  We consider the following problem in which a given number of items has to be
chosen from a predefined set. Each item is described by a vector of attributes
and for each attribute there is a desired distribution that the selected set
should have. We look for a set that fits as much as possible the desired
distributions on all attributes. Examples of applications include choosing
members of a representative committee, where candidates are described by
attributes such as sex, age and profession, and where we look for a committee
that for each attribute offers a certain representation, i.e., a single
committee that contains a certain number of young and old people, certain
number of men and women, certain number of people with different professions,
etc. With a single attribute the problem collapses to the apportionment problem
for party-list proportional representation systems (in such case the value of
the single attribute would be a political affiliation of a candidate). We study
the properties of the associated subset selection rules, as well as their
computation complexity.
