What do leaders know?

The ability of a society to make the right decisions on relevant matters relieson its capability to properly aggregate the noisy information spread across the individualsof which it is made. In this paper, we study the information aggregation performance ofa stylized model of a society, whose most influential individuals-the leaders-are highlyconnected among themselves and uninformed. Agents update their state of knowledge in aBayesian manner by listening to their neighbors. We find analytical and numerical evidenceof a transition, as a function of the noise level in the information initially available toagents, from a regime where information is correctly aggregated, to one where the populationreaches consensus on the wrong outcome with finite probability. Furthermore, informationaggregation depends in a non-trivial manner on the relative size of the clique of leaders, withthe limit of a vanishingly small clique being singular. © 2013 by the authors.