Counterfactual explanations have emerged as an important tool to understand, debug, and audit complex machine learning models. To offer global counterfactual explainability, state-of-the-art methods construct summaries of local explanations, offering a trade-off among conciseness, counterfactual effectiveness, and counterfactual cost or burden imposed on instances. In this work, we provide a concise formulation of the problem of identifying global counterfactuals and establish principled criteria for comparing solutions, drawing inspiration from Pareto dominance. We introduce innovative algorithms designed to address the challenge of finding global counterfactuals for either the entire input space or specific partitions, employing clustering and decision trees as key components. Additionally, we conduct a comprehensive experimental evaluation, considering various instances of the problem and comparing our proposed algorithms with state-of-the-art methods. The results highlight the consistent capability of our algorithms to generate meaningful and interpretable global counterfactual explanations.
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