Theory of Decision under Uncertainty [Hardcover]

This book describes the classical axiomatic theories of decision under uncertainty, as well as critiques thereof and alternative theories.This book describes classical axiomatic theories of decision under uncertainty, critiques thereof, and alternative theories. It discusses the meaning of probability, focusing on the behavioral definition of subjective probability by Savage's theorem. It also presents non-additive and multiple prior theories, as well as the case-based approach to the formation of beliefs.This book describes classical axiomatic theories of decision under uncertainty, critiques thereof, and alternative theories. It discusses the meaning of probability, focusing on the behavioral definition of subjective probability by Savage's theorem. It also presents non-additive and multiple prior theories, as well as the case-based approach to the formation of beliefs.This book describes the classical axiomatic theories of decision under uncertainty, as well as critiques thereof and alternative theories. It focuses on the meaning of probability, discussing some definitions and surveying their scope of applicability. The behavioral definition of subjective probability serves as a way to present the classical theories, culminating in Savage's theorem. The limitations of this result as a definition of probability lead to two directions  first, similar behavioral definitions of more general theories, such as non-additive probabilities and multiple priors, and second, cognitive derivations based on case-based techniques.1. Preface; 2. Motivating examples; 3. Free will and determinism; 4. The principle of indifference; 5. Relative frequencies; 6. Subjective probabilities; 7. A case study; 8. The role of theories; 9. Von Neumann and Morgenstern's theorem; 10. De Finetti's theorem; 11. Savage's theorem; 12. The definition of states; 13. A critique of Savage; 14. Objectivity and rationality; 15. Anscombe-Aumann's theorem; 16. Choquet expected utility; 17. Prospect theorylÃ(