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.