Related papers: Counterexamples in the theory of fair division

In recent years, machine learning algorithms have become ubiquitous in a multitude of high-stakes decision-making applications. The unparalleled ability of machine learning algorithms to learn patterns from data also enables them to…

We revisit the classic problem of fair division from a mechanism design perspective, using {\em Proportional Fairness} as a benchmark. In particular, we aim to allocate a collection of divisible items to a set of agents while incentivizing…

Feferman proved in 1962 that any arithmetical theorem is a consequence of a suitable transfinite iteration of full uniform reflection of $\mathsf{PA}$. This result is commonly known as Feferman's completeness theorem. The purpose of this…

We present a self-contained elementary and detailed exposition of Mertens' own proof of his theorem on the divergence of the series of the reciprocals of the primes and compare it with the modern proofs. His proof contains explicit…

The digitization of healthcare data coupled with advances in computational capabilities has propelled the adoption of machine learning (ML) in healthcare. However, these methods can perpetuate or even exacerbate existing disparities,…

Algorithmic fairness has become a central concern in computational decision-making systems, where ensuring equitable outcomes is essential for both ethical and legal reasons. Two dominant notions of fairness have emerged in the literature:…

In measure theory, Steinhaus theorem is a result that deals with a property of the difference between two sets of positive measure. We give a simple elementary proof of the result.

Distorted sums of models were introduced and discussed in [Sh:463]. This notion generalizes the notion of disjoint (or direct) sums of models by letting the summands overlap. In the first section we investigate types in distorted sums and…

We study fair allocation of indivisible items, where the items are furnished with a set of conflicts, and agents are not permitted to receive conflicting items. This kind of constraint captures, for example, participating in events that…

We revisit the problem of fair clustering, first introduced by Chierichetti et al., that requires each protected attribute to have approximately equal representation in every cluster; i.e., a balance property. Existing solutions to fair…

The issue of fairness in machine learning stems from the fact that historical data often displays biases against specific groups of people which have been underprivileged in the recent past, or still are. In this context, one of the…

Fairness is a major concern in contemporary decision problems. In these situations, the objective is to maximize fairness while preserving the efficacy of the underlying decision-making problem. This paper examines repeated decisions on…

Clustering is a foundational problem in machine learning with numerous applications. As machine learning increases in ubiquity as a backend for automated systems, concerns about fairness arise. Much of the current literature on fairness…

Counterfactual frameworks have grown popular in machine learning for both explaining algorithmic decisions but also defining individual notions of fairness, more intuitive than typical group fairness conditions. However, state-of-the-art…

With the growing adoption of machine learning (ML) systems in areas like law enforcement, criminal justice, finance, hiring, and admissions, it is increasingly critical to guarantee the fairness of decisions assisted by ML. In this paper,…

In a 1977 paper, Steffens identified an elegant criterion for determining when a countable graph has a perfect matching. In this paper, we will investigate the proof-theoretic strength of this result and related theorems. We show that a…

We discuss the back and forth technique in the context of presheaf model theory. The essence of the back and forth technique lies in showing the relationship between various hierarchies which calibrate similarity between two models and,…

Fairness assumptions are a valuable tool when reasoning about systems. In this paper, we classify several fairness properties found in the literature and argue that most of them are too restrictive for many applications. As an alternative…

How to handle division in systems that compute with logical formulas involving what would otherwise be polynomial constraints over the real numbers is a surprisingly difficult question. This paper argues that existing approaches from both…

Computer vision systems have witnessed rapid progress over the past two decades due to multiple advances in the field. As these systems are increasingly being deployed in high-stakes real-world applications, there is a dire need to ensure…