Alternate Theories of Belief and the Implications for Incoherence, Reconciliation, and Sensitivity Analysis
DECISION SCIENCE CONSORTIUM INC FALLS CHURCH VA
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In this paper we examine various theories of belief alternate to subjective probability. Initially, we examine the role of normative theories of decision making and belief, distinguishing carefully between the terms normative and prescriptive. We conclude that the decision analysis paradigm is compelling normatively, but not prescriptively. We discuss inconsistency with the decision analysis axioms, and define incoherence as the potential for forming inconsistent judgments. We propose that decision analysis is a means for reducing incoherence. We further argue that sensitivity analysis is used as a means for countering incoherence, and that many extended theories of belief may be viewed as formal justifications for sensitivity analysis. We examine theories of upper and lower probabilities from this perspective, together with second- order and fuzzy probabilities. We examine in detail the theory of Belief Functions of Shafer 1976, one form of upper and lower probability. We look at various measures of belief which have only ordinal properties including inductive probabilities Cohen, 1977 and possibility theory arising from fuzzy sets. Our overall conclusion is that the present-day practice of decision analysis is adequate, but that it might be refined, and sensitivity analysis improved, if note were taken of these alternate theories of belief.
- Statistics and Probability