Trade-offs in Fair Redistricting

What constitutes a 'fair' electoral districting plan is a discussion dating back to the founding of the United States and, in light of several recent court cases, mathematical developments, and the approaching 2020 U.S. Census, is still a fiercely debated topic today. In light of the growing desire and ability to use algorithmic tools in drawing these districts, we discuss two prototypical formulations of fairness in this domain: drawing the districts by a neutral procedure or drawing them to intentionally induce an equitable electoral outcome. We then generate a large sample of districting plans for North Carolina and Pennsylvania and consider empirically how compactness and partisan symmetry, as instantiations of these frameworks, trade off with each other -- prioritizing the value of one of these necessarily comes at a cost in the other.