Fairness in Resource Allocation and Slowed-down Dependent Rounding

TL;DR

This paper introduces a new dependent-rounding technique with slowing down and additional randomization to improve fairness guarantees in resource allocation problems, ensuring stronger correlation properties and verifiable fairness.

Contribution

It presents a simple, trust-based fairness approach and a novel dependent-rounding method with slowing down and extra randomization for better correlation guarantees.

Findings

Developed a dependent-rounding technique with slowing down.

Achieved stronger correlation properties than previous methods.

Ensured verifiable fairness through public lottery trust.

Abstract

We consider an issue of much current concern: could fairness, an issue that is already difficult to guarantee, worsen when algorithms run much of our lives? We consider this in the context of resource-allocation problems, we show that algorithms can guarantee certain types of fairness in a verifiable way. Our conceptual contribution is a simple approach to fairness in this context, which only requires that all users trust some public lottery. Our technical contributions are in ways to address the $k$-center and knapsack-center problems that arise in this context: we develop a novel dependent-rounding technique that, via the new ingredients of "slowing down" and additional randomization, guarantees stronger correlation properties than known before.