The effect of aggregation on city sustainability rankings

Although sustainability is a multifactorial concept, many sustainability indexes use weighted additive aggregation of sets of different indicators to derive a single index which can be used to rank different cities. One of the limitations of this approach is that a poor or low rating in one area can be compensated by a strong or high rating in another area. However sustainability cannot be measured linearly. There is at least a triple bottom line: environmental, social and economic. To be truly sustainable, a city must be sustainable in all areas. A deficiency in one area is likely to have a negative effect in larger proportion than suggested by the magnitude of the deficiency. Conversely, a strong result in an indicator is likely to have less effect on overall sustainability than its magnitude suggests. The concept of constraint and maximisation indicators has been proposed to represent this property of sustainability. We investigate the effect on city rankings of using aggregations that aim to represent the constraint and maximisation properties of sustainable development indicators, compared to the commonly used arithmetic (linear) aggregation. Three such aggregation methods (geometric, harmonic and an adjustable compensation method) can cause difficulties with ranking if one or more of the individual indices have a zero normalised value. We show that the use of a small offset can avoid this problem and enable practical use of these aggregation methods to better capture the nature of sustainability. We also formulate a similarity score for different ranking systems that compare a large number of cities.