Opinion dynamics under electoral shocks in competitive campaigns

We propose a computational framework for modeling opinion dynamics in electoral competitions that combines two realistic features: voter memory and exogenous shocks. The population is represented by a fully-connected network of agents, each holding a binary opinion that reflects support for one of two candidates. First, inspired by the classical voter model, we introduce a memory-dependent opinion update: each agent's probability of adopting a neighbor's stance depends on how many times they agreed with that neighbor in the agent's past $m$ states, promoting inertia and resistance to change. Second, we define an electoral shock as an abrupt external influence acting uniformly over all agents during a finite interval $[t_0, t_0+\Delta t]$, favoring one candidate by switching opinions with probability $p_s$, representing the impact of extraordinary events such as political scandals, impactful speeches, or sudden news. We explore how the strength and duration of the shock, in conjunction with memory length, influence the transient and stationary properties of the model, as well as the candidates' advantage. Our findings reveal a rich dynamical behavior: memory slows down convergence and enhances system resilience, whereas shocks of sufficient intensity and duration can abruptly realign collective preferences, particularly when occurring close to the election date. Conversely, for long memory lengths or large election horizons, shock effects are dampened or delayed, depending on their timing. These results offer insights into why some sudden political events reshape electoral outcomes while others fade under strong individual inertia. Finally, a qualitative comparison with real electoral shocks reported in opinion polls illustrates how the model captures the competition between voter inertia and abrupt external events observed in actual elections.