We consider aggregation of partially known qualitative preferences for a group of agents, considering necessary and potentially optimal choices with respect to different notions of optimality (consensus, extreme choices, Pareto optimality) and provide a theoretical characterization. We report statistics (obtained with simulations with synthetic data) about the cardinality of the sets of possible and necessarily optimal choices for the different cases. Finally we introduce preliminary ideas on a qualitative notion of fairness and on interactive elicitation.