Decision Principles to justify Carnap's Updating Method and to Suggest Corrections of Probability Judgments (Invited Talks)

TL;DR

This paper establishes a decision-theoretic foundation for Carnap's probability updating method, applicable to finite Bayesian networks, and discusses corrections for biases in probability assessments and alternatives to Dempster-Shafer belief functions.

Contribution

It provides a new, finite Bayesian foundation for Carnap's updating method, allowing for empirical risk aversion and bias correction in probability judgments.

Findings

Supports Carnap's method for finite Bayesian networks

Suggests bias correction techniques for probability assessments

Proposes an alternative to Dempster-Shafer belief functions

Abstract

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 r ntherefore allows FOR the empirically AND normatively desirable risk r naversion.Finally, BY identifying AND fixing utility IN an elementary r nmanner, our result can readily be applied TO identify methods OF r nprobability updating.Thus, a decision - theoretic foundation IS given r nto the computationally efficient method OF inductive reasoning r ndeveloped BY Rudolf Carnap.Finally, recent empirical findings ON r nprobability assessments are discussed.It leads TO suggestions FOR r ncorrecting biases IN probability assessments, AND FOR an alternative r nto the Dempster - Shafer belief functions that avoids the reduction TO r ndegeneracy after multiple updatings.r n