  Sortition is a political system in which decisions are made by panels of
randomly selected citizens. The process for selecting a sortition panel is
traditionally thought of as uniform sampling without replacement, which has
strong fairness properties. In practice, however, sampling without replacement
is not possible since only a fraction of agents is willing to participate in a
panel when invited, and different demographic groups participate at different
rates. In order to still produce panels whose composition resembles that of the
population, we develop a sampling algorithm that restores close-to-equal
representation probabilities for all agents while satisfying meaningful
demographic quotas. As part of its input, our algorithm requires probabilities
indicating how likely each volunteer in the pool was to participate. Since
these participation probabilities are not directly observable, we show how to
learn them, and demonstrate our approach using data on a real sortition panel
combined with information on the general population in the form of publicly
available survey data.
