Indicator Analyses: What Is Important—and for What?

Simple elements of partial order theory appear helpful for a causal analysis in the context of ranking. The Hasse diagrams may seem as a confusing system of lines and a high number of incomparabilities. Thus, they indicate that metric information may be lost, but, on the other side partial order tools offer a wide variety of additional information about the interplay between the objects of interest and indicators. In this chapter a series of tools are presented to reveal such information. As an illustrative example the so-called Failed State Index (FSI) is used. FSI is a composite indicator based on 12 individual indicators by simply summarizing the single values. The FSI comprises 177 states, which are the objects of our study. A selection of appropriate partial order tools are applied to reveal specific information about the interplay between the states and the 12 indicators, such as A: sensitivity analysis, where the indicators are ordered relatively to their impact on the structure of the partially ordered set, B: a “vertical,” i.e., chain analysis that is directed towards the comparabilities within a Hasse diagram, and C: a “horizontal,” i.e., antichain analysis focusing on incomparabilities, including also the use of tripartite graphs as well as a derivation of an ordinary graph. Partial order does not necessarily constitute as a Multicriteria Method solving all inherent problems. However, this chapter discloses that a detailed analysis by partial order tools prior to a possible derivation of a ranking index apparently is highly attractive.