Opinion dynamics and wisdom 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 may state an opinion that differs from their true opinion. The incentive to do so is induced by agents' preferences for conformity. We model opinion formation as a dynamic process and identify conditions for convergence to a 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 study how conformity affects the efficiency of information aggregation or the ``wisdom'' of the society. We show that the society becomes wiser, in the sense of a smaller mean squared error of their estimate, if players who are well informed (relative to their network importance) are less conform, while uninformed players (relative to their network importance) conform more with their neighbors.