Effect of influence in voter models and its application in detecting significant interference in political elections

In this article, we study the effect of vector-valued interventions in votes under a binary voter model, where each voter expresses their vote as a $0-1$ valued random variable to choose between two candidates. We assume that the outcome is determined by the majority function, which is true for a democratic system. The term intervention includes cases of counting errors, reporting irregularities, electoral malpractice etc. Our focus is to analyze the effect of the intervention on the final outcome. We construct statistical tests to detect significant irregularities in elections under two scenarios, one where exit poll data is available and more broadly under the assumption of a cost function associated with causing the interventions. Relevant theoretical results on the consistency of the test procedures are also derived. Through a detailed simulation study, we show that the test procedure has good power and is robust across various settings. We also implement our method on three real-life data sets. The applications provide results consistent with existing knowledge and establish that the method can be adopted for crucial problems related to political elections.