Hidden quantization phenomenon in the sznajd model with initial structure

Random initial conditions are extensively used in sociophysics models. However, hierarchically organized setups were recently used, producing interesting results which are not seen in the random case. We deepen those previous works by studying an opinion dynamics model where there are two initial opposing ideological groups and a third emergent party. We assume the same amount of adherents for each initial party and focus on varying the degree of their structure. Here we introduce a new approach that uses ternary diagrams as a tool to visualize phenomena that are otherwise hidden in conventional observables (e.g., parties’ probability of winning). We were able, through these diagrams, to unveil the presence of adherence quantization when the system is highly structured. We deduce an analytical expression finding an excellent agreement with simulated results. The explanation for this quantization is based on a new type of interaction, not between individuals, but among groups of individuals.