Modelling optimism and the spread of false rumours in sociophysics.

In the recent years, physicists have given a great deal of attention to the study of social models using tools from statistical physics, dubbed sociophysics. The main purpose of sociophysics is to use results from experiments in psychology as a guide to define microscopic rules to be used in computational models of different sociological and political phenomena. A great variety of such models exist, so a "unified language" is desirable for introducing modifications. In a previous work we introduced the idea of confidence rules [A. M. Timpanaro and C. P. C. do Prado, Phys. Rev. E 80, 021119 (2009)] as a framework to introduce biases and prejudices in these models.

In this work we apply the notion of confidence rules to the Sznajd and voter models in order to study 2 different situations:
\begin{itemize}
\item Optimistic and pessimistic voters, using a rule with four opinion states that are symmetric, but interacting in a non-associative way.
\item Propagation of false rumours, using a rule with three opinion states, reminiscent of the SIR model.
\end{itemize}

We are able to explain 50-50 splits with alternance of power in the case of the optimism/pessimism model and we find distinct network signatures in the time series obtained for the rumour spreading model.