This thesis investigates how collective opinions evolve in social networks, focusing on two crucial, real-world factors: individual stubbornness and antagonistic inter-actions. Classical models of opinion dynamics typically assume a cooperative environment, where all individuals collaborate to reach an agreement, causing opinions to naturally draw closer to each other. However, many real-world scenarios—from political debates to online discussions—are defined by stubbornness, where individuals resist changing their stance, and by rivalry or distrust, which can actively push opinions apart.

We address these phenomena through the framework of signed networks, which explicitly encodes antagonistic relationships. Unlike models that rely on structural balance—a clean division into two opposing camps—we adopt a repelling interaction mechanism, treating negative ties as additive repulsive forces. This approach offers a more flexible and realistic representation of complex, unbalanced social structures.

The first contribution is a thorough analysis of the signed Friedkin–Johnsen (SFJ) model, which combines stubborn attachment to initial opinions with antagonistic interactions. This combination fundamentally changes system behavior: while the classical FJ model is always stable, the SFJ model can diverge. Therefore, we establish sufficient stability conditions and show that even when the model is stable, antagonism allows opinions to escape the the convex hull of the initial opinions, meaning that agents can adopt positions more extreme than anyone held at the start.

The thesis then examines repeated discussions through a concatenated SFJ model, reflecting scenarios such as a series of negotiations. Here, stability in an individual discussion does not imply stability for the repeated process. Two distinct behaviors emerge when the individual discussion rounds are stable: opinions may temporarily move apart before reconverging to consensus inside the convex hull, or they may drift farther apart with each round, leading to divergence. The first case corresponds to a transient amplification, which is a known consequence of non-normal matrices and is often referred to as reactivity. Given these possibilities, we provide sufficient stability conditions for the concatenated SFJ model. This analysis is extended to explore the dynamics in more complex scenarios, including time-varying interaction structures and bipartite (two-camp) networks.

Next, we address multidimensional opinion dynamics models, where agents debate several interdependent topics (for example, climate policy is inherently linked to economic policy). We show that a set of topics that would be stable if discussed independently can become unstable and diverge when discussed together. The analysis of repeated (concatenated) multidimensional interactions reveal diverse outcomes, from full or partial or bipartite consensus to divergence.

Finally, we shift the focus from opinion convergence to the quality of resulting collective judgement and study the wisdom of crowds problem, i.e., analyze the conditions under which a group’s aggregated opinion becomes more accurate due to collective interactions. The improvement of wisdom depends entirely on the allocation of the social power vector—the centrality measure that each individual has in the group. In classical cooperative systems, the social power vector is positive, which confines the concentration region (the set of allocations that improve wisdom) to a simplex. In contrast, signed networks allow for negative social powers, which expands the concentration region beyond the simplex, to a hyperplane. The analysis on signed networks also leads to a critical insight: agreement does not imply accuracy. The group can become confidently wrong—converging with high certainty to a false truth. We also analyze the case where the agents’ initial opinions are correlated, and characterize the new concentration regions and their properties under these conditions.