Effects of inhomogeneous influence of individuals on an order-disorder transition in opinion dynamics

Kuramoto dilemma alleviated by optimizing connectivity and rationality

Recently, Antonioni and Cardillo proposed a coevolutionary model based on the intertwining of oscillator synchronization and evolutionary game theory [Phys. Rev. Lett. 118, 238301 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.238301], in which each Kuramoto oscillator can decide whether to interact or not with its neighbors, and all oscillators can receive some benefits from the local synchronization, but those who choose to interact must pay a cost. Oscillators are allowed to update their strategies according to payoff difference, wherein the strategy of an oscillator who has obtained higher payoff is more likely to be followed. Utilizing this coevolutionary model, we find that the global synchronization level reaches the highest level when the average degree of the underlying interaction network is moderate. We also study how synchronization is affected by the individual rationality in choosing strategy.

Opinion formation on social media: an empirical approach

Opinion exchange models aim to describe the process of public opinion formation, seeking to uncover the intrinsic mechanism in social systems; however, the model results are seldom empirically justified using large-scale actual data. Online social media provide an abundance of data on opinion interaction, but the question of whether opinion models are suitable for characterizing opinion formation on social media still requires exploration. We collect a large amount of user interaction information from an actual social network, i.e., Twitter, and analyze the dynamic sentiments of users about different topics to investigate realistic opinion evolution. We find two nontrivial results from these data. First, public opinion often evolves to an ordered state in which one opinion predominates, but not to complete consensus. Second, agents are reluctant to change their opinions, and the distribution of the number of individual opinion changes follows a power law. Then, we suggest a model in which agents take external actions to express their internal opinions according to their activity. Conversely, individual actions can influence the activity and opinions of neighbors. The probability that an agent changes its opinion depends nonlinearly on the fraction of opponents who have taken an action. Simulation results show user action patterns and the evolution of public opinion in the model coincide with the empirical data. For different nonlinear parameters, the system may approach different regimes. A large decay in individual activity slows down the dynamics, but causes more ordering in the system.

Local interaction scale controls the existence of a nontrivial optimal critical mass in opinion spreading

We study a model of opinion formation where the collective decision of a group is said to happen if the fraction of agents having the most common opinion exceeds a threshold value, a critical mass. We find that there exists a unique nontrivial critical mass giving the most efficient convergence to consensus. In addition, we observe that for small critical masses, the characteristic time scale for the relaxation to consensus splits into two. The shorter time scale corresponds to a direct relaxation and the longer one can be explained by the existence of intermediate metastable states similar to those found in [P. Chen and S. Redner, Phys. Rev. E 71, 036101 (2005)]. This longer time scale is dependent on the precise condition for consensus-with a modification of the condition it can go away.

Effects of social diversity on the emergence of global consensus in opinion dynamics

We propose a variant of the voter model by introducing the social diversity in the evolution process. Each individual is assigned a weight that is proportional to the power of its degree, where the power exponent alpha is an adjustable parameter that controls the level of diversity among individuals in the network. At each time step, a pair of connected individuals, say i and j , are randomly selected to update their opinions. The probability p(i) of choosing is opinion as their common opinion is proportional to i s weight. We consider the scale-free topology and concentrate on the efficiency of reaching the final consensus, which is significant in characterizing the self-organized systems. Interestingly, it is found that there exists an optimal value of alpha, leading to the shortest consensus time. This phenomenon indicates that, although a strong influence of high-degree individuals is helpful for quick consensus achievement, over strong influence inhibits the convergence process. Other quantities, such as the probability of an individual's initial opinion becomes the final opinion as a function of degree, the evolution of the number of opinion clusters, as well as the relationship between average consensus time and the network size, are also studied. Our results are helpful for better understanding the role of degree heterogeneity of the individuals in the opinion dynamics.