Collective choices and consensus resulting from the competition of positive feedbacks, are the subject of numerous studies. However, how the interindividual diversity of preferences among the group members affects these dynamics is usually overlooked apart from vertebrates based studies. Gregarism is a useful model for studying how the interindividual diversity of preferences affects the collective choices and consensus. The decision-making of three types of groups of the cockroach Periplaneta americana is tested in a choice between an odorous shelter and an odourless one: naïves (individuals showing an inherent preference towards the odorous shelter); conditioned (individuals with the preference for the odorous shelter inhibited); and mixed (a combination of conditioned individuals and a minority of naïve ones). We show that while the consensus is robust for all groups (>90% of the total population is in the same shelter), the group composition determines the rate to achieve a consensus and the frequency of selection of the odorous shelter. Indeed, increasing the proportion of naïves in the group leads to an increasing number of consensuses towards the odorous shelter and to an increasing rate to reach them. We also show that the minority of naïve individuals in mixed groups act as leaders or influencers.