Group Fair Matchings using Convex Cost Functions
Atasi Panda, Harsh Sharma, Anand Louis, and Prajakta Nimbhorkar

TL;DR
This paper introduces a flexible, cost-based approach to group fairness in item-platform matchings, balancing utility and fairness through convex cost functions, with efficient algorithms and theoretical analysis.
Contribution
It proposes a novel convex cost function framework for group fairness in matchings, replacing hard constraints with penalties, and provides polynomial-time approximation algorithms.
Findings
Efficient polynomial-time approximation algorithm with guarantees
Experimental validation demonstrating practical effectiveness
Hardness results for intersecting group cases
Abstract
We consider the problem of assigning items to platforms where each item has a utility associated with each of the platforms to which it can be assigned. Each platform has a soft constraint over the total number of items it serves, modeled via a convex cost function. Additionally, items are partitioned into groups, and each platform also incurs group-specific convex cost over the number of items from each group that can be assigned to the platform. These costs promote group fairness by penalizing imbalances, yielding a soft variation of fairness notions introduced in prior work, such as Restricted Dominance and Minority protection. Restricted Dominance enforces upper bounds on group representation, while Minority protection enforces lower bounds. Our approach replaces such hard constraints with cost-based penalties, allowing more flexible trade-offs. Our model also captures Nash Social…
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Taxonomy
TopicsGame Theory and Voting Systems · Korean Peninsula Historical and Political Studies
