This paper introduces source theory, a new theory for decision under ambiguity. It shows how probability weighting functions can be used to model ambiguity. It can do so in the Savage (& Gilboa) framework, 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 empirical implementations and calculations, and convenient graphical representations of ambiguity attitudes. It gives new ways to compare weighting functions, not between persons as is common, but within one person and between sources, giving Arrow-Pratt-like transformations “within” rather than “outside” the functions. Within-person between-sources comparisons are themain novelty of ambiguity over risk, first demonstrated by Ellsberg’s paradox.
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