Source Theory: A Tractable and Positive Ambiguity Theory

This paper introduces source theory, a new theory for decision under ambiguity (unknown probabilities). It shows how Savage's subjective probabilities, with sourcedependent nonlinear weighting functions, can model Ellsberg's ambiguity. It can do so in Savage's framework of state-contingent assets, permits nonexpected utility for risk, and avoids multistage complications. It is tractable, shows ambiguity attitudes through simple graphs, is empirically realistic, and can be used prescriptively. We provide a new tool to analyze weighting functions: pmatchers. They give Arrow-Pratt-like transformations but operate "within" rather than "outside" functions. We further show that ambiguity perception and inverse S probability weighting, seemingly unrelated concepts, are two sides of the same "insensitivity" coin.