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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
75:(a monotonically-increasing function of the utilities) is PM. This holds whether the welfare function operates on the absolute utilities or on the relative utilities. In particular, the Nash-optimal rule,
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appropriate for agents with different entitlements. Picking-sequences based on divisor methods are PM too. However, a picking-sequence based on the quota method is not PM.
387:
Chakraborty, Mithun; Schmidt-Kraepelin, Ulrike; Suksompong, Warut (2021-04-29). "Picking sequences and monotonicity in weighted fair division".
115:, if-and-only-if it assigns the houses iteratively, where at each iteration, at most two agents trade houses from their initial endowments.
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of seats in the congress among states. There, the property relates to the population of an individual state, which determines the state's
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A population-increase means that a state is entitled to more seats. This different property is described in the page
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are all PM. It is an open question whether concavity of the welfare function is necessary for PM.
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The term "population monotonicity" is used in an unrelated meaning in the context of
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350:"Strategy-proofness and population-monotonicity for house allocation problems"
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434:"Population-Monotonicity of the Nucleolus on a Class of Public Good Problems"
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293:"Resource-monotonicity and population-monotonicity in connected cake-cutting"
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205:. Handbook of Social Choice and Welfare. Vol. 2. pp. 393–506.
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rule and relative-equitable rules are weakly Pareto-optimal and PM.
90:, no Pareto-optimal proportional division rule is PM. The absolute-
498:"Population monotonicity in economies with one indivisible good"
457:
Chen, Xin; Gao, Xiangyu; Hu, Zhenyu; Wang, Qiong (2019-01-17).
530:
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problem, the Nash-optimal rule is no longer PM. In contrast,
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Ehlers, Lars; Klaus, Bettina; Pápai, Szilvia (2002-11-01).
236:"Monotonicity and competitive equilibrium in cake-cutting"
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to it so that it can be listed with similar articles.
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Segal-Halevi, Erel; Sziklai, Balázs R. (2018-09-01).
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Segal-Halevi, Erel; Sziklai, Balázs R. (2019-09-01).
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is PM. Moreover, round-robin can be adapted to yield
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least as much utility as in the original allocation.
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absolute-utilitarian and relative utilitarian rules
63:are not PM. Several rules are known to be PM:
459:"Population Monotonicity in Newsvendor Games"
8:
77:absolute-leximin and relative-leximin rules
159:PM in economies with one indivisible good.
59:problem, classic allocation rules such as
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180:. Cambridge, Massachusetts: MIT Press.
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178:Fair Division and Collective Welfare
546:needs additional or more specific
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354:Journal of Mathematical Economics
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432:Sonmez, Tayfun O. (2014-09-01).
319:10.1016/j.mathsocsci.2018.07.001
71:, any function that maximizes a
1:
366:10.1016/S0304-4068(02)00059-9
211:10.1016/s0169-7218(10)00021-3
44:state-population monotonicity
18:population-ratio monotonicity
514:10.1016/0165-4896(96)00814-1
502:Mathematical Social Sciences
496:Beviá, Carmen (1996-10-01).
411:10.1016/j.artint.2021.103578
297:Mathematical Social Sciences
27:Population monotonicity (PM)
129:round-robin item allocation
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262:10.1007/s00199-018-1128-6
201:Thomson, William (2011).
105:house allocation problem
99:In fair house allocation
86:When the pieces must be
73:concave welfare function
16:Not to be confused with
438:mpra.ub.uni-muenchen.de
389:Artificial Intelligence
156:PM in newsvendor games.
149:PM of the nucleolus in
119:In fair item allocation
67:When the pieces may be
23:Principle of allocation
475:10.1287/mnsc.2018.3053
203:Fair Allocation Rules
176:Herve Moulin (2004).
145:Resource monotonicity
125:fair item allocation
51:In fair cake cutting
107:, a rule is PM and
463:Management Science
588:Fairness criteria
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559:adding categories
133:picking sequences
61:divide and choose
57:fair cake-cutting
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109:strategyproof
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151:public good
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395:: 103578.
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164:References
567:July 2024
522:0165-4896
483:0025-1909
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374:0304-4068
327:0165-4896
303:: 19–30.
270:1432-0479
153:problems.
92:equitable
88:connected
582:Category
555:help out
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139:See also
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