A self-consistent assessment of multi-dimensional fitness of cities

Abstract: Given the importance of urban sustainability and resilience to the future of our planet, there is a need to better understand the interconnectedness between the social, economic, environmental, and governance outcomes that underline these frameworks. Here, we propose a synthesis of the independent scientific frameworks of economic complexity and urban scaling into a consistent mechanism - termed 'city complexity' - to measure the fitness of cities across multiple dimensions. Essentially, we propose the use of urban scaling as the basis to construct and populate a bipartite city-outcome matrix, whose entries are the deviations from scaling law for a given set of urban outcomes. This matrix forms the input into the economic complexity methodology, which iterates over a pair of coupled non-linear maps, computing fitness of cities and complexity of outcomes. We test our algorithm with data from American cities and find that the emergent city fitness measure is consistent with desired behavior across the set of outcomes studied. We also find temporal evolution of city fitness and outcome complexity to be in agreement with theoretical expectation. Overall, these findings suggest that the city complexity mechanism proposed here produces a robust measure of fitness and can be applied for any set of diverse outcomes, irrespective of the specifics of national urban contexts.