Navigating the Lobbying Landscape: Insights from Opinion Dynamics Models

While lobbying has been demonstrated to have an important effect on public opinion and policy making, existing models of opinion formation do not specifically include its effect. In this work we introduce a new model of lobbying-driven opinion influence within opinion dynamics, where lobbyists can implement complex strategies and are characterised by a finite budget. Individuals update their opinions through a learning process resembling Bayes-rule updating but using signals generated by the other agents (a form of social learning), modulated by under-reaction and confirmation bias. We study the model numerically and demonstrate rich dynamics both with and without lobbyists. In the presence of lobbying, we observe two regimes: one in which lobbyists can have full influence on the agent network, and another where the peer-effect generates polarisation. When lobbyists are symmetric, the lobbyist-influence regime is characterised by prolonged opinion oscillations. If lobbyists temporally differentiate their strategies, frontloading is advantageous in the peer-effect regime, whereas backloading is advantageous in the lobbyist-influence regime. These rich dynamics pave the way for studying real lobbying strategies to validate the model in practice.