A partial order toolbox for building synthetic indicators of sustainability with ordinal data

This paper designs and implements a statistical toolbox for the construction of synthetic indicators of sustainability and rankings of multidimensional systems of ordinal variables. The toolbox employs results from partial order theory to provide a purely ordinal way to perform the classical steps of indicator construction (i.e., with neither quantification nor aggregation of the input variables) and thus fills a gap in the statistical literature. ‘‘Ordinal’’ non-aggregative procedures are developed to score statistical units and assess the reliability of the final rankings as well as account for exogenous information relating to variable importance. The toolbox is introduced and shown in action through the real example of Sustainable Development Goal 16 (Peace, Justice, and Strong Institutions), specifically as it relates to Political Pluralism and Participation in North and South American countries.