Keeney & Raiffa’s (1976) multiattribute utility aggregates U(X1,…,Xn). Here Xj can refer to persons (welfare), timepoints (time preference), events (decision under uncertainty), commodities (consumer theory), etc. In applications one often has to aggregate over two or more kinds of attributes: risk & time, persons & commodities, etc. In classical models with complete separability the order of aggregation then does not matter. This gives our first result: the prettiest axiomatization of discounted expected utility you ever saw. Paradox 1: this is too simple to be true?
Modern behavioral generalizations relax complete separability (= sure-thing principle = time separability etc.) but maintain weak separability (= stochastic dominance = Pareto optimality etc.). Paradox 2: for two or more kinds of attributes this is just impossible.
A century-old forgotten theorem from macro-economics resolves our two modern paradoxes: Nataf (1948). He provided diagnoses and remedies for many ongoing debates, on ex-ante/ex-post fairness, incentive compatibility of random incentives, hedging in ambiguity measurements, equity in Harsanyi’s veil of ignorance, monotonicity in Anscombe-Aumann’s framework, etc. They all amount to the same million-$ question: “row-first or column-first aggregation?” Nataf resolved!
CO-AUTHORS: Chen Li & Kirsten Rohde