Partial Order Theory has been recently more and more employed in applied science to overcome the intrinsic disadvantage hidden in aggregation, if a multiple attribute system is available. Despite its numerous positive features, there are many practical cases where the interpretation of the partial order can be rather troublesome. In these cases the analysis of underlying dimensions could be useful to uncover particular data structures. The paper shows a way of addressing the problem with the help of an actual case study, which deals with European opinions on services of general interest. In particular, a partial order of countries is firstly provided and then a method to detect dimensions is discussed and applied. The analysis stems directly from the Partially Order Set (poset) and Lattice theory with particular references to dimension theory and Formal Concept Analysis. The study is eventually able to pinpoint role and relevance of different attributes characterizing EU countries which are used to define the partial order.