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.

This book describes the classical axiomatic theories of decision under uncertainty, as well as critiques thereof and alternative theories.

Ⅰ Intuitive Definitions 1. Motivation Examples 2. Free Will and Determinsm 3. The Principle of Indifference 4. Relative Frequencies 5. Subjective Probabilities Ⅱ Behavioral Definitions 6. A Case Study 7. The Role of Theories 8. Von Neumann-Morgenstern's Theorem 9. De Finetti's Theorem 10. Savage's Theorem 11. The Definition of States 12. A Critique of Savage 13. Objectivity and Rationality 14. Ansocombe-Aumann's Theorem Ⅲ Alternative Behavioral Theories 15. Choquet Expected Utility 16. Prospect Theory 17. Maxmin Expected Utility Ⅳ Cognitive Origins 18. Case-Based Qualitative Beliefs 19. Frequentism Revisited 20. Future Research