Martina Alutto

Martina Alutto, Lorenzo Zino, Karl H. Johansson et al.

Leadership in social groups emerges dynamically through interaction and opinion exchange. Empirical evidence indicates that individuals expressing strong opinions tend to gain influence, while sustained leadership critically depends on maintaining alignment with the surrounding social context. Motivated by these observations, we introduce a coupled dynamical model describing the simultaneous evolution of opinions and leadership in a networked population. Extending the Friedkin-Johnsen framework, we represent leadership as a time-varying susceptibility to social influence, which evolves according to a game-theoretic mechanism, consistent with social psychology evidence. Within this setting, agents strengthen their leadership by expressing decisive yet socially coherent opinions, whereas misalignment with the collective state results in a loss of influence. We analyze the coupled dynamics and establish sufficient conditions to identify which agents necessarily emerge as leaders and which act as followers in the social network.

Martina Alutto, Lorenzo Zino, Karl H. Johansson et al.

Leadership in social groups is often a dynamic characteristic that emerges from interactions and opinion exchange. Empirical evidence suggests that individuals with strong opinions tend to gain influence, at the same time maintaining alignment with the social context is crucial for sustained leadership. Motivated by the social psychology literature that supports these empirical observations, we propose a novel dynamical system in which opinions and leadership co-evolve within a social network. Our model extends the Friedkin-Johnsen framework by making susceptibility to peer influence time-dependent, turning it into the leadership variable. Leadership strengthens when an agent holds strong yet socially aligned opinions, and declines when such alignment is lost, capturing the trade-off between conviction and social acceptance. After illustrating the emergent behavior of this complex system, we formally analyze the coupled dynamics, establishing sufficient conditions for convergence to a non-trivial equilibrium, and examining two time-scale separation regimes reflecting scenarios where opinion and leadership evolve at different speeds.