Fast convergence in language games induced by majority rule

We propose a simple model to investigate the evolutionary dynamics of a naming game on well-mixed populations. We assume that each individual has an inherent propensity to maintain his own word about an object whereas other individuals would affect his decision when they communicate. On the one hand, individuals learn the word of another one with a probability pertaining to their propensities. On the other hand, the focal individual would adopt the word held by the majority in a randomly selected group. We have numerically explored how dynamical behavior evolves as a result of combination of these two competing update patterns. A parameter governs the time scale ratio at which the two update patterns separately progress. We find that an increasing tendency to adopt the word held by the majority results in a rapid extinction of most words, thus more easily induces the system to a global consensus. Large initial probabilities denoting propensity are found to be unfavorable for the achievement of the consensus. Interestingly, simulation results indicate that the convergence time is negligibly affected by the number of initial distinct words when this number exceeds a certain value. Results from our model may offer an insight into better understanding the intricate dynamics of naming games.