Influence maximisation and adaptive control of opinion dynamics on complex networks

Opinion shaping, by which a strategic attempts to influence the opinion of a social group, is a pervasive phenomenon in human behaviour, with clear examples in current societies in information campaigns, political competition, or marketing. However, the effect that influence attempts have in societies is not easy to foresee, as they are complex systems where interactions can cascade and compound in unpredictable ways. The research subfield of opinion dynamics employs a mathematical modelling approach to study these phenomena using tools from the more general field of complex systems. In this approach, the opinions held by an individual are typically modelled as mathematical variables, with changes in opinion dictated by simple rules triggering upon interactions, which typically only happen interact according to a complex network that reflects their social structure. By drawing from techniques from statistical physics, agent–based simulations, and optimisation research, this thesis studies the effects that different external control strategies have on opinion formation processes.

We first focus on a case where the external controller is a ‘perfect optimiser’, i.e. they can split their influence targets among the individuals and have information to do so strategically as to achieve the best possible result — a problem commonly known as Influence Maximisation. We place this optimising controller against an opponent in a scenario where individuals have preferences over two possible choices (e.g. products or political parties), propose an optimisation algorithm to find optimal targetting strategies, and analyse the characteristics of these to understand why they are effective. We find that optimal strategies can be characterised by two heuristics, shadowing and shielding, while the structure of the network only plays a secondary role. Shadowing entails targeting the same individuals as the opponent to directly block her influence in the network, unless the opponent’s influencing power is much higher, in which case these are avoided. Shielding entails ring–fencing the individuals targeted by the opponent to indirectly block the spreading of her influence. We then modify the previous scenario to incorporate different levels of bias against either opinion in individuals, and analyse optimal targetting strategies when the population is structured in different network topologies. We find a general pattern in which individuals that are difficult to control (i.e. biased against the controller, highly connected, or targeted by the opponent) are avoided if the influencing power is small and sought if the influencing power is high.

Last, we shift the scenario to one in which the controllers are not ‘perfect optimisers’ any more but only have very limited information and perform local moves to improve their situation in the short term. Therefore, their control strategies are ‘adaptive’, reacting to the dynamics of the opinions as they unfold and creating a dynamic interaction between the two. We focus on the specific agenda–setting scenario where political parties seek to increase votes by affecting the importance that different political dimensions have and how their strategies interferes with the process of arriving at consensus or polarisation within the social group. We find in this scenario that party competition often fosters the arrival of a polarised state with most individuals gathering in two opposed camps, although if parties perform frequent shifts in the issues they give importance to, their behaviour inadvertently fosters the arrival at a consensus in opinion in social group.