Related papers: Nonstandard numbers for qualitative decision makin…
We make precise sense of the idea of "molecular chaos" through algorithmic randomness of microscopic trajectories, and ground macroscopic irreversibility in the lack of symmetry under time reversal of this property. This concept of…
The random utility model (RUM, McFadden and Richter, 1990) has been the standard tool to describe the behavior of a population of decision makers. RUM assumes that decision makers behave as if they maximize a rational preference over a…
This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…
It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that standard approaches…
Random utility theory models an agent's preferences on alternatives by drawing a real-valued score on each alternative (typically independently) from a parameterized distribution, and then ranking the alternatives according to scores. A…
The random utility model, a cornerstone in economics, is axiomatized by Falmagne (1978) and McFadden and Richter (1990) with the assumption that if a menu is observable, the choice frequencies of all alternatives are also observable.…
We axiomatically define a cardinal social inefficiency function, which, given a set of alternatives and individuals' vNM preferences over the alternatives, assigns a unique number -- the social inefficiency -- to each alternative. These…
For statistical decision problems with finite parameter space, it is well-known that the upper value (minimax value) agrees with the lower value (maximin value). Only under a generalized notion of prior does such an equivalence carry over…
Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from…
We study consumption dependence in the context of random utility and repeated choice. We show that, in the presence of consumption dependence, the random utility model is a misspecified model of repeated rational choice. This…
We consider the egalitarian welfare aspects of random assignment mechanisms when agents have unrestricted cardinal utilities over the objects. We give bounds on how well different random assignment mechanisms approximate the optimal…
A general principle is advanced allowing the classification of nonunique solutions to nonlinear evolution equations, corresponding to different spatio-temporal patterns. This is done by defining the probability distribution of patterns,…
To choose between two discrete goods, a consumer pays attention to only those with prices below a threshold. From these, she chooses her most preferred good. We assume consumers in a population have the same preference but may have…
Decision theory does not traditionally include uncertainty over utility functions. We argue that the a person's utility value for a given outcome can be treated as we treat other domain attributes: as a random variable with a density…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
The well-studied problem of statistical rank aggregation has been applied to comparing sports teams, information retrieval, and most recently to data generated by human judgment. Such human-generated rankings may be substantially different…
When it comes to structural estimation of risk preferences from data on choices, random utility models have long been one of the standard research tools in economics. A recent literature has challenged these models, pointing out some…
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum…
A new notion of stochastic ordering is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of…
We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a broader sense.