Predicting Voting Outcomes in the Presence of Communities, Echo Chambers and Multiple Parties

TL;DR

This paper evaluates the effectiveness of the influence gap metric in predicting multi-party election outcomes on complex networks with community structures, finding that initial votes often outperform influence gap as predictors.

Contribution

It extends the influence gap metric to multi-party elections and analyzes its predictive power in networks with community structures and varying homophily levels.

Findings

Influence gap is less effective when no clear initial majority exists.

Counting initial votes generally predicts outcomes better than influence gap.

Initial votes have higher predictive power in multi-party elections.

Abstract

A recently proposed graph-theoretic metric, the influence gap, has shown to be a reliable predictor of the effect of social influence in two-party elections, albeit only tested on regular and scale-free graphs. Here, we investigate whether the influence gap is able to predict the outcome of multi-party elections on networks exhibiting community structure, i.e., made of highly interconnected components, and therefore more resembling of real-world interaction. To encode communities we build on the classical model of caveman graphs, which we extend to a richer graph family that displays different levels of homophily, i.e., how much connections and opinions are intertwined. First, we study the predictive power of the influence gap in the presence of communities. We show that when there is no clear initial majority the influence gap is not a good predictor of the election outcome. When we instead allow for varying majorities, although the influence gap improves as a predictor, counting the initial partisan majority does consistently better, across all levels of homophily. Second, we study the combined effect of the more predictive metrics, as function of the homophily levels. Using regression models, we demonstrate that the influence gap combined with the initial votes count does increase the overall predictive power for some levels of homophily. Third, we study elections with more than two parties. Specifically, we extend the definition of the influence gap to any number of parties, considering various generalisations, and show that the initial votes count has an even higher predictive power when compared to influence gap than it did in the two-party case.