of probability (indeed, mathematics are kept to a strict minimum); it is about the very meaning of probability— how probability ought to be understood in order to deal with uncertainty. On this latter point, Professor Lindley is uncompromisingly clear and, at the same time, draws yet another parallel to de Finetti’s two-volume work on probability Finetti (1974, 1975): probability is the measure for strength of belief, but probability does not exist in the sense of being a property of the outside world. On a first view, specialized readers of this Frontiers journal may find this proposition all too general, or even inappropriate. But it is not, for several reasons.