Document Type
Article
Publication Date
10-14-2026
Abstract
We introduce a framework for assessing fairness in electoral outcomes based on a new notion of representational power that determines a group's power as a combination of its size and how advantageously its voters are situated given the electoral rules. The framework is adaptable to a variety of contexts, and it produces intuitive results. When applied to redistricting, we call the measure the geographic representational baseline. The new measure is deterministic, accessible to non-experts, and relatively simple to calculate. The results generated by the new method are overall mutually reinforcing with those of a variety of ensemble methods for partisan seat allocations. However, in the context of determining numbers of majority-minority districts, race-blind ensembles can produce dramatically fewer such districts than extant maps. We show that the race-neutral, but not race-blind, approach of the geographic representational baseline provides an alternative that tracks extant maps very closely overall while also suggesting modest increases in minority representation for nearly all groups at the U.S. Congressional, state senate, and state house levels. We further show that the new method provides an indirect method for measuring residential segregation in U.S. states at the scale of a legislative district.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Rights
Licensed to Smith College and distributed CC-BY 4.0 under the Smith College Faculty Open Access Policy.
Version
Author's Submitted Manuscript
Recommended Citation
Barton, Jeffrey, "Representational Power as a Framework for Fairness with Applications to Redistricting" (2026). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/218