Opinion propagation in scale free networks

Author(s)

André Martin Timpanaro

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2012-10-05

Examining board members

Carmen Pimentel Cintra do Prado; Marcus Aloizio Martinez de Aguiar; Ibere Luiz Caldas; Eduardo Colli; Thierry Corrêa Petit Lobão

• Advisor: Carmen Pimentel Cintra do Prado

Abstract

In the recent years, a great number of opinion propagation models were proposed, motivated by the increasing interest among physicists in interdisciplinary problems, not only in sociology, but also in economics and biology. One of the goals of this work is to unify some of these models under a same formulation. In order to do that, we generalized the notion of bounded confidence to what we called confidence rules, that can be interpreted as the introduction of biases and prejudices in the interactions among agents holding differing points of view. Using this formulation, we decided to study how models that locally breed conformity (what is in accordance with experiments conducted by psichologists for small groups) could sustain diversity globally (explaining the persistence of different points of view in societies, for example). We studied the mean field version of the voter model and of variants of the Sznajd model. We used dynamical systems techniques and were able to solve analytically the qualitative behaviour of the models in the absence of noise and developed a perturbation theory for the Sznajd model with infinitesimal noise, that yielded a partial picture of the behaviour with noise. In the absence of noise, we found that the voter model has a completely different behaviour, while the other models have essentially the same behaviour. We also did simulations in Barabási-Albert and Watts-Strogatz networks for the voter and the Sznajd models and we collaborated with the research group of the Institute for Complex Systems and Mathematical Biology from the University of Aberdeen, studying a biodiversity model that can be seen as a modification of the voter model in a square lattice. Our conclusions point that the mean field results can be understood through connections with graph theory problems and that the different models that were simulated, in some sense, have the same behaviour, reinforcing the idea of universality for these models (due to the obvious difficulties in modelling human beings in a reliable and realistic way, some degree of universality in human behaviour is actually essential, in order for social modelling to be feasible). Roughly speaking, in all the systems that were studied, the coexistence or not of differing opinions, seems to depend more strongly on the network and on the type of confidence rule used, than in other specific details of the model. (AU)

• FAPESP's process: 07/03321-1 - Opinion propagation in scale-free networks
• Grantee: André Martin Timpanaro
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)