“Do similar individuals get similarly treated...?”
In this repository, we include all the necessary code to calculate the Spatial Inequality Index. This code was provided as part of our publication at The Web Conference 2021, Fair Partitioning of Public Resources: Redrawing District Boundary to Minimize Spatial Inequality in School Funding.
For anyone interested in using (or contributing to) our codebase, we provide complete documentation of our spatial_inequality package. For anyone otherwise interested in visualizing the impact of our algorithm in school redistricting, we also provide an interactive website. Also, an in-depth description of the whole algorithm (alongside its temporal complexity) can be found as a README at the package's source code directory.
The Spatial Inequality Index, as the name suggests, is an inequality index that measures statistical differences between individuals in a population. Whereas other inequality indices - like the Gini Index - will compare every individual in a population with one another, the Spatial Inequality Index compares similar individuals (for some notion of similarity).
Take a population of N individuals. For each individual i in the population, define their neighborhood Ni (i.e., which other individuals should be considered as similar) and their benefit yi (i.e., how much of a given resource they have). The full index can then be calculated as such:
The higher the difference observed between immediate neighbors, the higher the observed spatial inequality. You can find its (Python) implementation in both our repository and documentation.
In our study, we applied this concept to public schooling districts in the US. We considered (i) individuals as being districts, (ii) their neighborhood as their geographical neighbors and (iii) their benefit as the amount of funding (per-student) that they receive. Although we understand there are very valid reasons for different district to receive different amounts of funds, it still feels off that a school potentially meters away from being assigned to another district would get substantially lower/higher amount of funds than its immediate peers. By finding alternative districting strategies that minimize spatial inequality we prevent this from happening.
Besides our own use-case, however, the Spatial Inequality Index can be used any time one wants to measure if similar individuals are being similarly treated. For example, when recommender or add-delivery systems choose best-matching strategies between user profiles and a certain type of content, there are implicit notions of similarity. Similar users should be served similar type of content, so we can easily see this index as a benchmarking tool for such technologies.