Abstract
The influence maximization problem selects a set of seeds to initiate an optimal cascade of decisions. This paper uses parallel cascade evidence-based diffusion modelling, which views influence as a consequence of the evidence exchange between the connected actors, to investigate the temporal aspects of the social cascade propagation and effective time horizon for long-term campaign planning. Mixed-integer programming is used to explore the optimal timing of evidence injection and the ensuing network behaviour. The paper defines the notion of mid-term and long-term cascade stability and analyses the dynamics of social cascades for varied evidence discount factor values. This exploration reveals that the time horizon setting affects the optimal placement of seeds in a given problem and, hence, has to be set in a way to reflect the decision-maker's short-term or long-term goals. A Cplex-based heuristic algorithm is developed to iteratively find such a preferable cascade stability time horizon. Moreover, a conducted fractional factorial experiment reveals that the forgetfulness effect and the presence of competition significantly affect the cascade persistence. Somewhat counter-intuitively, it is discovered that a strong positive evidence can become more persistent (long-lasting) in the presence of weak opposing evidence.