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Fair division is the problem of dividing one or several goods amongst two or more agents in a way that satisfies a suitable fairness criterion. These Notes provide a succinct introduction to the field. We cover three main topics. First, we…

Artificial Intelligence · Computer Science 2018-06-13 Ulle Endriss

We study the problem of fairly allocating a set of indivisible goods to multiple agents and focus on the proportionality, which is one of the classical fairness notions. Since proportional allocations do not always exist when goods are…

Computer Science and Game Theory · Computer Science 2023-04-12 Yusuke Kobayashi , Ryoga Mahara

The assignment problem is one of the most well-studied settings in social choice, matching, and discrete allocation. We consider the problem with the additional feature that agents' preferences involve uncertainty. The setting with…

Computer Science and Game Theory · Computer Science 2016-10-11 Haris Aziz , Ronald de Haan , Baharak Rastegari

In many prediction problems, the predictive model affects the distribution of the prediction target. This phenomenon is known as performativity and is often caused by the behavior of individuals with vested interests in the outcome of the…

Machine Learning · Statistics 2024-06-03 Seamus Somerstep , Ya'acov Ritov , Yuekai Sun

We study the problem of selection in the context of Bayesian persuasion. We are given multiple agents with hidden values (or quality scores), to whom resources must be allocated by a welfare-maximizing decision-maker. An intermediary with…

Computer Science and Game Theory · Computer Science 2025-11-18 Yannan Bai , Kamesh Munagala , Yiheng Shen , Davidson Zhu

In many real-world situations, data is distributed across multiple self-interested agents. These agents can collaborate to build a machine learning model based on data from multiple agents, potentially reducing the error each experiences.…

Computers and Society · Computer Science 2023-02-28 Kate Donahue , Jon Kleinberg

The Assignment problem is a fundamental and well-studied problem in the intersection of Social Choice, Computational Economics and Discrete Allocation. In the Assignment problem, a group of agents expresses preferences over a set of items,…

Data Structures and Algorithms · Computer Science 2021-05-24 Barak Steindl , Meirav Zehavi

Assessing the spatial fairness of predictive models involves establishing whether they are statistically penalizing (favoring) individuals associated with certain geographical locations. Literature on this topic makes the fundamental…

Machine Learning · Computer Science 2026-05-25 Francesco Lettich , Mario A. Nascimento , Chiara Pugliese , Chiara Renso

To study discrimination in automated decision-making systems, scholars have proposed several definitions of fairness, each expressing a different fair ideal. These definitions require practitioners to make complex decisions regarding which…

Computers and Society · Computer Science 2021-02-23 Kweku Kwegyir-Aggrey , Rebecca Santorella , Sarah M. Brown

House Allocations concern with matchings involving one-sided preferences, where houses serve as a proxy encoding valuable indivisible resources (e.g. organs, course seats, subsidized public housing units) to be allocated among the agents.…

Computer Science and Game Theory · Computer Science 2025-11-11 Hadi Hosseini , Sanjukta Roy , Aditi Sethia

People are rated and ranked, towards algorithmic decision making in an increasing number of applications, typically based on machine learning. Research on how to incorporate fairness into such tasks has prevalently pursued the paradigm of…

Machine Learning · Computer Science 2019-02-07 Preethi Lahoti , Krishna P. Gummadi , Gerhard Weikum

We consider a multi-agent resource allocation setting that models the assignment of papers to reviewers. A recurring issue in allocation problems is the compatibility of welfare/efficiency and fairness. Given an oracle to find a…

Computer Science and Game Theory · Computer Science 2019-08-02 Haris Aziz , Xin Huang , Nicholas Mattei , Erel Segal-Halevi

Fair allocation of indivisible items among agents is a fundamental and extensively studied problem. However, fairness does not have a single universally accepted definition, leading to a variety of competing fairness notions. Some of these…

Computer Science and Game Theory · Computer Science 2025-10-14 Jugal Garg , Eklavya Sharma

In the peer selection problem a group of agents must select a subset of themselves as winners for, e.g., peer-reviewed grants or prizes. Here, we take a Condorcet view of this aggregation problem, i.e., that there is a ground-truth ordering…

Computer Science and Game Theory · Computer Science 2021-07-22 Omer Lev , Nicholas Mattei , Paolo Turrini , Stanislav Zhydkov

Algorithmic predictions are increasingly used to inform the allocations of goods and interventions in the public sphere. In these domains, predictions serve as a means to an end. They provide stakeholders with insights into likelihood of…

Computers and Society · Computer Science 2024-05-31 Juan Carlos Perdomo

Rationing of healthcare resources has emerged as an important issue, which has been discussed by medical experts, policy-makers, and the general public. We consider a rationing problem where medical units are to be allocated to patients.…

Computer Science and Game Theory · Computer Science 2021-09-28 Haris Aziz , Florian Brandl

We study fairness in classification, where individuals are classified, e.g., admitted to a university, and the goal is to prevent discrimination against individuals based on their membership in some group, while maintaining utility for the…

Computational Complexity · Computer Science 2011-11-30 Cynthia Dwork , Moritz Hardt , Toniann Pitassi , Omer Reingold , Rich Zemel

In the metric distortion problem, a set of voters and candidates lie in a common metric space, and a committee of $k$ candidates must be elected. The objective is to minimize a social cost, defined as a function of the distances between…

Computer Science and Game Theory · Computer Science 2025-10-16 Javier Cembrano , Golnoosh Shahkarami

Given an initial resource allocation, where some agents may envy others or where a different distribution of resources might lead to higher social welfare, our goal is to improve the allocation without reassigning resources. We consider a…

Computer Science and Game Theory · Computer Science 2021-12-15 Robert Bredereck , Andrzej Kaczmarczyk , Junjie Luo , Rolf Niedermeier , Florian Sachse

Several resource allocation settings involve agents with unequal entitlements represented by weights. We analyze weighted fair division from an asymptotic perspective: if $m$ items are divided among $n$ agents whose utilities are…

Computer Science and Game Theory · Computer Science 2025-09-16 Pasin Manurangsi , Warut Suksompong , Tomohiko Yokoyama