  Citizens' assemblies need to represent subpopulations according to their
proportions in the general population. These large committees are often
constructed in an online fashion by contacting people, asking for the
demographic features of the volunteers, and deciding to include them or not.
This raises a trade-off between the number of people contacted (and the
incurring cost) and the representativeness of the committee. We study three
methods, theoretically and experimentally: a greedy algorithm that includes
volunteers as long as proportionality is not violated; a non-adaptive method
that includes a volunteer with a probability depending only on their features,
assuming that the joint feature distribution in the volunteer pool is known;
and a reinforcement learning based approach when this distribution is not known
a priori but learnt online.
