| Abstract [eng] |
Models in sociophysics aim to describe real social processes with the use of agent based modelling. If the underlying assumptions of the model are too reductive, the empirical validation becomes difficult. Most of the currently developed models lack empirical validation. Some overcame this issue by accounting for spatial dynamics, i.e. migration or commuting. The need to validate with empirical data also poses challenges regarding the diversity of data. Opinion dynamics are concerned with data which are intrinsically difficult to compare, e.g. democratic elections, interactions in social networks, Eurovision voting, etc. Even though scores in these systems are uncomparable, the ranking (rank-size distributions) provide a general framework to compare such data. If ranks vary in time, rank dynamics can be analyzed. For some empirical data rank dynamics can be modelled as one-dimensional Markov processes - change of one rank over long enough period of time is enough to describe dynamics of the system. In this research we extend compartmental voter model to competing dynamics case by introducing state change and space exchange processes. The goal of this thesis is to approximate compartmental voter model with competing dynamics to one-dimensional Markov process. The main results are these: 1. Competing dynamics compartmental voter models stationary distribution of population in compartment is not necessarily distributed by Beta-binomial distribution. It is only the case for symmetric choice of idiosyncratic transition rates between states. 2. Competing dynamics compartmental voter model is well approximated by one-dimensional Fokker-Planck equation thus being a one-dimensional Markov processes. For rank dynamics, however, accounting for first two orders of Kramers-Moyal coefficients is not enough to approximate to one-dimensional Markov process. 3. First return times of ranking dynamics in the model depend on idiosyncratic transition rates and do not necessarily follow the power law of -3/2. Rank variable can change discontinuously thus leading to a jump-diffusion process, where as Fokker-Planck equation does not account for jump processes. |
