Abstract Cartographic maps aim to identify the order of generation and understand, by explaining in terms of syntactic strategies, the derived orders. In this work, we focus on the order of core verbal arguments and how the PP-NP order is derived from a basic NP-PP order. We test three models of syntactic operations (criterial model, meaningless movement, and external merge) and their predictions using quantitative and computational tools. Specifically, we implement two studies across nineteen treebanks in sixteen languages (four treebanks for Italian and Hebrew in Study 1; fifteen parallel treebanks in Study 2) to test the predictions in terms of locality for the different models. Our results show that the criterial model better predicts the data.