The paper "Inherent Trade-Offs in the Fair Determination of Risk Scores" by Jon Kleinberg, Sendhil Mullainathan, and Manish Raghavan explores the tensions between different notions of fairness in algorithmic classification. The authors formalize three key fairness conditions and prove that, except in highly constrained special cases, it is impossible to satisfy all three conditions simultaneously. Even approximately satisfying these conditions requires that the data lies in an approximate version of one of these special cases. This suggests that key notions of fairness are incompatible with each other, providing a framework for understanding the trade-offs between them. The paper discusses three example domains where these issues arise: criminal justice, internet advertising, and medical testing. In each domain, the authors highlight the importance of ensuring that decision-making is unbiased and fair across different groups. They define three fairness conditions: calibration within groups, balance for the negative class, and balance for the positive class. These conditions ensure that probability estimates are well-calibrated, and that the average scores received by positive and negative instances are equal across groups. The main result of the paper is a theorem that shows these conditions are generally incompatible. The theorem states that a risk assignment satisfying all three fairness conditions can only exist if the instance allows for perfect prediction or has equal base rates. The authors also provide a continuous relaxation of these conditions, showing that any approximate version of these conditions must approximately look like one of these two simple cases. The paper concludes by discussing the implications of these findings and related work in the field of fairness in machine learning. It emphasizes that the trade-offs between different fairness notions are unavoidable, regardless of the specific context or method used to compute risk scores.The paper "Inherent Trade-Offs in the Fair Determination of Risk Scores" by Jon Kleinberg, Sendhil Mullainathan, and Manish Raghavan explores the tensions between different notions of fairness in algorithmic classification. The authors formalize three key fairness conditions and prove that, except in highly constrained special cases, it is impossible to satisfy all three conditions simultaneously. Even approximately satisfying these conditions requires that the data lies in an approximate version of one of these special cases. This suggests that key notions of fairness are incompatible with each other, providing a framework for understanding the trade-offs between them. The paper discusses three example domains where these issues arise: criminal justice, internet advertising, and medical testing. In each domain, the authors highlight the importance of ensuring that decision-making is unbiased and fair across different groups. They define three fairness conditions: calibration within groups, balance for the negative class, and balance for the positive class. These conditions ensure that probability estimates are well-calibrated, and that the average scores received by positive and negative instances are equal across groups. The main result of the paper is a theorem that shows these conditions are generally incompatible. The theorem states that a risk assignment satisfying all three fairness conditions can only exist if the instance allows for perfect prediction or has equal base rates. The authors also provide a continuous relaxation of these conditions, showing that any approximate version of these conditions must approximately look like one of these two simple cases. The paper concludes by discussing the implications of these findings and related work in the field of fairness in machine learning. It emphasizes that the trade-offs between different fairness notions are unavoidable, regardless of the specific context or method used to compute risk scores.