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• New statistical procedures for the approximation of ordinal multi-indicator and partially ordered data systems. • Design of new algorithms for the extraction of bucket orders and rankings from sets of input posets. • To our knowledge, this is the first time these issues have been addressed in the statistical literature. Two greedy algorithms for the synthesis and approximation of multidomain systems of partially ordered data are proposed. Given k input partially ordered sets (posets) on the same elements, the algorithms search for the optimally approximating partial orders, minimizing the dissimilarity between the generated and input posets, based on their matrices of mutual ranking probabilities. A general approximation algorithm is developed, together with a specific procedure for approximation over bucket orders, which are the natural choice when the goal is to "condense" the inputs into rankings, possibly with ties. Different loss functions are also employed, and their outputs are compared. A real example pertaining to regional well-being in Italy motivates the algorithms and shows them in action. [ABSTRACT FROM AUTHOR]