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actions Allais ambiguity apply approach asserts assign assume assumption Bayes Bayesian behavior Bernoulli proposition best guess betting probabilities Black Bruno de Finetti Chapter choose coherence consequences considered consistent corresponding criteria decision problems decision rule decision-making definite probability degrees of belief deliberated discussion ducats Economics Ellsberg example expected utility Finetti Foundations of Statistics gambles given Howard Raiffa hypotheses imply indifferent individual infer intuitive probabilities Jacob Marschak Journal judgments Koopman L. J. Savage logic lottery Luce and Raiffa measure minimax mixed strategies neo-Bayesian neo-Bernoullian Neumann-Morgenstern utilities notion numbers numerical probabilities offer opinions option outcomes pair pattern of choices Paul Samuelson payoffs personal probability possible prob probability distribution Ramsey rational Red ball relevant restricted Hurwicz criterion Risk Savage Axioms Savage postulates Savage's situations stake a prize Statistical Decision Subjective Probability Sure-Thing Principle Thing Principle three-color urn tion uncertainty urn problem utility axioms utility function vagueness violate