These are methods for allocating seats in a parliament among federal states (or among political parties).
A method that fails to satisfy house-monotonicity is said to have the Alabama paradox.
In particular, large A and B had their fair share increase faster than small C. Therefore, the fractional parts for A and B increased faster than those for C. In fact, they overtook C's fraction, causing C to lose its seat, since the method examines which states have the largest remaining fraction.
This violation is known as the Alabama paradox due to the history of its discovery.
is house-monotone and satisfies both quotas if-and-only-if it is constructed recursively as follows (see mathematics of apportionment for the definitions and notation): Every coherent apportionment method is house-monotone.