Non-Bayesian Decision Theory: Beliefs and Desires as Reasons for ActionSpringer Science & Business Media, 2008 M06 6 - 170 pages 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 com- nitytosuchanextentthatalternative,non-Bayesianpositionsareseldomextensively 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 m- imise subjective expected utility, but contrary to what is claimed by Bayesians, ut- ity and subjective probability should not be de?ned 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 fu- tions 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 - cision 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. |
Contents
1 | |
Bayesian decision theory | 13 |
Choosing what to decide | 31 |
Indeterminate preferences | 61 |
6 | 95 |
8 | 125 |
Proofs | 143 |
Other editions - View all
Non-Bayesian Decision Theory: Beliefs and Desires as Reasons for Action Martin Peterson No preview available - 2008 |
Non-Bayesian Decision Theory: Beliefs and Desires as Reasons for Action Martin Peterson No preview available - 2010 |
Common terms and phrases
Allais paradox alternative acts applied Arguably argument Assume for reductio assumption axiomatisation Bayesian decision theory Bayesian theories beliefs and desires Chapter choice axiom choose claim concept Consider the following defined Definition denote Desideratum elements equally example expected utility principle false fatal outcome formal decision problem formal representation Furthermore Gamble Hence horse race lotteries ideal agents implies incomparable independence axiom indeterminate preferences indifferent intuition Lemma Luce maximising expected utility non-Bayesian non-ideal agent normative object permutability precautionary principle preference ordering preferences over uncertain principle of maximising probabilistic theory probability and utility probability function problem under certainty proof of Theorem proposed propositions reason revealed preference risk aversion rival representations satisfies Desiderata Savage's Section set of transformative strongly iterative subjective expected utility subjective probability subset Suppose sure-thing principle theorists trade-off principle transformative decision rules transformative rules u₁ uncertain prospects utility function л Є
Popular passages
Page 13 - The probability of any event is the ratio between the value at which an expectation depending on the happening of the event ought to be computed, and the value of the thing expected upon its happening...
Page 13 - If a person has an expectation depending on the happening of an event, the probability of the event is to the probability of its failure as his loss if it fails to his gain if it happens
Page 132 - ... the sense that the payoff depends only upon the state and not upon the act adopted. In other words, in the array representing problem 2, all entries in the same column are the same. If the decision maker knows only that he is playing problem 1 with probability p and problem 2 with probability 1 — p when he has to adopt an act, then he should adopt an act which is optimal for problem 1 , since problem 2, which enters with probability 1 — p, is irrelevant as far as his choice is concerned....
Page 13 - The aim of this chapter is to give an overview of the main TA methods and their applications, with sufficient references to provide reader access to more detailed information.
Page 65 - In words this means that if an individual selects batch one over batch two, he does not at the same time select two over one.
Page 130 - DDP) whose worst possible outcome is at least as good as the worst possible outcome of any other option (DDP).
Page 85 - M, if a >~ b, then there is a positive integer n such that (na oc) > (nb od), where na is defined inductively as la = a, (n + l)a = (ao no).