Abstract
This paper introduces source theory, a new theory for decision under ambiguity. It shows how Savage’s subjective probabilities, with source-dependent nonlinear weighting functions applied to them, can be used to model Ellsberg’s ambiguity (unknown probabilities). It can do so in Savage’s framework of state-contingent assets, and does not need complex two-stage gambles, multistage optimization principles, expected utility for risk (descriptively problematic), or any linear algebra. Still the mathematical analysis is simple, with intuitive preference axioms, tractable calculations and prescriptive implementability, empirically realistic fittings and predictions, and convenient graphical representations of ambiguity attitudes. We provide new ways to compare weighting functions, not between persons as is common, but within one person and between sources. So-called p-matchers turn out to capture uncertainty attitudes well, giving Arrow-Pratt-like transformations, however, “within” rather than “outside” functions. Within-person-between-sources comparisons are the main novelty of ambiguity over risk, first demonstrated by Ellsberg’s paradox