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The ability of a society to make the right decisions on relevant matters relies on its capability to properly aggregate the noisy information spread across the individuals it is made of. In this paper we study the information aggregation performance of a stylized model of a society whose most influential individuals - the leaders - are highly connected among themselves and uninformed. Agents update their state of knowledge in a Bayesian manner by listening to their neighbors. We find analyticaldoi:10.3390/e15083031 fatcat:acl2ztmt5ndrfjmyd3bpdldazq