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Machine learning systems are often expected to make fair decisions, yet the most widely used fairness criteria—independence, separation, and sufficiency—cannot generally be satisfied at the same time. In this study, students tested these criteria using a logistic regression model on a real-world student performance dataset and found that each criterion was met only at different prediction thresholds, with no threshold satisfying all three simultaneously. These results illustrate the inherent trade-offs in algorithmic fairness and highlight why achieving perfectly fair machine learning models is often impossible in practice.

Galaxy clusters offer several advantages for measuring H₀ compared to traditional methods, such as Cepheid variables or Type Ia supernovae. Unlike individual stars or supernovae, clusters are less affected by local variations in stellar population or interstellar medium properties, providing a more stable and consistent measure over large cosmological distances. This work proposes using galaxy clusters as an alternative method for determining the H₀. It provides an independent perspective on the H₀ debate and contribute to ongoing efforts to reconcile the differing values obtained from the other two measurements.