Local acceptance and emergence of consensus in a heterogeneous small-world network of agents with and without memory

We formulate a spatiotemporal model of social interaction that explores the role of local acceptance or influence in consensus-building. It is applied to a population of interacting agents that forms a small-world Watts–Strogatz network to determine the level of consensus that emerges as a function of the local acceptance parameter α(0≤α≤1), agent memory capacity, and interaction scale. Parameter α sets the probability that an agent copies the majority state of its neighbors while (1−α) is the corresponding likelihood that it conforms with the minority state. An agent with memory may retain its present state regardless of the local state of its neighborhood. We track the emergence of global agreement in a heterogeneous population of agents with and without memory, using density metrics that correspond to three different interaction scales — entire population, neighborhoods, and pairs of agents. We have found that for a given α and population heterogeneity, the degree of agreement would depend strongly on the chosen interaction scale and network connectivity. Unlike its disordered counterpart, a homogeneous small-world network with memory, is unable to reach a simple majority of 51% over a wide range of α < 0.83. The degree of agreement then peaks towards 80% at α=0.95 before decreasing rapidly back to 50% as α→1.0. Memory prevents a heterogeneous small-world network from achieving full agreement at α=1.0, even when the agents with memory is a weak minority. All density profiles are asymmetric about α=0.5, indicating the uneven impact of copying the majority or minority state in consensus building. They are also distinct and difficult to extrapolate from each other. The model provides an adaptive platform for exploring the spatiotemporal performance of existing collective decision-making strategies either separately or in multiple combination of each other. It can be deployed to probe the possible triggers of strategy modification in adaptive social networks. We have identified its presence in animal groups that were observed while in pursuit of predefined tasks such as group emergency evacuation.