Opinion Dynamics under Conformity

We present a model of opinion formation where individuals repeatedly engage in discussion and update their opinion in a social network similarly to the DeGroot model. Abstracting from the standard assumption that individuals always report their opinion truthfully, agents in our model interact strategically in the discussion such that their stated opinion can differ from their true opinion. The incentive to do so is induced by agents’ preferences for conformity. Highly conforming agents will state an opinion which is close to their neighbors’ while agents with low level of conformity may be honest or even overstate their opinion. We model opinion formation as a dynamic process and identify conditions for convergence to consensus. Studying the consensus in detail, we show that an agent’s social influence on the consensus opinion is increasing in network centrality and decreasing in the level of conformity. Thus, lower conformity fosters opinion leadership. Moreover, assuming that the initial opinion is a noisy signal about some true state of the world, we consider the mean squared error of the consensus as an estimator for the true state of the world. We show that a society is “wise”, i.e. the mean squared error is smaller, if players who are well informed are less conform, while uninformed players conform more with their neighbors.