This paper introduces a framework for fair classification, where individuals are classified while preventing discrimination based on group membership. The framework includes a task-specific similarity metric to determine how individuals should be treated similarly, and an algorithm to maximize utility under fairness constraints. It also addresses "fair affirmative action," ensuring statistical parity while treating similar individuals similarly. The paper discusses the relationship between fairness and privacy, noting that fairness can imply privacy and that differential privacy techniques can be applied to fairness. The authors propose a linear programming approach to achieve fairness, and show that the Lipschitz condition implies statistical parity when the Earthmover distance between groups is small. They also discuss the relationship between fairness and differential privacy, and present an efficient fairness mechanism that works well in metric spaces with small doubling dimension. The paper concludes with a discussion of the challenges of implementing fair affirmative action and the importance of defining a clear similarity metric.This paper introduces a framework for fair classification, where individuals are classified while preventing discrimination based on group membership. The framework includes a task-specific similarity metric to determine how individuals should be treated similarly, and an algorithm to maximize utility under fairness constraints. It also addresses "fair affirmative action," ensuring statistical parity while treating similar individuals similarly. The paper discusses the relationship between fairness and privacy, noting that fairness can imply privacy and that differential privacy techniques can be applied to fairness. The authors propose a linear programming approach to achieve fairness, and show that the Lipschitz condition implies statistical parity when the Earthmover distance between groups is small. They also discuss the relationship between fairness and differential privacy, and present an efficient fairness mechanism that works well in metric spaces with small doubling dimension. The paper concludes with a discussion of the challenges of implementing fair affirmative action and the importance of defining a clear similarity metric.