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In computational social choice, the distortion of a voting rule quantifies the degree to which the rule overcomes limited preference information to select a socially desirable outcome. This concept has been investigated extensively, but…

Computer Science and Game Theory · Computer Science 2023-12-11 Yannai A. Gonczarowski , Gregory Kehne , Ariel D. Procaccia , Ben Schiffer , Shirley Zhang

This paper studies decision problems where the decision maker's choice of action affects the probability distribution of a payoff relevant random variable. We establish sufficient conditions for the existence of an expected utility…

Theoretical Economics · Economics 2026-05-29 Ayush Gupta

Classic optimal transport theory is formulated through minimizing the expected transport cost between two given distributions. We propose the framework of distorted optimal transport by minimizing a distorted expected cost, which is the…

Optimization and Control · Mathematics 2025-05-20 Haiyan Liu , Bin Wang , Ruodu Wang , Sheng Chao Zhuang

We consider an agent interacting with an unknown environment. The environment is a function which maps natural numbers to natural numbers; the agent's set of hypotheses about the environment contains all such functions which are computable…

Artificial Intelligence · Computer Science 2007-12-31 Peter de Blanc

In this note, we study the utility maximization problem on the terminal wealth under proportional transaction costs and bounded random endowment. In particular, we restrict ourselves to the num\'eraire-based model and work with utility…

Mathematical Finance · Quantitative Finance 2016-02-05 Lingqi Gu , Yiqing Lin , Junjian Yang

In a consideration set model, an individual maximizes utility among the considered alternatives. I relate a consideration set additive random utility model to classic discrete choice and the extended additive random utility model, in which…

Econometrics · Economics 2024-05-24 Roy Allen

There is a duality theory connecting certain stochastic orderings between cumulative distribution functions F_1,F_2 and stochastic orderings between their inverses F_1^(-1),F_2^(-1). This underlies some theories of utility in the case of…

Statistics Theory · Mathematics 2011-08-05 Alessandra Giovagnoli , Henry P. Wynn

In this paper we study a robust utility maximization problem in continuous time under model uncertainty. The model uncertainty is governed by a continuous semimartingale with uncertain local characteristics. Here, the differential…

Mathematical Finance · Quantitative Finance 2023-08-04 David Criens , Lars Niemann

Motivated by several classic decision-theoretic paradoxes, and by analogies with the paradoxes which in physics motivated the development of quantum mechanics, we introduce a projective generalization of expected utility along the lines of…

Quantum Physics · Physics 2024-01-18 Pierfrancesco La Mura

The expected utility hypothesis is a popular concept in economics that is useful for making decisions when the payoff is uncertain. In this paper, we investigate the implications of a fluctuation theorem in the theory of expected utility.…

Statistical Mechanics · Physics 2024-01-17 Gianluca Francica , Luca Dell'Anna

The problem of demand inversion - a crucial step in the estimation of random utility discrete-choice models - is equivalent to the determination of stable outcomes in two-sided matching models. This equivalence applies to random utility…

Econometrics · Economics 2021-11-30 Odran Bonnet , Alfred Galichon , Yu-Wei Hsieh , Keith O'Hara , Matt Shum

We establish a variety of numerical representations of preference relations induced by set-valued risk measures. Because of the general incompleteness of such preferences, we have to deal with multi-utility representations. We look for…

Mathematical Finance · Quantitative Finance 2020-09-10 Cosimo Munari

The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex…

Quantum Physics · Physics 2012-04-26 Holger F. Hofmann

We study the dual formulation of the utility maximization problem in incomplete markets when the utility function is finitely valued on the whole real line. We extend the existing results in this literature in two directions. First, we…

Probability · Mathematics 2008-12-10 B. Bouchard , N. Touzi , A. Zeghal

The apparent failure of individual probabilistic expressions to distinguish uncertainty about truths from uncertainty about probabilistic assessments have prompted researchers to seek formalisms where the two types of uncertainties are…

Artificial Intelligence · Computer Science 2013-04-11 Judea Pearl

We say a model is continuous in utilities (resp., preferences) if small perturbations of utility functions (resp., preferences) generate small changes in the model's outputs. While similar, these two questions are different. They are only…

Theoretical Economics · Economics 2024-03-05 Pablo Schenone

Nontransitive choices have long been an area of curiosity within economics. However, determining whether nontransitive choices represent an individual's preference is a difficult task since choice data is inherently stochastic. This paper…

Theoretical Economics · Economics 2023-05-01 Mogens Fosgerau , John Rehbeck

Power transforms, such as the Box-Cox transform and Tukey's ladder of powers, are a fundamental tool in mathematics and statistics. These transforms are primarily used for normalizing and standardizing datasets, effectively by raising…

Machine Learning · Computer Science 2026-03-23 Jonathan T. Barron

Variance plays a crucial role in risk-sensitive reinforcement learning, and most risk measures can be analyzed via variance. In this paper, we consider two law-invariant risks as examples: mean-variance risk and exponential utility risk.…

Machine Learning · Computer Science 2019-07-12 Shuai Ma , Jia Yuan Yu

We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality…

Probability · Mathematics 2016-06-14 Mathias Beiglböck , Marcel Nutz , Nizar Touzi