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Abstract
Often objects are to be ranked. However, there is no measurable quantity available to express the ranking aim and to quantify it. The consequence is that indicators are selected, serving as proxies for the ranking aim. Although this set of indicators is of great importance for its own right, the most commonly used practice to obtain a ranking is an aggregation method. Any aggregation, however suffers from the effect of compensation, because the aggregation technique is in the broadest sense an averaging method. Here an alternative is suggested which avoids this averaging and which is derived from simple elements of the theory of partially ordered sets (posets). The central concept in partial order is the 'concept of comparison' and the most general outcome is a web of relations between objects according to their indicator values, respecting the ranking aim.
As an example the 'Failed State Index' (FSI), annually prepared by the Fund of Peace is selected. The FSI is based on twelve individual contextual different indicators, subsequently transformed into a single composite indicator, by simple addition of the single indicator values. Such an operation leaves space for compensation effects, where one or more indicators level out the effect of others. Hence, a comparison between the single states (in total 177) based on their mutual FSI ranking has its limitations as the comparisons are made based on the composite indicator. We show that brain drain is one of the indicators in the FSI-study that plays a crucial role in the ranking, whereby the ranking aim is the stabilization of nations.

Intro -- Preface -- Indicators and Partial Orders - An Introduction -- Role of Indicators -- Partial Order Methodology -- Graph Theory -- Combinatorics -- Algebra -- Indicators and Theoretical Developments -- Indicators for Special Purposes -- Indicators in Social Sciences -- Software -- References -- Acknowledgement -- Contents -- Contributors -- Part I Indicators and Theoretical Developments -- Some Basic Considerations on the Design and the Interpretation of Indicators in the Context of Modelling and Simulation -- 1 Indicators: In General, in Mathematics, in Modelling and Simulation -- 2 Functionality of Indicators -- 2.1 Typical Application Types for Indicators -- 2.1.1 Warnings -- 2.1.2 Decisions Between Alternatives -- 2.1.3 Optimization -- 2.1.4 Modelling Real Systems -- 2.2 Structural Alternatives for Indicators -- 2.2.1 Level 1: Observation and Transmission -- 2.2.2 Level 2: Judging -- 2.2.3 Level 3: Aggregation -- 2.2.4 Hierarchy of the Levels -- 2.3 Fitting Structural Alternatives to the Application Types -- 3 The Workflow for Building Indicators -- 4 The Structure of Complex Indicators with Sub-Indicators and Weightings -- 5 Complex Indicators as a Distinguished Valuation Model -- 6 Test and Validation of Indicator Models -- 7 Some Summary Remarks -- References -- -- Indicators in the Framework of Partial Order -- 1 Introduction: Indicators and Management of Complexity -- 2 Overview About Concepts in Partial Order Theory -- 2.1 Two Basic Approaches -- 2.2 Interplay: Indicators and Objects -- 2.3 Indicator Systems -- References -- Assessing Inhomogeneous Indicator-Related Typologies Through the Reverse Clustering Approach -- 1 Introduction -- 2 The Study with Its Narrow and Broader Motivations -- 3 On the Reverse Clustering -- 4 The Case Studied -- 5 The Outline of Results -- 6 Some Comments on the Relation to Indicator Dimension.