On an Aggregation Theory for Indicators Expressing Behaviors of Complex Systems With an Application to Sustainability

Certain attributes of large‐scale complex systems are often expressed through sets of indicators. For example, the sustainability of an entity, be it a nation, a city, an energy system, a corporation etc., can be effectively represented by indicators and corresponding data series. For such representations to be practical, aggregation methods should be devised that lead to concrete performance measures hierarchically. In this work a mathematical aggregation theory is presented for indicators regarding the behavior of complex systems. A set of relevant postulates leads to a simple model based on shifted geometric means combining values of basic indicators into an overall index. The model is augmented with a sensitivity analysis which pinpoints those indicators with the highest potential for improving performance, thus, providing decision‐makers with an important tool to compare alternative policies. An application is shown in detail regarding the sustainability of 161 countries and data up to 2024. We rank countries according to their sustainability standing and pinpoint those Sustainable Development Goals that are crucial in enhancing sustainability. European countries, Australia and Uruguay take the top 20 places, while most of the bottom places are taken by African states. Our analysis occasionally reveals surprising low rankings of some highly developed countries due to poor environmental performance. Plastics consumption, deforestation, renewable energy generation, and water stress are among the most frequent influential indicators for developed states. Low gross national income, corruption, plastics consumption, and deforestation are quite prevalent in developing and low‐income countries.