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on Utility Models and Prospect Theory |
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Issue of 2025–08–25
seven papers chosen by |
| By: | Sebastian Geissel; Christoph Knochenhauer |
| Abstract: | We propose a new class of monetary risk measures capable of assessing financial and ESG risk. The construction of these risk measures is based on an extension of classical shortfall risk measures in which the loss function is replaced by a multi-attribute utility function. We present an extensive theoretical analysis of these risk measures, showing in particular how properties of the utility function translate into properties of the associated risk measure. We furthermore discuss how these multi-attribute risk measures can be used to compute minimum risk portfolios and show in a numerical study that accounting for ESG risk in optimal portfolio choice has a significant influence on the composition of portfolios. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.23496 |
| By: | Arthur Paul Pedersen; Samuel Allen Alexander |
| Abstract: | We advance a general theory of coherent preference that surrenders restrictions embodied in orthodox doctrine. This theory enjoys the property that any preference system admits extension to a complete system of preferences, provided it satisfies a certain coherence requirement analogous to the one de Finetti advanced for his foundations of probability. Unlike de Finetti's theory, the one we set forth requires neither transitivity nor Archimedeanness nor boundedness nor continuity of preference. This theory also enjoys the property that any complete preference system meeting the standard of coherence can be represented by utility in an ordered field extension of the reals. Representability by utility is a corollary of this paper's central result, which at once extends H\"older's Theorem and strengthens Hahn's Embedding Theorem. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.00294 |
| By: | Michael Greinecker; Michael Nielsen |
| Abstract: | There exists a preference relation on infinite utility streams that does not discriminate between different periods, satisfies the Pareto criterion, and so that almost all pairs of utility streams are strictly comparable. Such a preference relation provides a counterexample to a claim in [Zame, William R. ``Can intergenerational equity be operationalized?'' Theoretical Economics 2.2 (2007): 187-202.] |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.20567 |
| By: | Behrooz Moosavi Ramezanzadeh |
| Abstract: | In this paper, I propose a new framework for representing multidimensional incomplete preferences through zonotope-valued utilities, addressing the shortcomings of traditional scalar and vector-based models in decision theory. Traditional approaches assign single numerical values to alternatives, failing to capture the complexity of preferences where alternatives remainmain incomparable due to conflicting criteria across multiple dimensions. Our method maps each alternative to a zonotope, a convex geometric object in \(\mathbb{R}^m\) formed by Minkowski sums of intervals, which encapsulates the multidimensional structure of preferences with mathematical rigor. The set-valued nature of these payoffs stems from multiple sources, including non-probabilistic uncertainty, such as imprecise utility evaluation due to incomplete information about criteria weights, and probabilistic uncertainty arising from stochastic decision environments. By decomposing preference relations into interval orders and utilizing an extended set difference operator, we establish a rigorous axiomatization that defines preference as one alternative's zonotope differing from another's within the non-negative orthant of \(\mathbb{R}^m\). This framework generalizes existing representations and provides a visually intuitive and theoretically robust tool for modeling trade-offs among each dimension, while preferences are incomparable. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.05844 |
| By: | Yiling Chen; Tao Lin; Wei Tang; Jamie Tucker-Foltz |
| Abstract: | The optimal signaling schemes in information design (Bayesian persuasion) problems often involve non-explainable randomization or disconnected partitions of state space, which are too intricate to be audited or communicated. We propose explainable information design in the context of information design with a continuous state space, restricting the information designer to use $K$-partitional signaling schemes defined by deterministic and monotone partitions of the state space, where a unique signal is sent for all states in each part. We first prove that the price of explainability (PoE) -- the ratio between the performances of the optimal explainable signaling scheme and unrestricted signaling scheme -- is exactly $1/2$ in the worst case, meaning that partitional signaling schemes are never worse than arbitrary signaling schemes by a factor of 2. We then study the complexity of computing optimal explainable signaling schemes. We show that the exact optimization problem is NP-hard in general. But for Lipschitz utility functions, an $\varepsilon$-approximately optimal explainable signaling scheme can be computed in polynomial time. And for piecewise constant utility functions, we provide an efficient algorithm to find an explainable signaling scheme that provides a $1/2$ approximation to the optimal unrestricted signaling scheme, which matches the worst-case PoE bound. A technical tool we develop is a conversion from any optimal signaling scheme (which satisfies a bi-pooling property) to a partitional signaling scheme that achieves $1/2$ fraction of the expected utility of the former. We use this tool in the proofs of both our PoE result and algorithmic result. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.14196 |
| By: | Michael Keinprecht (Department of Economics, WU Vienna University of Economics and Business) |
| Abstract: | The growing inequalities around the world are becoming increasingly alarming making redistribution more relevant than ever. One reason why people may oppose redistribution is third party loss aversion. In a pre-registered online experiment with a within-subjects design, I show that redistribution decisions by third parties are affected by loss aversion. Overall, spectators are 7%-points less likely to redistribute from a status quo to an alternative if the alternative entails a loss for one person, even if inequality aversion, maximin preferences and efficiency concerns favor the alternative. This effect is stronger the higher the loss is compared to the gain and the higher the individual loss aversion of the spectator. The key contribution of the paper is to disentangle third party loss aversion from pure status quo bias, rank reversal aversion and other distributional preferences in multiple loss scenarios and to link it to individual loss aversion. |
| Keywords: | Third party loss aversion, loss aversion, redistribution, spectators, fairness |
| JEL: | D91 D63 |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:wiw:wiwwuw:wuwp382 |
| By: | Jugal Garg; Yixin Tao; L\'aszl\'o A. V\'egh |
| Abstract: | The Probabilistic Serial (PS) mechanism -- also known as the simultaneous eating algorithm -- is a canonical solution for the assignment problem under ordinal preferences. It guarantees envy-freeness and ordinal efficiency in the resulting random assignment. However, under cardinal preferences, its efficiency may degrade significantly: it is known that PS may yield allocations that are $\Omega(\ln{n})$-worse than Pareto optimal, but whether this bound is tight remained an open question. Our first result resolves this question by showing that the PS mechanism guarantees $(\ln(n)+2)$-approximate Pareto efficiency, even in the more general submodular setting introduced by Fujishige, Sano, and Zhan (ACM TEAC 2018). This is established by showing that, although the PS mechanism may incur a loss of up to $O(\sqrt{n})$ in utilitarian social welfare, it still achieves a $(\ln{n}+2)$-approximation to the maximum Nash welfare. In addition, we present a polynomial-time algorithm that computes an allocation which is envy-free and $e^{1/e}$-approximately Pareto-efficient, answering an open question posed by Tr\"obst and Vazirani (EC 2024). The PS mechanism also applies to the allocation of chores instead of goods. We prove that it guarantees an $n$-approximately Pareto-efficient allocation in this setting, and that this bound is asymptotically tight. This result provides the first known approximation guarantee for computing a fair and efficient allocation in the assignment problem with chores under cardinal preferences. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.03359 |