This paper proposes a unified framework for optimization over two or more components (e.g., risk and time). We identify a common cause (the “monotonicity problem”) underlying many current debates in behavioral decision theory, concerning correlation preference in intertemporal choice, incentive compatibility of the random incentive system, hedging in ambiguity measurements, the judgment aggregation paradox, ex post versus ex ante fairness in welfare, and many others. Further, the monotonicity problem implies that a “middle ground” for single component optimization, used in virtually all behavioral theories, is not available for multi-component optimization. That leads to an unavoidable bifurcation dilemma, where one has to choose one of only two disjoint routes available. Stances taken in the above debates all amount to a choice of one of those two routes. We provide general techniques for properly choosing in this dilemma, thus clarifying and unifying many debates, and obtaining many generalizations and new insights for many fields. For instance, our analysis supports the validity of the random incentive system and of ambiguity measurements despite hedging, criticisms of monotonicity in the Anscombe-Aumann framework of ambiguity, ex post over ex ante fairness, and it favors particular framings over others in experiments.

This paper describes the history of prospect theory, focusing on risk, and gives suggestions for future research, focusing on ambiguity. In particular, this paper shows how the state of the art in these fields could only come about through inputs from both psychologists and economists and from their interactions.

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.

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: 14 Jan. 2026