@GrottoGuazziniBagnoli; @GuazziniCiniBagnoliRamasco; @ViloneCarlettibagnoliGuazzini]. Many such models adopt an approach similar to that of the Ising model. In such cases one has two opinions, say A and B or -1 and 1, and one is interested in the establishment of a majority (magnetic phase transitions) or in the effects of borders, or in the influence of some leader (social impact theory) [@latane]. This opinion space can be seen as the first ingredient of these models.

The second ingredient is how to model the response to an external influence. It is common to classify the attitude of people (agents) as either conformist or contrarian (also known as nonconformist). A conformist tends to agree with his neighbors and a contrarian to disagree.

It is also easy to map this attitude onto Ising terms: conformist agents correspond to ferromagnetic coupling and contrarians to antiferromagnetic ones [@review]. The effects induced by the presence of contrarian agents in a society have been studied in models related to the voter model [@masuda2013; @crokidakis2014; @Independence; @schneider2004; @delalama2005; @corcos02; @galam04; @Biswas; @Galam-Gemrev; @Galam-chaotic; @sudoyi2013; @bagnoli2013; @bagnoli2015].

In general, agents that are under a strong social pressure tend to agree with the great majority even when they are certain that 