Grzegorz Lisowski (Warwick) - Viva Special

Title: An Algorithmic Analysis of Deliberation and Representation in Collective Behaviour

Abstract: The selection of a nominee by a group of players in the process of selecting a winner is present in many contexts. In sports, it is a major strategic problem to select the best team members. Crucially, in politics, this problem is essential for the process of primaries. We study the strategic behaviour of coalitions from the game-theoretic perspective. More precisely, we analyse the existence of a pure Nash equilibrium in the games capturing the strategic nomination problem. First, we adapt the well-known Hotelling-Downs model, capturing the strategic behaviour of political parties in primaries. Subsequently, we explore this problem for tournament-based rules. Nominee selection can also be influenced by the deliberation between the voters. To account for that, we investigate the complexity of checking the convergence of a synchronous, threshold-based protocol. Furthermore, we explore computational aspects of majority illusion, which occurs when a large number of agents in a network perceives the opinion, which is a minority view, as the one which is held by the majority of agents.