Collective decision-making plays a central role in group-living animals and can be crucial to the survival of a group and the fitness of its members. As group-level properties emerge from individual decisions, personality variation can be a major determinant of collective behaviours. Here, we explore the relationship between personality and social interactions to explain the speed and cohesion of collective decision making during the aggregation process of the American cockroach (Periplaneta americana). We composed groups solely with shy individuals (spending a long time sheltered) or bold individuals (spending a short time sheltered) and tested them in a binary setup (arena with two shelters) for 3 consecutive days. We analysed the shelter use of individuals and groups to compare behavioural consistency among days and analyse the collective decision-making process. Contrary to the bold groups, shy groups had a faster aggregation process with more individuals sheltered mainly because shy individuals found the shelter more rapidly. Moreover, we show that personality is modulated by social interactions. We show high behavioural plasticity in bold groups, where some individuals act shy. This also suggests that learning and regulation mechanisms may take place. This study sheds some light on the implications of individual personality for collective decision making and the key role of shy individuals in gregarious species, such as P. americana.