Optimally Interpolating between Ex-Ante Fairness and Welfare

Fuente: arXiv
Guardado en:
Detalles Bibliográficos
Autores principales: Høgsgaard, Mikael Møller, Karras, Panagiotis, Ma, Wenyue, Rathi, Nidhi, Schwiegelshohn, Chris
Formato: Preprint
Publicado: 2023
Materias:
Acceso en línea:
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
_version_ 1866929478344638464
author Høgsgaard, Mikael Møller
Karras, Panagiotis
Ma, Wenyue
Rathi, Nidhi
Schwiegelshohn, Chris
author_facet Høgsgaard, Mikael Møller
Karras, Panagiotis
Ma, Wenyue
Rathi, Nidhi
Schwiegelshohn, Chris
contents For the fundamental problem of allocating a set of resources among individuals with varied preferences, the quality of an allocation relates to the degree of fairness and the collective welfare achieved. Unfortunately, in many resource-allocation settings, it is computationally hard to maximize welfare while achieving fairness goals. In this work, we consider ex-ante notions of fairness; popular examples include the \emph{randomized round-robin algorithm} and \emph{sortition mechanism}. We propose a general framework to systematically study the \emph{interpolation} between fairness and welfare goals in a multi-criteria setting. We develop two efficient algorithms ($\varepsilon-Mix$ and $Simple-Mix$) that achieve different trade-off guarantees with respect to fairness and welfare. $\varepsilon-Mix$ achieves an optimal multi-criteria approximation with respect to fairness and welfare, while $Simple-Mix$ achieves optimality up to a constant factor with zero computational overhead beyond the underlying \emph{welfare-maximizing mechanism} and the \emph{ex-ante fair mechanism}. Our framework makes no assumptions on either of the two underlying mechanisms, other than that the fair mechanism produces a distribution over the set of all allocations. Indeed, if these mechanisms are themselves approximation algorithms, our framework will retain the approximation factor, guaranteeing sensitivity to the quality of the underlying mechanisms, while being \emph{oblivious} to them. We also give an extensive experimental analysis for the aforementioned ex-ante fair mechanisms on real data sets, confirming our theoretical analysis.
format Preprint
id arxiv_https___arxiv_org_abs_2302_03071
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Optimally Interpolating between Ex-Ante Fairness and Welfare
Høgsgaard, Mikael Møller
Karras, Panagiotis
Ma, Wenyue
Rathi, Nidhi
Schwiegelshohn, Chris
Computer Science and Game Theory
Data Structures and Algorithms
For the fundamental problem of allocating a set of resources among individuals with varied preferences, the quality of an allocation relates to the degree of fairness and the collective welfare achieved. Unfortunately, in many resource-allocation settings, it is computationally hard to maximize welfare while achieving fairness goals. In this work, we consider ex-ante notions of fairness; popular examples include the \emph{randomized round-robin algorithm} and \emph{sortition mechanism}. We propose a general framework to systematically study the \emph{interpolation} between fairness and welfare goals in a multi-criteria setting. We develop two efficient algorithms ($\varepsilon-Mix$ and $Simple-Mix$) that achieve different trade-off guarantees with respect to fairness and welfare. $\varepsilon-Mix$ achieves an optimal multi-criteria approximation with respect to fairness and welfare, while $Simple-Mix$ achieves optimality up to a constant factor with zero computational overhead beyond the underlying \emph{welfare-maximizing mechanism} and the \emph{ex-ante fair mechanism}. Our framework makes no assumptions on either of the two underlying mechanisms, other than that the fair mechanism produces a distribution over the set of all allocations. Indeed, if these mechanisms are themselves approximation algorithms, our framework will retain the approximation factor, guaranteeing sensitivity to the quality of the underlying mechanisms, while being \emph{oblivious} to them. We also give an extensive experimental analysis for the aforementioned ex-ante fair mechanisms on real data sets, confirming our theoretical analysis.
title Optimally Interpolating between Ex-Ante Fairness and Welfare
topic Computer Science and Game Theory
Data Structures and Algorithms
url https://arxiv.org/abs/2302.03071