Related papers: Tight Guarantees in the Commons
We study the fair division of indivisible items among $n$ agents with heterogeneous additive valuations, subject to lower and upper quotas on the number of items allocated to each agent. Such constraints are crucial in various applications,…
We present a flexible framework for learning predictive models that approximately satisfy the equalized odds notion of fairness. This is achieved by introducing a general discrepancy functional that rigorously quantifies violations of this…
The higher characteristics w_m(G) for a finite abstract simplicial complex G are topological invariants that satisfy k-point Green function identities and can be computed in terms of Euler characteristic in the case of closed manifolds,…
By discussing several examples, the theory of generalized functional models is shown to be very natural for modeling some situations of reasoning under uncertainty. A generalized functional model is a pair (f, P) where f is a function…
Let $(X,\mathcal W)$ be a balayage space, $1\in \mathcal W$, or - equivalently - let $\mathcal W$ be the set of excessive functions of a Hunt process on a locally compact space $X$ with countable base such that $\mathcal W$ separates…
We consider the problem of fairly allocating indivisible public goods. We model the public goods as elements with feasibility constraints on what subsets of elements can be chosen, and assume that agents have additive utilities across…
This paper introduces marginal fairness, a new individual fairness notion for equitable decision-making in the presence of protected attributes such as gender, race, and religion. This criterion ensures that decisions based on generalized…
Fair Influence Maximization (FIM) seeks to mitigate disparities in influence across different groups and has recently garnered increasing attention. A widely adopted notion of fairness in FIM is the maximin constraint, which directly…
In this note besides two abstract versions of the Vitali Covering Lemma an abstract Hardy-Littlewood Maximal Inequality, generalizing weak type (1,1) maximal function inequality, associated to any outer measure and a family of subsets on a…
We introduce a new paradigm for risk sharing that generalizes earlier models based on discrete agents and extends them to allow for sharing risk within a continuum of agents. Agents are represented by points of a measure space and have…
By use of window functions, time-frequency analysis tools like Short Time Fourier Transform overcome a shortcoming of the Fourier Transform and enable us to study the time- frequency characteristics of signals which exhibit transient os-…
We introduce a novel generative formulation of deep probabilistic models implementing "soft" constraints on their function dynamics. In particular, we develop a flexible methodological framework where the modeled functions and derivatives…
Real-world applications of machine learning tools in high-stakes domains are often regulated to be fair, in the sense that the predicted target should satisfy some quantitative notion of parity with respect to a protected attribute.…
This paper explores the emergence of norms in agents' societies when agents play multiple -even incompatible- roles in their social contexts simultaneously, and have limited interaction ranges. Specifically, this article proposes two…
There are p heterogeneous objects to be assigned to n competing agents (n > p) each with unit demand. It is required to design a Groves mechanism for this assignment problem satisfying weak budget balance, individual rationality, and…
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 typically arise from applying decision rules…
We consider a committee voting on whether to adopt a reform under a quota rule, where members differ in how much they value the reform some supporting it, others opposing it. We examine how members can influence each other's votes through…
In the work of Donoho and Stark, they study a manifestation of the uncertainty principle in signal recovery. They conjecture that, for a function with support of bounded size T, the maximum concentration of its Fourier transform in the low…
Representation learning is increasingly employed to generate representations that are predictive across multiple downstream tasks. The development of representation learning algorithms that provide strong fairness guarantees is thus…
A quota mechanism, such as a mandatory grading curve, links together multiple decisions. We analyze the performance of quota mechanisms when the number of linked decisions is finite and the designer has imperfect knowledge of the type…