Decision-Principles to Justify Carnap's Updating Method and to Suggest Corrections of Probability Judgments
This paper uses decision-theoretic principles to obtain new insights into the assessment and updating of probabilities. First, a new foundation of Bayesianism is given. It does not require infinite atomless uncertainties as did Savage's classical result, and can therefore be applied to any finite Bayesian network. It neither requires linear utility as did de Finetti's classical result, and therefore allows for the empirically and normatively desirable risk aversion. Finally, by identifying and fixing utility in an elementary manner, our result can readily be applied to identify methods of probability updating. Thus, a decision-theoretic foundation is given to the computationally efficient method of inductive reasoning developed by Rudolf Carnap. Finally, recent empirical findings on probability assessments are discussed. It leads to suggestions for correcting biases in probability assessments, and for an alternative to the Dempster-Shafer belief functions that avoids the reduction to degeneracy after multiple updatings.