# A discrete districting plan

## TL;DR

This paper introduces a discrete, graph-based model for electoral districting aimed at understanding and optimizing district shapes to prevent gerrymandering, moving beyond traditional continuous approaches.

## Contribution

It presents a novel parameter-dependent discrete model for districting, providing a foundation for more realistic analysis of electoral boundary design.

## Key findings

- Analysis of model properties
- Foundation for further research
- Potential to improve districting fairness

## Abstract

The outcome of elections is strongly dependent on the districting choices, making thus possible (and frequent) the gerrymandering phenomenon, i.e.\ politicians suitably changing the shape of electoral districts in order to win the forthcoming elections. While so far the problem has been treated using continuous analysis tools, it has been recently pointed out that a more reality-adherent model would use the discrete geometry of graphs or networks. Here we propose a parameter-dependent discrete model for choosing an "optimal" districting plan. We analyze several properties of the model and lay foundations for further analysis on the subject.