Fair Indivisible Payoffs through Shapley Value
This addresses fairness issues in resource allocation for applications like political representation and feature attribution in AI, but it is incremental as it adapts an existing concept to indivisible settings.
The paper tackles the problem of fair payoff division in indivisible coalitional games, such as allocating parliamentary seats or key features in machine learning models, by proposing the indivisible Shapley value and demonstrating its application in case studies like image classification.
We consider the problem of payoff division in indivisible coalitional games, where the value of the grand coalition is a natural number. This number represents a certain quantity of indivisible objects, such as parliamentary seats, kidney exchanges, or top features contributing to the outcome of a machine learning model. The goal of this paper is to propose a fair method for dividing these objects among players. To achieve this, we define the indivisible Shapley value and study its properties. We demonstrate our proposed technique using three case studies, in particular, we use it to identify key regions of an image in the context of an image classification task.