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Mathematical optimization of resource allocation
Optimal apportionment is an approach to apportionment that is based on mathematical optimization. In a problem of apportionment, there is a resource to
Optimal_apportionment
How 435 seats are distributed to 50 states
Huntington–Hill method became the official method of apportionment and was used in the 2020 apportionment and redistricting cycle. The current method solves
United States congressional apportionment
United_States_congressional_apportionment
Mathematical principles
an apportionment problem involves distributing seats in a legislature between different federal states or political parties. However, apportionment methods
Mathematics_of_apportionment
Way to distribute seats in a legislative body
related to apportionment. The apportionment by country page describes the specific practices used around the world. The mathematics of apportionment page describes
Apportionment_(politics)
Voting system that makes outcomes proportional to vote totals
Koriyama, Y.; Macé, A.; Laslier, J.-F.; Treibich, R. (2013). "Optimal apportionment". Journal of Political Economy. 121 (3): 584–608. doi:10.1086/670380
Proportional_representation
Concept in political science
legislatures by number of members United States congressional apportionment Wyoming Rule Apportionment in the European Parliament Lutz, Donald S. (2006). Principles
Cube_root_law
Rule for proportional allocation
to find the apportionment for a given state we must round (using the signpost sequence) after dividing. Thus, each party's apportionment is given by:
Highest_averages_method
Proportional-representation electoral system
Different apportionment methods, of which the Sainte-Laguë method is one, exist to distribute the seats according to the votes. Different apportionment methods
Sainte-Laguë_method
Theorem in political science
ambiguous in that two different spatial representations imply two different optimal winners. This is the ambiguity we sought to avoid earlier by adopting a
Median_voter_theorem
Type of heuristic technique
Biometrika, 25(3–4):285–294, 1933. Thompson, W. R. (1935). On the theory of apportionment. American Journal of Mathematics, 57(2), 450-456. Daniel J. Russo, Benjamin
Thompson_sampling
Mathematical model of animal foraging behavior
broader models such as MVT. Diminishing returns Optimal foraging theory Charnov, E. L. 1976. Optimal foraging: the marginal value theorem. Theoretical
Marginal_value_theorem
Apportionment approach
Treaty negotiations, rather than a specific formula, determine the apportionment between member states.[citation needed] Each German state has three
Degressive_proportionality
Type of heterotrophic nutrition based on decayed organic matter
saprotrophic organism to facilitate optimal growth and repair, favourable conditions and nutrients must be present. Optimal conditions refers to several conditions
Saprotroph
Principle of allocation
connected, no Pareto-optimal proportional division rule is PM. The absolute-equitable rule and relative-equitable rules are weakly Pareto-optimal and PM. In the
Population_monotonicity
Searching for wild food resources
Krebs, with work on the optimal diet model in relation to tits and chickadees; John Goss-Custard, who first tested the optimal diet model against behavior
Foraging
Rules and methods for pricing transactions between enterprises under common ownership
PLC v. Franchise Tax Board, the formulary apportionment method, which is also known as the unitary apportionment method, has at least three major advantages
Transfer_pricing
by Martin L. Shooman, who used square root biased sampling in a test apportionment model for software reliability. Press' later proposal to use square
Square_root_biased_sampling
Impossibility of straightforward game forms
outcomes to two options only. The process is not straightforward; the optimal ballot for a voter "requires strategic voting", i.e. it depends on their
Gibbard's_theorem
Multiple-winner electoral system
approval method that extends the D'Hondt method of apportionment commonly used to calculate apportionments for party-list proportional representation. However
Proportional_approval_voting
Set preferred to any other by a majority
for mathematician John H. Smith. The Smith set provides one standard of optimal choice for an election outcome. An alternative, stricter criterion is given
Smith_set
Method by which voters make a choice between options
results using votes cast in the district and elsewhere. Biproportional apportionment is a system where the total number of votes is used to calculate the
Electoral_system
American and French mathematician
and apportionment on the one hand, and voting on the other. His 1982 book with H. Peyton Young has had direct practical application in apportioning the
Michel_Balinski
Provision of the United States Constitution
be subject to the requirement of apportionment. As the income taxes imposed under the 1894 Act were not apportioned in such a manner, they were held unconstitutional
Taxing_and_Spending_Clause
Non-native organism causing damage to an established environment
nutrition Insectivore Mesopredators Mesopredator release hypothesis Omnivores Optimal foraging theory Planktivore Predation Prey switching Decomposers Chemoorganoheterotrophy
Invasive_species
results are used as entitlements (also called weights) in rules of apportionment, or in algorithms of fair division with different entitlements. Fractional
Fractional_approval_voting
Organism that eats mostly or exclusively plant material
strategy, but employ several strategies and eat a variety of plant parts. Optimal foraging theory is a model for predicting animal behavior while looking
Herbivore
Religious donation
the content of documents such as the content of deeds of merger and apportionment maps. Rent charges in lieu of abolished English tithes paid by landowners
Tithe
make optimal use of the annual Pacific whiting allowable harvest allocated to the catcher/processor sector, PWCC members negotiated the apportionment of
Pacific Whiting Conservation Cooperative
Pacific_Whiting_Conservation_Cooperative
Country in North America
ISBN 978-0-3133-0000-4. Butenko, Sergiy; Gil-Lafuente, Jaime; Pardalos, Panos M. (2010). Optimal Strategies in Sports Economics and Management. Springer Science & Business
Canada
List of statements that appear to contradict themselves
what they thought that everybody else wanted to do. Apportionment paradox: Some systems of apportioning representation can have unintuitive results due to
List_of_paradoxes
Electoral district for a European Parliament seat
the European Council. Member of the European Parliament Constituency Apportionment in the European Parliament Oelbermann, Kai-Friederike; Palomares, Antonio;
European Parliament constituency
European_Parliament_constituency
Tax paid directly to the government by the person on whom it is imposed
taxes have been subject to the rule of uniformity but not the rule of apportionment. Before then, the principal sources of revenue for the federal government
Direct_tax
Local boundary-limited electrical grid
the slowest) control level, which considers economical concerns in the optimal operation of the microgrid (sampling time is from minutes to hours), and
Microgrid
arisen from treaty negotiations, there is no precise formula for the apportionment of seats among member states. No change in this configuration can occur
Elections to the European Parliament
Elections_to_the_European_Parliament
De facto state in West Asia and the Mediterranean Sea
BÜYÜKLÜĞÜ VE OPTİMAL ÜRETİM DESENİNİN DOĞRUSAL PROGRAMLAMA YÖNTEMİ İLE TESPİTİ [DETERMINATION OF SUFFICIENTLY PROFITABLE FARM SIZE AND OPTIMAL PRODUCTION
Northern_Cyprus
Criterion that prevents lesser-evil voting
giving a favorite candidate the maximum level of support is always the optimal strategy. Examples of systems that are both spoilerproof and monotonic
Sincere_favorite_criterion
Type of eye defect
vectors for planning refractive surgery such that the surgery is apportioned optimally between both the refractive and topographic components. A number
Astigmatism
Method of allocating voting weight by population
state will have 100% voting power (i.e., an index of 1). For the EU-27, an optimal threshold, at which the voting powers of all citizens in any member state
Penrose_method
Value that a party would ideally get
(the seats) among agents with different entitlements. It is called the apportionment problem. The allocation of seats by size of population can leave small
Entitlement_(fair_division)
President of the United States from 1825 to 1829
in the 2008 HBO television miniseries John Adams. Adams's method for apportionment List of abolitionists List of presidents of the United States List of
John_Quincy_Adams
Choosing a candidate other than preferred to undercut a less desired one
manipulate in the absence of an electoral threshold. However, biased apportionment methods can create opportunities for strategic voting, as can small
Strategic_voting
Group of European states without mutual border controls
Political groups of the European Parliament Spitzenkandidat Constituencies Apportionment Referendums related to the EU European elections 1979 1984 1989 1994
Schengen_Area
Spoiler effect in RCV and two-round systems
choice voting. In a center squeeze, the majority-preferred and socially optimal candidate is eliminated in favor of a more extreme alternative in an early
Center_squeeze
Currency of the European Union
beginning of the Great Recession and Euro area crisis. In economics, an optimum currency area, or region (OCA or OCR), is a geographical region in which
Euro
Biological process to convert light into chemical energy
PMID 24424488. Verduin J (1953). "A table of photosynthesis rates under optimal, near natural conditions". Am. J. Bot. 40 (9): 675–679. Bibcode:1953AmJB
Photosynthesis
Management concept
larva, then there is an optimal life stage (size or age class) to harvest, with no harvest of all other life stages. Hence the optimal strategy is to harvest
Maximum_sustainable_yield
Criterion for evaluating fairness of electoral systems
some rounding method should be used, and this can be done by various apportionment methods. In recent years, there is a growing dissatisfaction with the
Justified_representation
Potential candidates for admission into the European Union
Political groups of the European Parliament Spitzenkandidat Constituencies Apportionment Referendums related to the EU European elections 1979 1984 1989 1994
Potential enlargement of the European Union
Potential_enlargement_of_the_European_Union
Tax based on taxable income
and there being no power to impose any other than a direct tax by apportionment. In 1913, the Sixteenth Amendment to the United States Constitution
Income_tax
2011 European Union common tax scheme proposal
participating Member States have previously agreed upon. The so-called formula apportionment (FA) usually employs factors like capital, sales and labour on which
Common Consolidated Corporate Tax Base
Common_Consolidated_Corporate_Tax_Base
Theory of laying bets
O (2025). "Optimal online bookmaking for binary games". arXiv:2501.06923 [cs.GT]. Lorig, Matthew; Zhou, Zhou; Zou, Bin (2021). "Optimal bookmaking".
Mathematics_of_bookmaking
Political groups of the European Parliament Spitzenkandidat Constituencies Apportionment Referendums related to the EU European elections 1979 1984 1989 1994
European_Union_citizenship
N-th root of the product of n numbers
MathWorld Geometric Meaning of the Geometric Mean Computing Congressional apportionment using Geometric Mean Geometric Mean Definition and Formula The Distribution
Geometric_mean
Directly elected legislature of the European Union
have to be revised to reflect demographic changes. Pursuant to this apportionment, the constituencies are formed. In four EU member states (Belgium, Ireland
European_Parliament
Electronic visitor authorisation system
Political groups of the European Parliament Spitzenkandidat Constituencies Apportionment Referendums related to the EU European elections 1979 1984 1989 1994
European Travel Information and Authorisation System
European_Travel_Information_and_Authorisation_System
Single-winner electoral system
those candidates that have a positive prospective rating. This strategy is optimal in the sense that it maximizes the voter's expected utility, subject to
Approval_voting
Political groups of the European Parliament Spitzenkandidat Constituencies Apportionment Referendums related to the EU European elections 1979 1984 1989 1994
Languages of the European Union
Languages_of_the_European_Union
Rate of generation of biomass in an ecosystem
Guild Habitat Marine Semiaquatic Terrestrial Limiting similarity Niche apportionment models Niche construction Niche differentiation Ontogenetic niche shift
Productivity_(ecology)
Management concept
strategic settings in which people compete and develop the implications for optimal labor contracts. Expectancy theory Social psychology Predicted outcome
Equity_theory
Fixed tax paid by every liable individual
indirect excises (i.e. excises, duties, and imposts) – thus requiring no apportionment, a practice that would remain unchanged into the 21st century. Various
Poll_tax
Flow of energy through food chains in ecological energetics
nutrition Insectivore Mesopredators Mesopredator release hypothesis Omnivores Optimal foraging theory Planktivore Predation Prey switching Decomposers Chemoorganoheterotrophy
Energy_flow_(ecology)
Composite material used for paving
estimated at 50%. Research has demonstrated that the use of rejuvenators at optimal doses can allow for mixes with 100% recycled components to meet the performance
Asphalt_concrete
Executive branch of the European Union
Political groups of the European Parliament Spitzenkandidat Constituencies Apportionment Referendums related to the EU European elections 1979 1984 1989 1994
European_Commission
Devices, and technologies invented or used in the Inca civilisation
Major Inca centers were chosen by experts who decided the site, its apportionment, and the basic layout of the city. In many cities we see great hydraulic
Inca_technology
Water-distribution treaty between India and Pakistan
the treaty recognises the rights and obligations of each country for the optimum water use from the Indus system of rivers in a spirit of goodwill, friendship
Indus_Waters_Treaty
Ecological theory
nutrition Insectivore Mesopredators Mesopredator release hypothesis Omnivores Optimal foraging theory Planktivore Predation Prey switching Decomposers Chemoorganoheterotrophy
Mesopredator release hypothesis
Mesopredator_release_hypothesis
Policy on permits required to enter the Schengen Area
Political groups of the European Parliament Spitzenkandidat Constituencies Apportionment Referendums related to the EU European elections 1979 1984 1989 1994
Visa policy of the Schengen Area
Visa_policy_of_the_Schengen_Area
Ecological theory concerning the selection of life history traits
provide a more mechanistic causative link between an environment and an optimal life history (Wilbur et al. 1974; Stearns 1976, 1977). The r- and K-selection
R/K_selection_theory
European free trade zone established in 1994
Political groups of the European Parliament Spitzenkandidat Constituencies Apportionment Referendums related to the EU European elections 1979 1984 1989 1994
European_Economic_Area
EU regulations which are not imposed by member states by agreement
Political groups of the European Parliament Spitzenkandidat Constituencies Apportionment Referendums related to the EU European elections 1979 1984 1989 1994
Opt-outs in the European Union
Opt-outs_in_the_European_Union
2015 U.S. Supreme Court case on same-sex marriage
which established the one-person, one-vote concept in legislative apportionment; and Obergefell v. Hodges, the 2015 same-sex-marriage ruling. Chappell
Obergefell_v._Hodges
Biological interaction
suitable patch locations and return to them at intervals to feed. The optimal foraging strategy for search has been modelled using the marginal value
Predation
1562/2005-11-23-RA-739. PMID 16454580. S2CID 36351333. Relethford, J. H. (2002). "Apportionment of global human genetic diversity based on craniometrics and skin color"
Human_skin_color
Mathematical principle
the only one that remains RM is the Nash-optimal rule. When the pieces must be connected, no Pareto-optimal proportional division rule is RM. The absolute-equitable
Resource_monotonicity
Rivalry between Formula One drivers Lewis Hamilton and Nico Rosberg
management has frequently allowed him to push on for longer, often enabling optimum race strategies, and his fuel usage has regularly been better than almost
Hamilton–Rosberg_rivalry
Use of approximation algorithms in voting
voting aims to find an alternative whose social welfare is approximately optimal. The quality of approximation for a voting rule is measured by its distortion
Implicit_utilitarian_voting
Motor racing championship
adjustments to the ride height of the car, thereby keeping the ride height at an optimal level throughout the race and providing stability during braking. The FIA
2012 Formula One World Championship
2012_Formula_One_World_Championship
Single-winner electoral system
popular when all the ballots are combined. Sincere favorite criterion The optimal voting strategy for an individual should always include giving their favorite
Kemeny_method
Series of secondary extinctions
nutrition Insectivore Mesopredators Mesopredator release hypothesis Omnivores Optimal foraging theory Planktivore Predation Prey switching Decomposers Chemoorganoheterotrophy
Cascade_effect_(ecology)
Body of criticism of the European Union
Political groups of the European Parliament Spitzenkandidat Constituencies Apportionment Referendums related to the EU European elections 1979 1984 1989 1994
Euroscepticism
Principle that voting for a candidate should help them
1016/0022-0531(88)90253-0. Pukelsheim, Friedrich (2014). Proportional representation : apportionment methods and their applications. Internet Archive. Cham; New York : Springer
Participation_criterion
Proposals to federalise the European Union
Political groups of the European Parliament Spitzenkandidat Constituencies Apportionment Referendums related to the EU European elections 1979 1984 1989 1994
Federalisation of the European Union
Federalisation_of_the_European_Union
Collective decision-making procedure
participants) based on quadratic voting, noting that such a mechanism allows for optimal production of public goods without needing to be determined by a centralized
Quadratic_voting
Concealment in plain sight by any means, e.g. colour, pattern and shape
better. For example, a cod can see prey that are 98 percent transparent in optimal lighting in shallow water. Therefore, sufficient transparency for camouflage
Camouflage
Method to take decisions in the EU Council
discussion at the June council. The given percentage is the game theoretical optimal threshold, and is known as the "Jagiellonian Compromise". The Penrose method
Voting in the Council of the European Union
Voting_in_the_Council_of_the_European_Union
Evolutionary mechanism
why some plants make this investment in defenses against herbivores. The optimal defense hypothesis attempts to explain how the kinds of defenses a particular
Plant defense against herbivory
Plant_defense_against_herbivory
Marine consumer-resource system
Guild Habitat Marine Semiaquatic Terrestrial Limiting similarity Niche apportionment models Niche construction Niche differentiation Ontogenetic niche shift
Marine_food_web
Problem of sharing resources
division Online fair division Strategic fair division Apportionment and mathematics of apportionment Equity (economics) International trade Justice (economics)
Fair_division
Legislative act of the European Union
Political groups of the European Parliament Spitzenkandidat Constituencies Apportionment Referendums related to the EU European elections 1979 1984 1989 1994
Directive_(European_Union)
Proof all ranked voting rules have spoilers
Majority judgment STAR voting Proportional representation Party-list Apportionment Highest averages Largest remainders National remnant Biproportional
Arrow's_impossibility_theorem
Natural interconnection of food chains
nutrition Insectivore Mesopredators Mesopredator release hypothesis Omnivores Optimal foraging theory Planktivore Predation Prey switching Decomposers Chemoorganoheterotrophy
Food_web
Study of rational collective decision-making
contrasts with May's theorem, which shows that simple majority is the optimal voting mechanism when there are only two outcomes, and only ordinal preferences
Social_choice_theory
Accession of new countries to the EU
Political groups of the European Parliament Spitzenkandidat Constituencies Apportionment Referendums related to the EU European elections 1979 1984 1989 1994
Enlargement of the European Union
Enlargement_of_the_European_Union
1917 American flying bomb
Board supported him, and formally requested the Secretary of Navy to apportion $50,000 for the work. The government thus included the development of
Hewitt–Sperry Automatic Airplane
Hewitt–Sperry_Automatic_Airplane
Type of EU legislative act
Political groups of the European Parliament Spitzenkandidat Constituencies Apportionment Referendums related to the EU European elections 1979 1984 1989 1994
Regulation_(European_Union)
Tax on the transfer of property or assets between parties
that the estate tax was a direct tax and that, since it had not been apportioned among the states according to population, it was unconstitutional. The
Transfer_tax
can apportion the purchase price under a recognised HMRC formula, and this is where the inherent property skill can maximise the claim with optimal costing
Capital_allowance
Electoral systems with independent candidate ratings
are allowed. In this setting, the optimal strategy for Range voting is the same as for approval voting, and the optimal strategy for cumulative voting is
Rated_voting
Monetary exemption from taxes that would otherwise be levied
jurisdiction. U.S. states and Canadian provinces provide for formulary apportionment of certain business income to achieve a similar result. See, e.g., the
Tax_exemption
biparietal, parietal pars part- -pert- piece apart, apartment, apportion, apportionment, bipartient, bipartisan, bipartite, bipartition, champerty, compart
List of Latin words with English derivatives
List_of_Latin_words_with_English_derivatives
OPTIMAL APPORTIONMENT
OPTIMAL APPORTIONMENT
Boy/Male
Hindu
To do something systematically, Optimum utilization of resources
Boy/Male
Tamil
The primal God
Boy/Male
Indian, Sanskrit
The Primal Head of Religious Sacrifice
Boy/Male
Hindu, Indian
To do Something Systematically or Optimum Utilization of Resources
Girl/Female
Hindu, Indian
Primal; A Wife of Agni
Boy/Male
Indian, Sanskrit
The Primal Root
Boy/Male
Tamil
To do something systematically, Optimum utilization of resources
Boy/Male
Indian, Sanskrit
One God; The Primal God
Girl/Female
Tamil
Boy/Male
Indian, Sanskrit
The Primal Idol
Girl/Female
Hindu, Indian
The Primal Energy
Girl/Female
Hindu, Indian
The Primal Mother
Boy/Male
Hindu, Indian, Marathi
The Primal God
Boy/Male
Hindu
The primal God
Girl/Female
Indian
Optional
Boy/Male
Gujarati, Hindu, Indian, Kannada, Marathi, Punjabi, Sikh
Lord Shiva; God's Name; Primal Being
Boy/Male
Indian, Sanskrit
The Primal Residue
Boy/Male
Arabic, Muslim
First; New; Another Name for God; Novel; Primal
Girl/Female
Hindu
Girl/Female
Hindu, Indian, Traditional
The Primal Lakshmi
OPTIMAL APPORTIONMENT
OPTIMAL APPORTIONMENT
Girl/Female
Hindu, Indian, Marathi
Goddess Name
Boy/Male
French
Son of a German.
Biblical
people despised or obscure
Girl/Female
Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
Polite Nature; Tender; Good Character
Girl/Female
Tamil
Hetanshi | ஹேதாஂஷீ
Boy/Male
Australian, French, German, Greek, Italian
People's Ruler
Girl/Female
Australian, French, Hebrew, Jewish, Swedish
Sweetness; Pleasantness; My Delight
Boy/Male
Tamil
Malaimakal Makan | மாஂலாமாஂகால மகாந
Lord Murugan
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Marathi, Sindhi, Telugu
Power and Dignity of Indra
Girl/Female
Hebrew
Gift from God.
OPTIMAL APPORTIONMENT
OPTIMAL APPORTIONMENT
OPTIMAL APPORTIONMENT
OPTIMAL APPORTIONMENT
OPTIMAL APPORTIONMENT
n.
An optical toy similar to the phenakistoscope. See Phenakistoscope.
n.
An instrument for showing the optical effects of color.
a.
One who deals in optical glasses and instruments.
a.
Relating to the science of optics; as, optical works.
n.
See Elective, n.
n.
Of or pertaining to the science of vision; optical.
n.
A nobleman or aristocrat; a chief man in a state or city.
a.
Involving an option; depending on the exercise of an option; left to one's discretion or choice; not compulsory; as, optional studies; it is optional with you to go or stay.
n.
One of those who stand in the second rank of honors, immediately after the wranglers, in the University of Cambridge, England. They are divided into senior and junior optimes.
n.
An optical glass that is convex on both sides.
adv.
In an optional manner.
n.
An optical glass; a telescope.
n.
A reflecting optical glass or instrument; a mirror.
a.
Alt. of Optical
n.
Collectively, the nobility.
n.
The space covered by an optical instrument at one view.
a.
Of or pertaining to the nobility or aristocracy.
a.
Of or pertaining to vision or sight.
n.
Government by the nobility.
a.
Of or pertaining to the eye; ocular; as, the optic nerves (the first pair of cranial nerves) which are distributed to the retina. See Illust. of Brain, and Eye.