Group recommender systems help users make collective choices but often lack transparency, leaving group members uncertain about why items are suggested. Existing explanation methods focus on individuals, offering limited support for groups where multiple preferences interact. In this work, we introduce and formalize the problem of finding counterfactual explanations for group recommendations. We introduce a comprehensive set of item- and explanation-level metrics that capture different aspects, such as relevance, popularity, explanation utility, interpretability, and fairness. We design five algorithms that employ techniques such as search-space pruning, greedy selection, early stopping, and incremental refinement to reduce computational cost and the number of recommender calls while producing high-quality explanations. The algorithms consider different trade-offs; for example, some prioritize computational efficiency at the expense of explanation quality, while others focus on improving explanation quality at a higher computational cost. Experiments on real-world datasets analyze these trade-offs in terms of explanation size, computational cost, utility, and fairness.

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