This paper examines optimal risk sharing for empirically realistic risk attitudes, providing results on Pareto optimality, competitive equilibria, utility frontiers, and the first and second theorems of welfare. Empirical studies suggest, contrary to classical assumptions, that risk seeking is prevalent in particular subdomains, and even is the majority finding for losses, underlying for instance the disposition effect. We first analyze cases of expected utility agents, some of who may be risk seeking. Yet more empirical realism is obtained by allowing agents to be risk averse in some subdomains but risk seeking in others, which requires generalizing expected utility. Here we provide first results, pleading for more future research. Our main new tool for analyzing generalized risk attitudes is a counter-monotonic improvement theorem.
This comment shows that Oprea’s (2024) findings do not falsify, but corroborate, probability weighting and loss aversion, contrary to his claims. Complexity does not replace them, but is an important factor supporting and explaining them. Oprea’s contribution lies in his ingenious stimuli. They reveal irrationalities in risky preferences, general perceptual principles underlying them, and the importance of biases for economics, more convincingly than done before.
This paper proposes a unified framework for optimization over two or more components (risk/time; risk/welfare; etc). Using a century-old theorem on macro-micro aggregation, we show that many existing debates, on incentive compatibility of random incentives, hedging confoundings in ambiguity measurements, equity in Harsanyi’s veil of ignorance, multiattribute risk aversion, and many others, all concern the same bifurcation question “row-first or column-first aggregation?” For a single component, behavioral models typically relax separability while maintaining monotonicity. For two or more components, this is, surprisingly, no longer possible. Then at least one monotonicity must be violated. The question of which one is equivalent to the above bifurcation question. Our analysis clarifies many ongoing debates in many fields, including the aforementioned ones. We provide diagnoses and techniques for overcoming undesirable violations of monotonicity. A mathematical online appendix shows how our framework can be used theoretically to generalize many well-known preference axiomatizations.
To avoid admitting mistakes in their preceding works pointed out by Wakker (2023), Bernheim & Sprenger (2023) use fallacies and miscitations, most of them easy to see through.
Bernheim and Sprenger (2020, Econometrica) presented experimental evidence aimed to falsify rank dependence (and, thus, prospect theory). We argue that their experiment captured heuristics and not preferences. The same tests, but with procedures that avoid heuristics, have been done before, and they confirm rank dependence. Many other violations of rank dependence have been published before. Bernheim and Sprenger recommend rank-independent probability weighting with complexity aversion, but this is theoretically unsound and empirically invalid. In view of its many positive results, prospect theory with rank dependence remains the best model of probability weighting and the existing model that works best for applied economics.
Last updated: 22 July 2025