I need help defining a sampling procedure. Here is problem the set up:
I have a population consisting of 50 sets of different sizes. Each set contains instances belonging to one of two classes: $C_1$ or $C_2$. Note that each set contains elements from both classes. In one of the classes, say $C_1$, the instances, by definition, appear in multiple sets. In the other, $C_2$, the instances, by definition, are unique to which ever set they are in.
I would like to draw a sample from this population. The two constraints are: 1) that the distribution of samples drawn from each set be close to uniform and 2) that the number of samples drawn from each set be maximized, given constraint 1).