Abstract
Social groups of interacting agents display an ability to coordinate in the absence of a central authority, a phenomenon that has been recently amplified by the widespread availability of social networking technologies. Models of opinion formation in a population of agents have proven a very useful tool to investigate these phenomena that arise independently of the heterogeneities across individuals and can be used to identify the factors that determine whether widespread consensus on an initial small majority is reached. Recently, we introduced a model in which individual agents can have conservative and partisan biases. Numerical simulations for finite populations showed that while the inclusion of conservative agents in a population enhances the population's efficiency in reaching consensus on the initial majority opinion, even a small fraction of partisans leads the population to converge on the opinion initially held by a minority. To further understand the mechanisms leading to our previous numerical results, we investigate analytically the noise driven transition from a regime in which the population reaches a majority consensus (efficient), to a regime in which the population settles in deadlock (non-efficient). We show that the mean-field solution captures what we observe in model simulations. Populations of agents with no opinion bias show a continuous transition to a deadlock regime, while populations with an opinion bias, show a discontinuous transition between efficient and partisan regimes. Furthermore, the analytical solution reveals that populations with an increasing fraction of conservative agents are more robust against noise than a population of naive agents because in the efficient regime there are relatively more conservative than naive agents holding the majority opinion. In contrast, populations with partisan agents are less robust to noise with an increasing fraction of partisans, because in the efficient regime there are relatively more naive agents than partisan agents holding the majority opinion.
Highlights
An intriguing feature of social groups is the ability of interacting agents to efficiently coordinate in the absence of a central authority
We recently introduced a model in which agents may have conservative or partisan biases toward one of the two possible opinions
While all types of agents may change their state in response to peer pressure, a partisan agent will defect back to his preferred state if peer pressure decreases below a threshold value
Summary
An intriguing feature of social groups is the ability of interacting agents to efficiently coordinate in the absence of a central authority. We recently introduced a model in which agents may have conservative or partisan biases toward one of the two possible opinions These agents update their opinions using a modified local majority rule that takes into account the potential effect of noise in the communication channel and the personal bias of each agent [9,10]. The theoretical study of consensus formation in a population has received attention in the modeling community, especially because simple spin models already display consensus formation in a similar way to that observed in real social systems In such systems, agents(spins) can hold two possible opinions z1 or {1 and update their opinions according to some rule. If one organizes the population into loosely connected topological communities, each community may reach their own independent consensus [17,18]
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