Gallagher index for sociophysical models

The use of physical formalism and methods as a tool for the analysis of sociological problems became popular since the papers of Galam or Stauffer, followed by the authors of some interesting models, based often on the study of cellular automata evolution. In this paper we are going to deduce some characteristics concerning the results of elections on the basis of the multi-opinion Sznajd model. The values of interest are: Gallagher index, measuring the disproportionality of elections; the efficiency of election process measured with the possibility of government creation and government stability. The results show that it is possible to obtain some well known effects even using quite a simple model of social behaviour and that different methods of votes counting respond to different needs formulated as the aim of elections.