# Percolation Threshold for Competitive Influence in Random Networks

## TL;DR

This paper introduces a new model for competitive influence in networks, identifying a percolation threshold of seeded voters needed for a candidate to win, supported by theoretical analysis and experiments on random and real-world networks.

## Contribution

It presents a novel averaging influence model and establishes a percolation threshold for candidate victory in stochastic block model networks.

## Key findings

- Percolation threshold accurately predicts election outcomes in random networks.
- Theoretical thresholds closely match simulation results within 10% error.
- Model applies to both synthetic and real-world network data.

## Abstract

In this paper, we propose a new averaging model for modeling the competitive influence of $K$ candidates among $n$ voters in an election process. For such an influence propagation model, we address the question of how many seeded voters a candidate needs to place among undecided voters in order to win an election. We show that for a random network generated from the stochastic block model, there exists a percolation threshold for a candidate to win the election if the number of seeded voters placed by the candidate exceeds the threshold. By conducting extensive experiments, we show that our theoretical percolation thresholds are very close to those obtained from simulations for random networks and the errors are within $10\%$ for a real-world network.