Preface

What is rationality? What is the solution to the problem of scientific induction? I don’t think it reasonable to expect sharp answers to such questions. One might as well ask for precise definitions of life or consciousness. But we can still try to push forward the frontier of rational decision theory beyond the Bayesian paradigm that represents the current orthodoxy.

Many people see no need for such an effort. They think that Bayesianism already provides the answers to all questions that might be asked. I believe that Bayesians of this stamp fail to understand that their theory applies only in what Jimmie Savage (1951) called a small world in his famous Foundations of Statistics. But the world of scientific inquiry is large—so much so that scientists of the future will look back with incredulity at a period in intellectual history when it was possible be taken seriously when claiming that Bayesian updating is the solution to the problem of scientific induction.

Jack Good once claimed to identify 46,656 different kinds of Bayesians. My first priority is therefore to clarify what I think should be regarded as the orthodoxy on Bayesian decision theory—the set of foundational assumptions that offer the fewest hostages to fortune. This takes up most of the book, since I take time out to review various aspects of probability theory along the way. My reason for spending so much time offering an ultra-orthodox review of standard decision theory is that I feel the need to deny numerous misapprehensions (both positive and negative) about what the theory really says—or what I think it ought to say—before getting on to my own attempt to extend a version of Bayesian decision theory to worlds larger than those considered by Savage (chapter 9).

I don’t for one moment imagine that my extension of Bayesian decision theory comes anywhere near solving the problem of scientific induction, but I do think my approach will sometimes be found useful in applications. For example, my theory allows the mixed strategies of game theory to be extended to what I call muddled strategies (much as pure strategies were extended to mixed strategies by the creators of the theory).

What is the audience for this book? I hope that it will be read not just by the economics community from which I come myself, but also by statisticians and philosophers. If it only succeeds in bridging some of the gaps between these three communities, it will have been worthwhile. However, those seeking a survey of all recent research will need to look for a much bigger book than this. I have tried to include references to literatures that lie outside its scope, but I never stray very far from my own take on the issues. This streamlined approach means that the book may appeal to students who want to learn a little decision theory without being overwhelmed by masses of heavy mathematics or erudite philosophical reasoning, as well as to researchers in the foundations of decision theory.

Sections in which I haven’t succeeded in keeping the mathematics at a low level, or where the going gets tough for some other reason, are indicated with an arrow pointing downward in the margin. When such an arrow appears, you may wish to skip to the next full section.

Finally, I want to acknowledge the debt that everyone working on decision theory owes to Duncan Luce and Howard Raiffa, whose Games and Decisions remains a source of inspiration more than fifty years after it was written. I also want to acknowledge the personal debt I owe to Francesco Giovannoni, Larry Samuelson, Jack Stecher, Peter Wakker, and Zibo Xu for their many helpful comments on the first draft of this book.