Related papers: Coordinate-free utility theory
We propose a multivariate extension of Yaari's dual theory of choice under risk. We show that a decision maker with a preference relation on multidimensional prospects that preserves first order stochastic dominance and satisfies…
We introduce the anonymity group, the neutrality group and the symmetry group of a social preference function. Inspired by a problem posed by Kelly in 1991 and remained unsolved, we investigate the problem of recognizing which permutation…
This paper provides a general framework to explore the possibility of agenda manipulation-proof and proper consensus-based preference aggregation rules, so powerfully called in doubt by a disputable if widely shared understanding of Arrow's…
When allocating indivisible objects via lottery, planners often use ordinal mechanisms, which elicit agents' rankings of objects rather than their full preferences over lotteries. In such an ordinal informational environment, planners…
This paper presents a comprehensive formalization of the von Neumann-Morgenstern (vNM) expected utility theorem using the Lean 4 interactive theorem prover. We implement the classical axioms of preference-completeness, transitivity,…
We propose multi-type probabilistic serial (MPS) and multi-type random priority (MRP) as extensions of the well known PS and RP mechanisms to the multi-type resource allocation problem (MTRA) with partial preferences. In our setting, there…
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…
Classic decision-theory is based on the maximum expected utility (MEU) principle, but crucially ignores the resource costs incurred when determining optimal decisions. Here we propose an axiomatic framework for bounded decision-making that…
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…
The desirable gambles framework provides a foundational approach to imprecise probability theory but relies heavily on linear utility assumptions. This paper introduces function-coherent gambles, a generalization that accommodates…
Ranking entities such as algorithms, devices, methods, or models based on their performances, while accounting for application-specific preferences, is a challenge. To address this challenge, we establish the foundations of a universal…
Linear Logic and Defeasible Logic have been adopted to formalise different features relevant to agents: consumption of resources, and reasoning with exceptions. We propose a framework to combine sub-structural features, corresponding to the…
When building classification systems with demographic fairness considerations, there are two objectives to satisfy: 1) maximizing utility for the specific task and 2) ensuring fairness w.r.t. a known demographic attribute. These objectives…
It is generally believed (and for the most part is probably true) that Lie theory, in contrast to the characteristic zero case, is insufficient to tackle the representation theory of algebraic groups over prime characteristic fields.…
We study the existence of equilibrium when agents' preferences may not beconvex. For some specific utility functions, we provide a necessary and sufficientcondition under which there exists an equilibrium. The standard approach cannot be…
It is challenging to quantify numerical preferences for different objectives in a multi-objective decision-making problem. However, the demonstrations of a user are often accessible. We propose an algorithm to infer linear preference…
We revisit the discrete heterogeneous two-facility location problem, in which there is a set of agents that occupy nodes of a line graph, and have private approval preferences over two facilities. When the facilities are located at some…
We demonstrate that a ubiquitous feature of network games, bilateral strategic interactions, is equivalent to having player utilities that are additively separable across opponents. We distinguish two formal notions of bilateral strategic…
We propose generalized versions of strong equity and Pigou-Dalton transfer principle. We study the existence and the real valued representation of social welfare relations satisfying these two generalized equity principles. Our results…
This paper studies preference aggregation under risk. In our model, each agent has an incomplete preference relation represented by a set of expected utility functions. The classical Pareto principle is silent on agreement involving…