Population monotonicity (PM) is a principle of consistency in allocation problems. It says that, when the set of agents participating in the allocation changes, the utility of all agents should change in the same direction. For example, if the resource is good, and an agent leaves, then all remaining agents should receive at least as much utility as in the original allocation.[1]: 46–51 [2]
The term "population monotonicity" is used in an unrelated meaning in the context of apportionment of seats in the congress among states. There, 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. This different property is described in the page state-population monotonicity.
^Herve Moulin (2004). Fair Division and Collective Welfare. Cambridge, Massachusetts: MIT Press. ISBN 9780262134231.
^Thomson, William (2011). Fair Allocation Rules. Handbook of Social Choice and Welfare. Vol. 2. pp. 393–506. doi:10.1016/s0169-7218(10)00021-3. ISBN 9780444508942.
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Populationmonotonicity (PM) is a principle of consistency in allocation problems. It says that, when the set of agents participating in the allocation...
divisor methods satisfy populationmonotonicity, i.e. voting for a party can never cause it to lose seats. Such population paradoxes occur by increasing...
The participation criterion, also called vote or populationmonotonicity, is a voting system criterion that says that a candidate should never lose an...
to 5 over the 2,000-year period), but not strictly monotonic: A noticeable dip in world population is assumed due to the Black Death in the mid-14th century...
Resource monotonicity (RM; aka aggregate monotonicity) is a principle of fair division. It says that, if there are more resources to share, then all agents...
a j − 1 {\displaystyle a_{i}\geq a_{j}-1} . Concordance (=Weak populationmonotonicity) means that an agent with a strictly higher entitlement receives...
allocation is better for some users and not worse for anyone. Populationmonotonicity: when a user leaves the system, the allocations of remaining users...
rich behavior, with bistability in some parameter range, as well as a monotonic decay to zero, smooth exponential growth, punctuated unlimited growth...
x_{n}\end{cases}}} As this article's first figure shows, in the presence of monotonicity violations the resulting interpolated curve will have flat (constant)...
strata, others may instead assume monotonicity. All will assume the absence of defiers within the experimental population. Some of these assumptions may...
are below subsistence. Assuming the demand for labor to be a given monotonically decreasing function of the real wage rate, the theory then predicted...
bundle that contains 1 / n {\displaystyle 1/n} of each resource. Populationmonotonicity: when an agent leaves the scene and the resources are re-divided...
House monotonicity: 134–141 (also called house-size monotonicity) is a property of apportionment methods. These are methods for allocating seats in a...
settlers in the Caucasus generally became assimilated into the indigenous population, particularly in Georgia, where Byzantine Greeks shared a common Christian...
marriages in which both spouses were of the same educational level rose monotonically from 47% in 1960 to 53% by the mid- to late-1980s. Similarly, the share...
criteria, the ranked pairs method passes the majority criterion, the monotonicity criterion, the Smith criterion (which implies the Condorcet criterion)...
monotonic, IRV is not. D R Woodall, "Monotonicity and Single-Seat Election Rules", Voting matters, Issue 6, 1996. This article calls the monotonicity...
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