Wakker, Peter P. (2024) “A Criticism of Bernheim & Sprenger,” working paper.

ABSTRACT. 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.

Principi, Giulio , Peter P. Wakker, & Ruodu Wang (2023) “Antimonotonicity for Preference Axioms: The Natural Counterpart to Comonotonicity,” working paper.

ABSTRACT. Comonotonicity ("same variation") of random variables minimizes hedging possibilities and has been widely used in many fields. Comonotonic restrictions of traditional axioms have led to impactful inventions in decision models, including Gilboa and Schmeidler's ambiguity models. This paper investigates antimonotonicity ("opposite variation"), the natural counterpart to comonotonicity, minimizing leveraging possibilities. Surprisingly, antimonotonic restrictions of traditional axioms often do not give new models but, instead, give generalized axiomatizations of existing ones. We, thus, generalize: (a) classical axiomatizations of linear functionals through Cauchy's equation; (b) as-if-risk-neutral pricing through no-arbitrage; (c) subjective probabilities through bookmaking; (d) Anscombe Aumann expected utility; (e) risk aversion in Savage's subjective expected utility. In each case, our generalizations show where the most critical tests of classical axioms lie: in the antimonotonic cases (maximal hedges). We, finally, present cases where antimonotonic restrictions do weaken axioms and lead to new models, primarily for ambiguity aversion in nonexpected utility.

Baillon, Aurélien, Han Bleichrodt, Chen Li, & Peter P. Wakker (2023) “Source Theory: A Tractable and Positive Ambiguity Theory,” working paper.

ABSTRACT. This paper introduces source theory, a new theory for decision under ambiguity. It shows how probability weighting functions can be used to model ambiguity. It can do so in the Savage (& Gilboa) framework, and does not need complex two-stage gambles, multistage optimization principles, expected utility for risk (descriptively problematic), or any linear algebra. Still the mathematical analysis is simple, with intuitive preference axioms, tractable empirical implementations and calculations, and convenient graphical representations of ambiguity attitudes. It gives new ways to compare weighting functions, not between persons as is common, but within one person and between sources, giving Arrow-Pratt-like transformations “within” rather than “outside” the functions. Within-person between-sources comparisons are the main novelty of ambiguity over risk, first demonstrated by Ellsberg’s paradox.

Li, Chen, Kirsten I.M. Rohde, & Peter P. Wakker (2023) “The Deceptive Beauty of Monotonicity, and the Million-Dollar Question: Row-First or Column-First Aggregation?,” working paper.

ABSTRACT. 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.

Abdellaoui, Mohammed, Chen Li, Peter P. Wakker, & George Wu (2020) “A Defense of Prospect Theory in Bernheim & Sprenger’s Experiment,” working paper.

ABSTRACT. 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:** 11 July, 2024

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