The Bayes mind : from the St. Petersburg paradox to the New York Stock Exchange
The thesis is an exposition and defence of Bayesianism as the preferred methodology of reasoning under uncertainty in social contexts. Chapter 1 gives a general outline of the foundations of probabilistic reasoning, as well as a critical exposition of the main non- Bayesian approaches to probability. After a brief discussion of the formal theory of probability, the thesis examines some non-Bayesian interpretations of the probability calculus, and purports to show their insufficiency. Chapter 2 provides an outline of the Bayesian (subjectivist) research programme. The opening sections of the chapter contain a historical overview of Bayesianism, as well as a defence of the assumptions on which it rests. The concluding sections then examine some of the key issues of contention between Bayesians and their critics, such as the nature of empirical confirmation and learning from experience. Since it is the author's contention that any sound methodology should be applicable, if necessary with modifications, across a wide range of contexts, the concluding two chapters make a Bayesian case first in a theoretical, and next in a practical setting. In particular, Chapter 3 discusses the issue of simplicity as a theoretical virtue. It argues that a Bayesian can coherently and successfully account for the structural or formal simplicity of the hypotheses that he entertains, by using his assignments of subjective prior probabilities in the process known as 'Bayesian Conditionalisation'. It also argues that some of the recent criticisms voiced against the Bayesian account of simplicity are inconsistent and/or question-begging. The process known in statistics as 'curve-fitting' provides the material for the discussion. Finally, Chapter 4 presents an extension of the Bayesian methodology to practical decision-making, using the context of investing activity. It purports to show that the most convincing picture of economic agents' investing behaviour is best explained by assuming that in the course of such behaviour, the agents maximise their expected utility, as is stipulated by the Bayesian decision theory. The argument revolves around the 'Efficient Markets Hypothesis' in the theory of finance, and the conclusion hinges both on the empirical adequacy of the various versions of this hypothesis and on its behavioural underpinnings. The thesis contains two appendices, intended to illustrate certain points made in the main body. The first appendix is a critical appraisal of a popular non-Bayesian account of causal inference in statistical contexts, with a bearing on the discussion in Chapter 3, while the second appendix provides a real-life illustration of some of the issues raised in Chapter 4. The overall structure of the thesis is intended to show how, from highly plausible assumptions, one can derive a powerful theory of reasoning under uncertainty that faithfully and uniformly represents both the theoretical and the practical concerns of the human mind.