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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
86:(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.
398:
Chakraborty, Mithun; Schmidt-Kraepelin, Ulrike; Suksompong, Warut (2021-04-29). "Picking sequences and monotonicity in weighted fair division".
126:, 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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361:"Strategy-proofness and population-monotonicity for house allocation problems"
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445:"Population-Monotonicity of the Nucleolus on a Class of Public Good Problems"
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304:"Resource-monotonicity and population-monotonicity in connected cake-cutting"
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216:. 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.
101:, no Pareto-optimal proportional division rule is PM. The absolute-
509:"Population monotonicity in economies with one indivisible good"
468:
Chen, Xin; Gao, Xiangyu; Hu, Zhenyu; Wang, Qiong (2019-01-17).
541:
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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).
247:"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
74:are not PM. Several rules are known to be PM:
470:"Population Monotonicity in Newsvendor Games"
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88:absolute-leximin and relative-leximin rules
170:PM in economies with one indivisible good.
70:problem, classic allocation rules such as
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191:. Cambridge, Massachusetts: MIT Press.
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189:Fair Division and Collective Welfare
557:needs additional or more specific
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365:Journal of Mathematical Economics
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443:Sonmez, Tayfun O. (2014-09-01).
330:10.1016/j.mathsocsci.2018.07.001
82:, any function that maximizes a
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377:10.1016/S0304-4068(02)00059-9
222:10.1016/s0169-7218(10)00021-3
55:state-population monotonicity
29:population-ratio monotonicity
525:10.1016/0165-4896(96)00814-1
513:Mathematical Social Sciences
507:Beviá, Carmen (1996-10-01).
422:10.1016/j.artint.2021.103578
308:Mathematical Social Sciences
38:Population monotonicity (PM)
140:round-robin item allocation
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273:10.1007/s00199-018-1128-6
212:Thomson, William (2011).
116:house allocation problem
110:In fair house allocation
97:When the pieces must be
84:concave welfare function
27:Not to be confused with
449:mpra.ub.uni-muenchen.de
400:Artificial Intelligence
167:PM in newsvendor games.
160:PM of the nucleolus in
130:In fair item allocation
78:When the pieces may be
34:Principle of allocation
486:10.1287/mnsc.2018.3053
214:Fair Allocation Rules
187:Herve Moulin (2004).
156:Resource monotonicity
136:fair item allocation
62:In fair cake cutting
18:Population monotonic
118:, a rule is PM and
474:Management Science
599:Fairness criteria
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570:adding categories
144:picking sequences
72:divide and choose
68:fair cake-cutting
16:(Redirected from
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406:: 103578.
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175:References
578:July 2024
533:0165-4896
494:0025-1909
430:233443832
385:0304-4068
338:0165-4896
314:: 19–30.
281:1432-0479
164:problems.
103:equitable
99:connected
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150:See also
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