# A model of anonymous influence with anti-conformist agents

## TL;DR

This paper introduces a stochastic social influence model incorporating conformist and anti-conformist agents, analyzing how their interactions lead to various societal opinion dynamics including polarization, cycles, and opinion reversal.

## Contribution

It provides a comprehensive qualitative analysis of opinion convergence in societies with mixed conformist and anti-conformist agents under different aggregation rules.

## Key findings

- Anti-conformists induce polarization and instability.
- Presence of anti-conformists can cause opinion reversal.
- Identifies conditions for stable and unstable opinion states.

## Abstract

We study a stochastic model of anonymous influence with conformist and anti-conformist individuals. Each agent with a `yes' or `no' initial opinion on a certain issue can change his opinion due to social influence. We consider anonymous influence, which depends on the number of agents having a certain opinion, but not on their identity. An individual is conformist/anti-conformist if his probability of saying `yes' increases/decreases with the number of `yes'-agents. We focus on three classes of aggregation rules (pure conformism, pure anti-conformism, and mixed aggregation rules) and examine two types of society (without, and with mixed agents). For both types we provide a complete qualitative analysis of convergence, i.e., identify all absorbing classes and conditions for their occurrence. Also the pure case with infinitely many individuals is studied. We show that, as expected, the presence of anti-conformists in a society brings polarization and instability: polarization in two groups, fuzzy polarization (i.e., with blurred frontiers), cycles, periodic classes, as well as more or less chaotic situations where at any time step the set of `yes'-agents can be any subset of the society. Surprisingly, the presence of anti-conformists may also lead to opinion reversal: a majority group of conformists with a stable opinion can evolve by a cascade phenomenon towards the opposite opinion, and remains in this state.