Source Theory: A Tractable and Positive Ambiguity Theory

Abstract

This paper introduces source theory, a new theory for decision under ambiguity (unknown probabilities). It shows how Savage’s subjective probabilities, with source-dependent 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.This paper was accepted by Manel Baucells, behavioral economics and decision analysis.Funding: H. Bleichrodt acknowledges financial support from the Spanish Ministry of Science, Innovation and Universities [Project PID2022-142356NB-I00 financed by Grant MICIU/AEI/10.13039/501100011033 and by FEDER] and from the Consellería de Innovación Universidades, Ciencia y Sociedad Digital de la Generalitat Valenciana [Grant Prometeo/2021/073].Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2023.03307 .