Artifacts of opinion dynamics at one dimension

The dynamics of a one dimensional Ising spin system is investigated using three families of local update rules, the Galam majority rules, Glauber inflow influences and Sznadj outflow drives. Given an initial density p of up spins the probability to reach a final state with all spins up is calculated exactly for each choice. The various formulas are compared to a series of previous calculations obtained analytically using the Kirkwood approximation. They turn out to be identical. The apparent discrepancy with the Galam unifying frame is addressed. The difference in the results seems to stem directly from the implementation of the local update rule used to perform the associated numerical simulations. The findings lead to view the non stepwise exit probability as an artifact of the one dimensional finite size system with fixed spins. The suitability and the significance to perform numerical simulations to model social behavior without solid constraints is discussed and the question of what it means to have a mean field result in this context is addressed.

[1]  S. Galam,et al.  Ising model versus normal form game , 2009, 0910.5139.

[2]  Serge Galam,et al.  Local dynamics vs. social mechanisms: A unifying frame , 2005 .

[3]  M. Ausloos,et al.  Coexistence of opposite opinions in a network with communities , 2007, physics/0703266.

[4]  S. Ghirlanda,et al.  Modeling society with statistical mechanics: an application to cultural contact and immigration , 2006, physics/0606062.

[5]  Guillaume Deffuant,et al.  Mixing beliefs among interacting agents , 2000, Adv. Complex Syst..

[6]  K. Sznajd-Weron,et al.  Some new results on one-dimensional outflow dynamics , 2007, 0712.2035.

[7]  Katarzyna Sznajd-Weron,et al.  Opinion evolution in closed community , 2000, cond-mat/0101130.

[8]  A. O. Sousa,et al.  Outward-inward information flux in an opinion formation model on different topologies , 2006 .

[9]  André C. R. Martins,et al.  An opinion dynamics model for the diffusion of innovations , 2008, 0809.5114.

[10]  J. Kirkwood,et al.  The Radial Distribution Function in Liquids , 1942 .

[11]  S. Fortunato,et al.  Statistical physics of social dynamics , 2007, 0710.3256.

[12]  André C R Martins,et al.  Mobility and social network effects on extremist opinions. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  S. Redner,et al.  Dynamics of non-conservative voters , 2007, 0712.0364.

[14]  Galam.  Self-consistency and symmetry in d dimensions. , 1996, Physical review. B, Condensed matter.

[15]  T. Liggett,et al.  Stochastic Interacting Systems: Contact, Voter and Exclusion Processes , 1999 .