Amalgamating Urban Scaling and Economic Complexity for New Metrics of Urban Fitness

We propose a synthesis of the independent scientific frameworks of economic complexity and urban scaling into a consistent mechanism—city complexity—to measure multi-dimensional fitness of cities. Essentially, we use deviations from scaling law for a given set of urban outcomes as the basis to construct a bipartite city-outcome matrix. 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 expected 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. Finally, we perturb the metrics to conditions of widespread socioeconomic stress and find that outcomes are indicative of the robustness of the city complexity algorithm. Overall, these findings suggest that the city complexity mechanism proposed here produces systematic, self-consistent metrics and can be applied across any set of diverse outcomes, irrespective of the specifics of national urban contexts.