A reapportionment in which an increase
in the total number of seats results in a loss of seats
for some state is called the Alabama paradox.
When there is a fixed number of seats,
a reapportionment that causes a state to lose a seat to
another state even though the percent increase in the
population of the state of the state that loses the seat
is larger than the percent increase of the state that
wins the seat is called the population paradox.
A reapportionment in which an increase
in the total number of seats causes a shift in the apportionment
of the existing states is called the new states paradox.
Any apportionment plan that does not
violate the quota rule must produce paradoxes. Recall,
the quota rule says that the number assigned to
each represented unit must be either the standard quota
rounded down to the nearest integer, or the standard quota
rounded up to the nearest integer. Also, any apportionment
plan that does not produce paradoxes must violate the
quota rule.
