Polarization and Consensus in a Voter Model under Time-Fluctuating Influences

We study the effect of time-fluctuating social influences on the formation of polarization and consensus in a three-party community consisting of two types of voters (leftists and rightists) holding extreme opinions, and moderate agents acting as centrists. The former are incompatible and do not interact, while centrists hold an intermediate opinion and can interact with extreme voters. When a centrist and a leftist/rightist interact, they can become either both centrists or both leftists/rightists. The population eventually either reaches consensus with one of the three opinions, or a polarization state consisting of a frozen mixture of leftists and rightists. As a main novelty, here agents interact subject to time-fluctuating external influences favouring in turn the spread of leftist and rightist opinions, or the rise of centrism. The fate of the population is determined under various scenarios, and it is shown how the rate of change of external influences can drastically affect the polarization and consensus probabilities, as well as the mean time to reach the final state.

Automated summary

This study examines the impact of time-fluctuating social influences on the formation of polarization and consensus in a three-party community. The community consists of extreme leftists, extreme rightists, and centrists with intermediate opinions. The ability of centrists to interact with extreme voters can lead to either consensus or a polarization state. An interesting aspect of this study is the introduction of time-fluctuating external influences that favor the spread of certain opinions. The results show that the rate of change of these influences greatly affects the probabilities of polarization and consensus, as well as the time taken to reach a final state.