Modeling of Political Systems using Wasserstein Gradient Flows

TL;DR

This paper introduces a mathematical model using Wasserstein gradient flows to analyze the evolution and polarization of political parties' ideologies over time, validated with real US Congress data.

Contribution

It formulates a novel gradient flow model for political systems, characterizes equilibria, and demonstrates its ability to explain polarization phenomena.

Findings

Model explains increasing polarization of political parties.

Model matches real-world ideological evolution data.

Predicts convergence of party members to similar ideologies.

Abstract

The study of complex political phenomena such as parties' polarization calls for mathematical models of political systems. In this paper, we aim at modeling the time evolution of a political system whereby various parties selfishly interact to maximize their political success (e.g., number of votes). More specifically, we identify the ideology of a party as a probability distribution over a one-dimensional real-valued ideology space, and we formulate a gradient flow in the probability space (also called a Wasserstein gradient flow) to study its temporal evolution. We characterize the equilibria of the arising dynamic system, and establish local convergence under mild assumptions. We calibrate and validate our model with real-world time-series data of the time evolution of the ideologies of the Republican and Democratic parties in the US Congress. Our framework allows to rigorously reason about various political effects such as parties' polarization and homogeneity. Among others, our mechanistic model can explain why political parties become more polarized and less inclusive with time (their distributions get "tighter"), until all candidates in a party converge asymptotically to the same ideological position.