Apportionment method criteria

State-population monotonicity

State-population monotonicity is a property of apportionment methods, which are methods of allocating seats in a parliament among federal states. The property says that, if the population of a state increases faster than that of other states, then it should not lose a seat. An apportionment method that fails to satisfy this property is said to have a population paradox. In the apportionment literature, this property is simply called population monotonicity. However, the term "population monotonicity" is more commonly used to denote a very different property of resource-allocation rules: * In resource allocation, the property relates to the set of agents participating in the division process. A population-increase means that the previously-present agents are entitled to fewer items, as there are more mouths to feed. See population monotonicity for more information. * In apportionment, the property relates to the population of an individual state, which determines the state's entitlement. A population-increase means that a state is entitled to more seats. The parallel property in fair division is called weight monotonicity: when the "weight" (- entitlement) of an agent increases, his utility should not decrease. There are several variants of the state-population monotonicity (PM); see mathematics of apportionment for definitions and notation. (Wikipedia).

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