Combining Blotto Networks and Voter Models to Simulate Voter Behavior in Response to Competitive Election Spending

TL;DR

The paper formalizes a Voter-Blotto framework that combines the Voter Model with the Blotto Game to study how competitive spending interacts with networked voter dynamics on Small World graphs. It defines a logistic boost mechanism, $C = \frac{1}{1 + e^{-k(r_1/r_2 - 1.5)}}$, linking resource allocations to updating rules and analyzes convergence and polarization via large-scale simulations and heatmaps. Key findings show that density, clustering, and degree centrality strongly shape convergence behavior and winnability, with denser, less clustered networks and lower maximum degree generally yielding more favorable, controllable outcomes for campaigns. The work also proposes several resource-allocation strategies and outlines avenues for AI-driven improvements, including random forests and reinforcement learning, to predict convergence and optimize strategy, highlighting practical implications for targeted political advertising and information campaigns.

Abstract

In the past, the Voter Model has been explicitly used to model the impact of propaganda on a dynamic, interconnected population, and certain factors have been identified that influence the behavior of voters when under outside influence. The Blotto Game has also been explicitly used to study information wars between two opposing parties, whether in regards to a political issue or advertising war. Both the graph theory behind the Voter Model and the game theory aspects of the Blotto Game are relevant to the behavior of voters or consumers when they are under the influence of competing propaganda campaigns, and for this reason both are useful to understand the most effective spending strategy. In this project, we seek to combine the two problems into a Voter-Blotto Game and examine what components of the graph most effect its value in the eyes of the competing players.