A group's collective intelligence reflects its capacity to perform well across a variety of cognitive tasks and it transcends the individual intelligence of its members. Previous research shows that group members' social sensitivity is a potential antecedent of collective intelligence, yet it is still unclear whether individual or group-level indices are responsible for the positive association between social sensitivity and collective intelligence. In a comprehensive manner, we test the extent to which both compositional (lowest and highest individual score) and compilational aspects (emergent group level) of social sensitivity are associated with collective intelligence. This study has implications for research that explores groups as information processors, and for group design as it indicates how a group should be composed with respect to social sensitivity if the group is to reach high levels of collective intelligence. Our empirical results indicate that collectively intelligent groups are those in which the least socially sensitive group member has a rather high score on social sensitivity. Differently stated, (socially sensitive) group members cannot compensate for the lack of social sensitivity of the other group members.