House monotonicity[1]: 134–141 (also called house-size monotonicity[2]) is a property of apportionment methods. These are methods for allocating seats in a parliament among federal states (or among political parties). The property says that, if the number of seats in the "house" (the parliament) increases, and the method is re-activated, then no state (or party) should have fewer seats than it previously had. A method that fails to satisfy house-monotonicity is said to have the Alabama paradox.
In the context of committee election, house monotonicity is often called committee monotonicity. It says that, if the size of the committee increases, then all the candidate that were previously elected, are still elected.
House monotonicity is the special case of resource monotonicity for the setting in which the resource consists of identical discrete items (the seats).
^Balinski, Michel L.; Young, H. Peyton (1982). Fair Representation: Meeting the Ideal of One Man, One Vote. New Haven: Yale University Press. ISBN 0-300-02724-9.
^Pukelsheim, Friedrich (2017), Pukelsheim, Friedrich (ed.), "Securing System Consistency: Coherence and Paradoxes", Proportional Representation: Apportionment Methods and Their Applications, Cham: Springer International Publishing, pp. 159–183, doi:10.1007/978-3-319-64707-4_9, ISBN 978-3-319-64707-4, retrieved 2021-09-02
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Alabama paradox gave rise to the axiom known as housemonotonicity, which says that, when the house size increases, the allocations of all states should...
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change, the rule would still select x. Limit monotonicity (inspired by resource monotonicity and housemonotonicity) says that, if a rule selects project x...
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great town house, by its large size and design, accentuated its owner's power by its contrast with the monotony of the smaller terraced houses surrounding...
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irrelevant alternatives (like most other vote-based ordering systems) and monotonicity. The relative performance of political parties in STV systems is sometimes...
8859-7 and Unicode. ISO 8859-7 supports only the monotonic orthography; Unicode supports both the monotonic and polytonic orthographies. For the range A0–FF...
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