Many social species are able to perform collective decisions and reach consensus. However, how the interplay between social interactions, the diversity of preferences among the group members and the group size affects these dynamics is usually overlooked. The collective choice between odourous and odorless shelters is tested for the following three groups of social cockroaches (Periplaneta americana) which are solitary foragers: naive (individuals preferring the odorous shelter), conditioned (individuals without preference), and mixed (combining, unevenly, conditioned, and naive individuals). The robustness of the consensus is not affected by the naive individuals' proportion, but the rate and the frequency of selection of the odorous shelter are correlated to this proportion. In mixed groups, the naive individuals act as influencers. Simulations based on the mechanisms highlighted in our experiments predict that the consensus emerges only for intermediate group sizes. The universality of these mechanisms suggests that such phenomena are widely present in social systems.

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