Quantifying Fairness

Abstract: $\textit{Quantitative justice}$ comprises an emergent research field addressing real world problems of societal inequity via the development of new and robust mathematical, computational, and statistical approaches. In this context, mathematical tools are used to quantify notions of ``fairness'' in a given domain, generating both new mathematics and impacting society at large. Intense public debate and increasingly available computational resources have focused significant interest on fairness in redistricting in recent years. Here the notion of shape is ubiquitous when investigating the political geography of a state. In this talk we will motivate the use of metrics as a tool for shape comparison. By representing an object as a finite metric space, we can utilize families of metrics like Hausdorff and Gromov-Hausdorff distances to develop similarity measures between shapes. In particular, we will discuss how metrics were used in a recent effort to quantify the idea of ‘communities of interest’ in the most recent redistricting cycle.

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