A general model of binary opinions updating

We generalise Grabisch and Rusinowska (2013) to non-conformist societies. Agents in a network are iteratively picking a yes/no opinion, where updating stems from mutual influence. We introduce a notion of groups based on the signs of influence. We examine a few canonical societies, namely, conformist, communitarian, with leaders, with anti-conformist agents. We investigate stability issues. Any kind of opinion updating model can be hosted by our formalism, provided that: (i) alternatives are binary; (ii) opinion adoption is reversible and independent among agents; (iii) the process is Markovian and stationary; (iv) the number of agents is finite; (v) time is discrete.