We consider a simple model of interacting agents, each holding an opinion about herself and the others. This model is the opinion propagation submodel of [1]. During random encounters by pairs, agents modify their opinions under the noisy influence of others. The influence is attractive and agents’ opinions are more strongly attracted by the opinions of whom they value higher than themselves and vice versa. We focus on two unexpected emerging patterns: (1) Starting from zero, agents’ opinions tend to grow and then their average stabilizes at a significantly positive value, implying each agent benefit from a positive consensus (see the red columns on the fig.1 on the left); (2) When introducing gossips, this pattern is inverted; the opinions tend to decrease and stabilize on average at a negative value, then a majority of agents is seen negatively (blue columns on the fig.1 on the right). With the aim to disclose the mechanisms behind the emergence of these patterns, we study simplified settings where the opinions about only one agent change whereas the self-opinions of the others are fixed. This allows us to show that the patterns’ emergence is related to both the amplitude of the fluctuations on the agent’s self-opinion, responsible for a positive bias, and the amplitude of the fluctuations on the others’ opinions on her, responsible for a negative bias. The gossips increase the negative bias on the opinions about others and can overcome the positive bias on self-opinions, which otherwise dominates.
