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The construction of deprivation indices is complicated by the inherentambiguity in defining deprivation as well as the potential for partisanmanipulation. Nevertheless, deprivation indices provide an essential tool formitigating the effects of deprivation and reducing it through policyinterventions. Here we demonstrate the construction of a deprivation indexusing diffusion maps, a manifold learning technique capable of finding thevariables that optimally describe the variations in a dataset in the sense ofpreserving pairwise relationships among the data points. The method is appliedto the 2010 US decennial census. In contrast to other methods the proposedprocedure does not select particular columns from the census, but ratherconstructs an indicator of deprivation from the complete dataset. Due to itsconstruction the proposed index does not introduce biases except those alreadypresent in the source data, does not require normative judgment regarding thedesirability of certain life styles, and is highly resilient against attemptsof partisan manipulation. We demonstrate that the new index aligns well withestablished income-based deprivation indices but deviates in aspects that areperceived as problematic in some of the existing indices. The proposedprocedure provides an efficient way for constructing accurate, high resolutionindices. These indices can thus have the potential to become powerful tools forthe academic study of social structure as well as political decision making.

Mathematical construction of a low-bias high-resolution deprivation index for the United States