Related papers: Axiomatic Foundations for a Class of Generalized E…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…
Traditional learning approaches for classification implicitly assume that each mistake has the same cost. In many real-world problems though, the utility of a decision depends on the underlying context $x$ and decision $y$. However,…
In this paper we have devised an alternative methodological approach for quantifying utility in terms of expected information content of the decision-maker's choice set. We have proposed an extension to the concept of utility by…
The Ellsberg and Machina paradoxes reveal that expected utility theory is problematical when real subjects take decisions under uncertainty. Suitable generalizations of expected utility exist which attempt to solve the Ellsberg paradox, but…
For any injective von Neumann algebra R and any discrete, countable group G, which acts by *-automorphisms on R, we construct an idempotent mapping of an ultra-weakly dense subspace of B(H) onto the reducerd crossed product von Neumann…
Budget aggregation is a process in which citizens vote by declaring their individual ideal budget allocation, and a pre-determined rule aggregates all votes into a single outcome. Recent theoretical work has proposed various aggregation…
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…
This paper axiomatizes, in a two-stage setup, a new theory for decision under risk and ambiguity. The axiomatized preference relation $\succeq$ on the space $\tilde{V}$ of random variables induces an ambiguity index $c$ on the space…
We provide a general theoretical analysis of expected out-of-sample utility, also referred to as decision-theoretic classification, for non-decomposable binary classification metrics such as F-measure and Jaccard coefficient. Our key result…
In the large financial market, which is described by a model with countably many traded assets, we formulate the problem of the expected utility maximization. Assuming that the preferences of an economic agent are modeled with a stochastic…
We propose a simple yet effective solution to tackle the often-competing goals of fairness and utility in classification tasks. While fairness ensures that the model's predictions are unbiased and do not discriminate against any particular…
By embedding uncertainty into time, we obtain a conjoint axiomatic characterization of both Exponential Discounting and Subjective Expected Utility that accommodates arbitrary state and outcome spaces. In doing so, we provide a novel and…
We provide foundations for decisions in face of unlikely events by extending the standard framework of Savage to include preferences indexed by a family of events. We derive a subjective lexicographic expected utility representation which…
The goal of this note is to provide a geometric setting in which generalized arithmetic means are best predictors in an appropriate metric. This characterization provides a geometric interpretation to the concept of certainty equivalent.…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
Standard decision theory seeks conditions under which a preference relation can be compressed into a single real-valued function. However, when preferences are incomplete or intransitive, a single function fails to capture the agent's…
Recent literature in the last Maximum Entropy workshop introduced an analogy between cumulative probability distributions and normalized utility functions. Based on this analogy, a utility density function can de defined as the derivative…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
We consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering a decomposition of the space in terms of the supports of the measures representing our…
We extend well-known comparative results under expected utility to models of non-expected utility by providing novel conditions on local utility functions. We illustrate how our results parallel, and are distinct from, existing results for…