Quantification of Partially Ordered Data and the Evaluation of Financial Literacy

In this paper, we address the problem of the quantification of partially ordered data arising from multi-indicator systems of binary attributes and develop a procedure for the evaluation of Financial Literacy, on a real dataset pertaining to Italy. The procedure is based on the concept of “quantification” of chains (i.e. on the assignment of non-negative scores to sequences of comparable elements), in the poset arising from the attribute system, and aims at providing a two-dimensional representation of the data, in the spirit of a dimensionality reduction procedure. Due to the existence of incomparabilities in the poset, statistical units can be assessed only to some degree of indeterminacy and the goal of the procedure is to find out the “coordinate axes” that maximally reduce such indeterminacy.