Simulations to Analyze Cellular Voting Systems for Side Effects of Democratic Redistricting

TL;DR

This paper proposes a novel electoral system called democratic cellular voting to counteract gerrymandering, using simulations and advanced Markov chain models to analyze its effectiveness and stability.

Contribution

Introduces democratic cellular voting system CV0 and a new Markov chain theory using semiring algebra for modeling electoral dynamics.

Findings

Democratic cellular voting reduces effects of gerrymandering strategies.

The CV0 system maintains long-term stability in simulations.

New mathematical framework for modeling voter-district interactions.

Abstract

Motivated by the problem of partisan gerrymandering, we introduce an electoral system for a representative democracy called democratic cellular voting, designed to make modern packing and cracking strategies irrelevant by allowing districts to be influenced directly by voters through elections. We introduce an example of a democratic cellular voting system, called CV0, that is suitable for dynamic modelling. We develop a modification of the theory of discrete Markov chains using the algebraic structure of the semiring $[0,\infty]$, which is used as a space of correlation coefficients. We use this to measure voter preferences and model representatives, voters, and districts in computationally feasible models with a guarantee of long-term stability.