Nonbayesian Decision Theory

  • Peterson M
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Abstract

For quite some time, philosophers, economists, and statisticians have endorsed a view on rational choice known as Bayesianism. The work on this book has grown out of a feeling that the Bayesian view has come to dominate the academic community to such an extent that alternative, non-Bayesian positions are seldom extensively researched. Needless to say, I think this is a pity. Non-Bayesian positions deserve to be examined with much greater care, and the present work is an attempt to defend what I believe to be a coherent and reasonably detailed non-Bayesian account of decision theory. The main thesis I defend can be summarised as follows. Rational agents maximise subjective expected utility, but contrary to what is claimed by Bayesians, utility and subjective probability should not be defined in terms of preferences over uncertain prospects. On the contrary, rational decision makers need only consider preferences over certain outcomes. It will be shown that utility and probability functions derived in a non-Bayesian manner can be used for generating preferences over uncertain prospects, that support the principle of maximising subjective expected utility. To some extent, this non-Bayesian view gives an account of what modern decision theory could have been like, had decision theorists not entered the Bayesian path discovered by Ramsey, de Finetti, Savage, and others. I will not discuss all previous non-Bayesian positions presented in the literature. Some demarcation lines between alternative non-Bayesian positions will simply be taken for granted. Most notably, I assume that some version of the Humean beliefdesire model of action is correct. Decision theories that seek to derive normative conclusions from other entities than beliefs and desires (such as objective frequencies or propensities) will hardly be discussed at all. By sticking to the traditional belief-desire model of action, I hope to retain as much as possible of what I think are the good features of the Bayesian approach, without being committed to accepting the less attractive parts. The present work is mainly concerned with philosophical issues in decision theory. Although a number of technical results are presented, the focus is set on conceptual and normative problems. All proofs appear in the appendix. Only the most elementary kinds of decision problems are considered, that is, single decisions taken v vi Preface by a single agent at a given point in time. More complicated decisions problems inevitably require a more complex technical apparatus, but the philosophical significance of those problems seldom stand in proportion to the technical apparatus required for handling them. * * * The opportunity to write this book arose when I accepted a research position in the Department of History and Philosophy of Science at the University of Cambridge. I wish to thank all my colleagues for their support and for creating such a stimulating research atmosphere in the department. The book is, however, based on a number of articles I have written over the past five years while working at the Royal Institute of Technology in Stockholm and at Lulea University of Technology, so I am also deeply indebted to my colleges there. In particular, I would like to thank Sven Ove Hansson for comments and helpful criticism of nearly all views and arguments put forward in this book. Without his ability to quickly and precisely identify the weak part of an argument, this book could never have been completed. I would also like to thank Nicholas Espinoza for stimulating discussions on indeterminate preferences. A large number of people have given invaluable comments on individual chapters or the papers on which they are based. In particular, I would like to thank Barbro Bj¨orkman, Anna Bjurman, Sven Danielsson, John Cantwell, Johan Gustafsson, Stephen John, Peter Kesting, Karsten Klint Jensen, Duncan Luce, Wlodek Rabionowicz, Per Sandin, Tor Sandqvist, Nils-Eric Sahlin, and Teddy Seidenfeld. My work on this project has been partially funded by a generous grant from the Swedish Rescue Services Agency. Chapters 1, 2, 5 and 6 are based on previously unpublished material. Chapter 3 is based on, but not identical to, Peterson (2003a), (2003b), and (2004a) and Peterson and Hansson (2004). Most of Chapter 4 is taken from Peterson (2006a) and Espinoza and Peterson (2006). I wish to thank Espinoza and Hansson for allowing me to include material from our joint papers. The formal results in Chapter 7 originally appeared in Peterson (2002a) and (2004b). Chapter 8 is based on Peterson (2002b), (2006b), and (2006c). I thank the editors of the journals in which the papers appeared for letting me reproduce substantial sections of them here.

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APA

Peterson, M. (2008). Nonbayesian Decision Theory. Nonbayesian Decision Theory. Springer Netherlands. https://doi.org/10.1007/978-1-4020-8699-1

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