Rational Choice Using Imprecise Probabilities and Utilities (Elements in Decision Theory and Philosophy)

Description

An agent often does not have precise probabilities or utilities to guide resolution of a decision problem. I advance a principle of rationality for making decisions in such cases. To begin, I represent the doxastic and conative state of an agent with a set of pairs of a probability assignment and a utility assignment. Then I support a decision principle that allows any act that maximizes expected utility according to some pair of assignments in the set. Assuming that computation of an option's expected utility uses comprehensive possible outcomes that include the option's risk, no consideration supports a stricter requirement. Cover Title page Copyright page Rational Choice Using Imprecise Probabilities and Utilities Contents 1 Introduction 2 Imprecision 2.1 A Decision Model 2.2 Probability 2.3 Utility 2.4 Constructivism 2.5 Representing Imprecision 2.6 Measurement 2.7 Summary 3 Rational Imprecision 3.1 Sources and Consequences of Rational Imprecision 3.2 Dilation 4 Probabilism 4.1 Probabilism Defined 4.2 Types of Argument for Probabilism 4.3 Preliminaries 4.4 Necessary Conditions 4.5 Additivity 5 The Expected-Utility Principle 5.1 Expected Utility 5.2 Justifying the Expected-Utility Principle 6 Norms for Imprecise Attitudes 6.1 Imprecise Probabilities 6.2 Imprecise Utilities 6.3 Norms Given Imprecision 7 The Permissive Principle of Choice 8 Sequences of Choices 9 Choices in Games of Strategy 10 Conclusion References Acknowledgments