  How to fairly apportion congressional seats to states has been debated for
centuries. We present an alternative perspective on apportionment, centered not
on states but "families" of state, sets of states with "divisor-method" quotas
with the same integer part. We develop ``impartial" and ``unbiased"
apportionment methods. Impartial methods apportion the same number of seats to
families of states containing the same total population, whether a family
consists of many small-population states or a few large-population states.
Unbiased methods apportion seats so that if states are drawn repeatedly from
the same distribution, the expected number of seats apportioned to each family
equals the expected divisor-method quota for that family.
