Bert O. Baumgaertner | Searcharxiv

arXiv2018

Spatial Opinion Dynamics and the Effects of Two Types of Mixing

Spatially-situated opinions that can be held with different degrees of conviction lead to spatio-temporal patterns such as clustering (homophily), polarization, and deadlock. Our goal is to understand how sensitive these patterns are to changes in the local nature of interactions. We introduce two different mixing mechanisms, spatial relocation and non-local interaction ("telephoning"), to an earlier fully spatial model (no mixing). Interestingly, the mechanisms that create deadlock in the fully spatial model have the opposite effect when there is a sufficient amount of mixing. With telephoning, not only is polarization and deadlock broken up, but consensus is hastened. The effects of mixing by relocation are even more pronounced. Further insight into these dynamics is obtained for selected parameter regimes via comparison to the mean-field differential equations.

cs.SI↗

arXiv2016

Voter Models and External Influence

In this paper, we extend the voter model (VM) and the threshold voter model (TVM) to include external influences modelled as a jump process. We study the newly-formulated models both analytically and computationally, employing diffusion approximations and mean field approximations. We derive results pertaining to the probability of reaching consensus on a particular opinion and also the expected consensus time. We find that although including an external influence leads to a faster consensus in general, this effect is more pronounced in the VM as compared to the TVM. Our findings suggest the potential importance of "macro-level" phenomena such as the external influences as compared to "micro-level" local interactions.

physics.soc-ph↗