In multi-label classification (MLC), each instance can be assigned to none, one or multiple labels from a predefined label set, and the task is to predict the relevant subset of labels for each new instance. A common challenge in MLC is class imbalance, which often leads to biased classifiers that underestimate rare labels. In this paper, we propose a framework that combines probabilistic classifier chains (PCC) with a minimax learning strategy based on the Discrete minimax classifier. PCC allows us to model label dependencies and optimize various loss functions, including the subset 0/1 loss, Hamming loss, and F1-measure, while the minimax learning strategy mitigates the class imbalance problem by minimizing and balancing the class conditional risks. We conduct experiments on ten benchmark datasets using multiple models of different learning strategies. Our analysis focuses on the ability of models to optimize a loss function while also reducing the false positive and false negative rates. To this end, we use two complementary metrics designed to measure imbalance in class-conditional accuracies.