https://doi.org/10.1140/epjb/e2003-00278-0
Analytical results for the Sznajd model of opinion formation
1
Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 18221 Praha, Czech Republic
2
Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Břehová 7, 11519 Praha 1, Czech Republic
Corresponding author: a slanina@fzu.cz
Received:
17
April
2003
Revised:
21
July
2003
Published online:
2
October
2003
The Sznajd model, which describes opinion formation and social influence, is treated analytically on a complete graph. We prove the existence of the phase transition in the original formulation of the model, while for the Ochrombel modification we find smooth behaviour without transition. We calculate the average time to reach the stationary state as well as the exponential tail of its probability distribution. An analytical argument for the observed 1/n dependence in the distribution of votes in Brazilian elections is provided.
PACS: 89.65.-s – Social and economic systems / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.50.-r – Probability theory, stochastic processes, and statistics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2003
