# A Stochastic Binary Opinion Model: Opinion Dominance vs. Balance

## TL;DR

This paper introduces a stochastic binary opinion model analyzing how individual personalities influence the long-term balance or dominance of opinions in large groups.

## Contribution

It presents a novel Markov process framework for opinion dynamics incorporating personality traits and examines long-term opinion distributions.

## Key findings

- Long-term probabilities depend on group personalities.
- Balance occurs when opinions are nearly equally present.
- Dominance occurs when one opinion prevails.

## Abstract

We propose and study a stochastic binary opinion model where agents in a group are considered to hold an opinion of 0 or 1 at each moment. An agent in the group updates his/her opinion based on the group's opinion configuration and his/her \emph{personality}. Considering the number of agents with opinion 1 as a continuous time Markov process, we analyze the long-term probabilities for large population size in relation to the personalities of the group. In particular, we focus on the question of ``balance'' where both opinions are present in nearly equal numbers as opposed to ``dominance'' where one opinion is present in a greater number.