Beyond networks: Opinion formation in triplet-based populations

We study a process of opinion formation in a population of agents whose interaction pattern is defined on the basis of randomly distributed groups of three agents, or triplets -in contrast to networks, which are defined on the basis of agent pairs. Results for the time needed to reach full consensus are compared between a triplet-based structure with a given number of triplets and a random network with the same number of triangles. The full-consensus time in the triplet structure is systematically lower than in the network. This discrepancy can be ascribed to differences in the shape of the probability distribution for the number of triplets and triangles per agent in each interaction pattern.