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Fair division problem for discrete items
Fair item allocation is a kind of the fair division problem in which the items to divide are discrete rather than continuous. The items have to be divided
Fair_item_allocation
Fair item allocation procedure
procedure for fair item allocation. It can be used to allocate several indivisible items among several people, such that the allocation is "almost" envy-free:
Round-robin_item_allocation
goals are Pareto efficiency and fairness. Since the objects are indivisible, there may not exist any fair allocation. For example, when there is a single
Efficient approximately fair item allocation
Efficient_approximately_fair_item_allocation
Fair item allocation problem
Envy-free (EF) item allocation is a fair item allocation problem, in which the fairness criterion is envy-freeness - each agent should receive a bundle
Envy-free_item_allocation
Fair item allocation problem
Egalitarian item allocation, also called max-min item allocation is a fair item allocation problem, in which the fairness criterion follows the egalitarian
Egalitarian_item_allocation
Fair allocation of items and money is a class of fair item allocation problems in which, during the allocation process, it is possible to give or take
Fair allocation of items and money
Fair_allocation_of_items_and_money
Fairness notion in fair item allocation
any item (EFX) is a fairness notion in fair item allocation. It is a relaxation of envy-free item allocation. Determining whether EFX allocations always
Envy-freeness_up_to_any_item
Fair item allocation problem
Proportional item allocation is a fair item allocation problem, in which the fairness criterion is proportionality - each agent should receive a bundle
Proportional_item_allocation
Value that a party would ideally get
treated by them. In the more complex setting of fair item allocation, there are multiple different items with possibly different values to different people
Entitlement_(fair_division)
houses. Fair item allocation - each agent may get any number of objects. Abdulkadiroğlu, Atila; Sönmez, Tayfun (1999-10-01). "House Allocation with Existing
House_allocation_problem
Principle of allocation
endowments. In the fair item allocation problem, the Nash-optimal rule is no longer PM. In contrast, round-robin item allocation is PM. Moreover, round-robin
Population_monotonicity
For example: Revenue-maximizing auctions. Multi-item exchange. Fair cake-cutting and fair item allocation. Combinatorial auctions. Envy-free pricing. As
Single-minded_agent
Criterion of fair item allocation
Maximin share (MMS) is a criterion of fair item allocation. Given a set of items with different values, the 1-out-of-n maximin-share is the maximum value
Maximin_share
Course allocation is the problem of allocating seats in university courses among students. Many universities impose an upper bound on the number of students
Course_allocation
Algorithm for trading indivisible items
Shapley. The basic TTC algorithm is illustrated by the following house allocation problem. There are n {\displaystyle n} students living in the student
Top_trading_cycle
Mathematical optimization problem
to construct subsets that satisfy a given criterion of fairness, such as max-min item allocation. When m is variable (a part of the input), both problems
Multiple_subset_sum
Topics referred to by the same term
NASA Massachusetts Medical Society Maximin share, a criterion of fair item allocation Methyl methanesulfonate Moment magnitude scale of earthquake energy
MMS
Fair division problem
fairness is attained using monetary payments, instead of randomization. Fair item allocation is a setting in which agents may get more than one item.
Fair_random_assignment
Procedure for fair item allocation
procedure) is a procedure for fair item allocation. It can be used by several people who want to divide among them several discrete items, such as heirlooms, sweets
Envy-graph_procedure
Fair division protocol in computing
to the setting in which the users' demands are indivisible (as in fair item allocation). For the indivisible setting, they relax envy-freeness to EF1. They
Dominant_resource_fairness
Problem of fair division
Rental harmony is a kind of a fair division problem in which indivisible items and a fixed monetary cost have to be divided simultaneously. The housemates
Rental_harmony
Fair division problem
want to get pieces on as few cakes as possible. Fair item allocation – a similar problem in which the items to divide are indivisible. Cake sharing - a problem
Fair_cake-cutting
Concept in the field of computational social choice
Envy-free item allocation Participatory budgeting algorithm Multiwinner elections Consensus halving Fair division among groups - a variant of fair division
Agreeable_subset
Mathematical puzzle
inheritance puzzle is a mathematical puzzle involving unequal but fair allocation of indivisible goods, usually stated in terms of inheritance of a number
17-animal_inheritance_puzzle
the term OXS valuation (not to be confused with XOS valuation). Fair item allocation in this setting was studied by Benabbou, Chakraborty, Elkind, Zick
Assignment_valuation
Criterion for fair division
problems such as fair resource allocation, fair cake-cutting and fair item allocation. Group-envy-freeness is a very strong fairness requirement: a group-envy-free
Group_envy-freeness
Weakly optimal allocation of resources
strengthening of Pareto efficiency in the context of fair item allocation. An allocation of indivisible items is fractionally Pareto efficient ('fPE or fPO)
Pareto_efficiency
Matching where no person wants to switch their thing with someone else's
the efficiency of envy-free cake-cutting. Envy-free item allocation Rental harmony House allocation problem Segal-Halevi, Erel; Aigner-Horev, Elad (2022)
Envy-free_matching
partners trying to divide a single valuable item). See also fair item allocation. Consequently, in the price of fairness calculations, the instances in which
Price_of_fairness
-democratic 1-out-of-c MMS-fair allocation. These allocations can be found efficiently using a variant of round-robin item allocation, with weighted approval
Fair_division_among_groups
Kind of fair item allocation
is a kind of fair item allocation. There is a single seller that owns some items, and a set of buyers who are interested in these items. The buyers have
Envy-free_pricing
Distribution procedure
objects are taken; this leads to the round-robin item allocation procedure. This procedure is fairer, but it is not strategyproof. Both procedures are
Random priority item allocation
Random_priority_item_allocation
Topics referred to by the same term
companies Equitable up to any item, a type of object allocation that is part of efficient approximately fair item allocation This disambiguation page lists
EQX
Topics referred to by the same term
EF1 may refer to: EF1 item allocation - a rule for fair allocation of indivisible objects among people with different preferences. A tornado intensity
EF1
Holiday party game
someone else's gift, even a gift that is out of play.[citation needed] Fair item allocation Secret Santa White elephant sale Other names include Shifty Santa
White_elephant_gift_exchange
Problem of sharing resources
problems have been studied: Fair item assignment – dividing a set of indivisible and heterogeneous goods. Fair resource allocation – dividing a set of divisible
Fair_division
Mathematical and computational problem
least a given threshold. In the fair indivisible chore allocation problem (a variant of fair item allocation), the items represent chores, and there are
Bin_packing_problem
Rule in social choice theory: choose the alternative maximizing the product of utilities
In fair item allocation, for agents with additive valuations, Caragiannis, Kurokawa, Moulin, Procaccia, Shah and Wang prove that every allocation maximizing
Nash_welfare_rule
constraints on the allocation. One may want to maximize the welfare among all allocations that are fair, for example, envy-free up to one item (EF1), proportional
Welfare_maximization
The Decreasing Demand procedure is a procedure for fair item allocation. It yields a Pareto-efficient division that maximizes the rank of the agent with
Decreasing_Demand_procedure
Decision rule of maximizing utility
particular rule for fair item allocation. Welfare maximization problem. Utilitarian stable matching Egalitarian rule Proportional-fair rule Utility maximization
Utilitarian_rule
Mathematical criterion for fair division
has also been studied in the context of fair item allocation. With indivisible items, an equitable allocation might not exist, but it can be approximated
Equitability
Maximum size of an independent set of the matroid
been used to represent utility functions of agents in problems of fair item allocation. If the utility function of the agent is an MRF, it means that: The
Matroid_rank
the smallest sum. This objective corresponds to the application of fair item allocation, particularly the maximin share. It also appears in voting manipulation
Multiway_number_partitioning
only gets one item. Overall-EF1 can be found by creating T copies of each item and using the Biswas-Barman algorithm for fair allocation with partition
Temporal_fair_division
Rule for fair division of invisible items
(RM) allocation is a rule for fair division of indivisible items. Suppose we have to allocate some items among people. Each person can rank the items from
Rank-maximal_allocation
seats. But the classic fair division problem assumes that items may not be added. An allocation is called EF1 (envy-free up to one item) if, for any two agents
List of unsolved problems in fair division
List_of_unsolved_problems_in_fair_division
Mathematical principle
increases. Alice has an incentive to oppose growth. In the fair item allocation problem, classic allocation procedures such as adjusted winner and envy-graph are
Resource_monotonicity
Assignment of resources among possible uses
included in the plan, showing which items should be sacrificed if total funding must be reduced. Resource allocation may be decided by using computer programs
Resource_allocation
German computer scientist (born 1949)
development of fair item allocation algorithms. In particular, he participated in proving the existence of envy-free up to any item allocations for three agents
Kurt_Mehlhorn
Class of greedy algorithms for multiway number partitioning
sum. In the fair item allocation problem, there are n items and k people, each of which assigns a possibly different value to each item. The goal is
Greedy_number_partitioning
procedure for fair item assignment. It was developed by Eric Budish. CEEI (Competitive Equilibrium from Equal Incomes) is a fundamental rule for fair division
Approximate Competitive Equilibrium from Equal Incomes
Approximate_Competitive_Equilibrium_from_Equal_Incomes
Protocol for fair item assignment
for fair item assignment. Suppose m items have to be divided among n agents. One way to allocate the items is to let one agent select a single item, then
Picking_sequence
Mathematical principles
exact number of items that should be given to i {\displaystyle i} . In general, a "fair" apportionment is one in which each allocation a i {\displaystyle
Mathematics_of_apportionment
Algorithm for allocating divisible objects
agent can rank the items from best to worst, but cannot (or does not want to) specify a numeric value for each item. The SE allocation satisfies SD-efficiency
Simultaneous_eating_algorithm
Fair division class using unique allocation methods
online variant of fair allocation of indivisible goods. Each time, a single item arrives; each agent declares his/her value for this item; and the mechanism
Online_fair_division
Generalizations in graph theory
both). Similar algorithms have been applied for solving problems of fair item allocation, in particular the santa-claus problem. We say that a set K of edges
Hall-type theorems for hypergraphs
Hall-type_theorems_for_hypergraphs
Operations research problem of packing items into the largest number of bins
optimal solution. In the fair item allocation problem, there are different people each of whom attributes a different value to each item. The goal is to allocate
Bin_covering_problem
Criterion for fair division
procedure. Finding approximately-fair allocations; see envy-free item allocation. Finding partial envy-free allocations that are as large as possible; see
Envy-freeness
for fair item assignment between two people. It finds an envy-free item assignment of a subset of the items. Moreover, the resulting allocation is Pareto
AL_procedure
Method of resource allocation
do not specify a numeric value for each item. This may cause an ambiguity regarding whether certain allocations are Pareto-efficient or not. As an example
Ordinal_Pareto_efficiency
efficiency used in the setting of fair allocation of discrete objects. An allocation of objects is called discrete if each item is wholly allocated to a single
Fractional_Pareto_efficiency
Application of goodwill accounting
Purchase price allocation (PPA) is an application of goodwill accounting whereby one company (the acquirer), when purchasing a second company (the target)
Purchase_price_allocation
Topics referred to by the same term
Everett Efax file format, see List of file formats EFX item allocation - a rule for fair allocation of indivisible objects among people with different preferences
EFX
Scientific tests related to game theory
her 8 grandchildren. It was divided using a decentralized, fair and efficient allocation procedure, which combined market equilibrium and a Vickrey auction
Fair_division_experiments
Tool for working with matrices
of fair random assignment: given a randomized allocation of items, Birkhoff's algorithm can decompose it into a lottery on deterministic allocations. A
Birkhoff_algorithm
Rawlsian decision rule for social choice
Division of a single homogeneous resource; Fair subset sum problem; Egalitarian cake-cutting; Egalitarian item allocation; Egalitarian (leximin) bargaining; Leximin
Egalitarian_rule
Economical computational problem
equilibrium. Efficient envy-free division Efficient approximately fair item allocation Fixed-point computation and Nash equilibrium computation - two closely
Market equilibrium computation
Market_equilibrium_computation
Statistic measuring inter-rater agreement for categorical items
the same item as k, while p k , ⋅ ^ {\displaystyle {\widehat {p_{k,\cdot }}}} is the estimated probability that rater 1 will classify an item as k (and
Cohen's_kappa
Criterion for evaluating rules for fair division
criterion for evaluating rules for fair division. Coherence requires that the outcome of a fairness rule is fair not only for the overall problem, but
Coherence_(fairness)
Economic equilibrium concept
absence of Pareto improvements. It does not in any way opine on the fairness of the allocation (in the sense of distributive justice or equity). An efficient
Competitive_equilibrium
Method of fairly dividing property
Adjusted Winner (AW) is an algorithm for envy-free item allocation. Given two parties and some discrete goods, it returns a partition of the goods between
Adjusted_winner_procedure
2 equal-entitlement agents and 9 items, then the allocations (4,5) and (5,4) are both allowed, but the allocations (3,6) or (6,3) are not - a difference
Balance_(apportionment)
Problem in computer science and operations research
fairness perspective, one would like to find an envy-free item allocation - an allocation in which no agent envies another agent. That is: no agent prefers
Envy_minimization
reveal their true value functions, and then calculate an allocation that satisfies some fairness and efficiency objectives. The common efficiency objectives
Truthful_resource_allocation
Legal agreement between divorcing couples
division. While equitable does not guarantee equal sharing, it ensures a fair allocation. Alternatively, some states follow community property principles, where
Divorce_settlement
Problem in social choice
sharing an item must pay the same price for the item. The definition is the same for cardinal ballots as for approval ballots. A priceable allocation is computed
Combinatorial participatory budgeting
Combinatorial_participatory_budgeting
Proposal to reform United States tax code
owns it before the FairTax takes effect or if the FairTax has been paid previously on the good, which may be different from the item being sold previously
FairTax
CE-from-equal-incomes (CEEI) as a rule for fair allocation of items. They related it to four other fairness criteria assuming all agents have additive
Fisher_market
Suksompong, Warut (2016). "Asymptotic existence of proportionally fair allocations". Mathematical Social Sciences. 81: 62–65. arXiv:1806.00218. doi:10
Proportional_division
Two-leveled set of preferences in economics
can either "approve" or "reject" each alternative. In the context of fair item assignment, DP can be represented by a mathematical logic formula: for
Dichotomous_preferences
Procedure for fair item assignment
undercut procedure is a procedure for fair item assignment between two people. It provably finds a complete envy-free item assignment whenever such assignment
Undercut_procedure
Class of apportionment methods
combined allocation, then the result is exactly the vector ( a 1 , … , a k ) {\displaystyle (a_{1},\ldots ,a_{k})} . In other words: every part of a fair allocation
Rank-index_method
Social choice problem
fair share. Round robin share (RRS): each voter receives at least as much utility as he could attain if the rounds were divided by round-robin item allocation
Multi-issue_voting
French economist
Conversation. Alkan, Ahmet; Demange, Gabrielle; Gale, David (1991). "Fair Allocation of Indivisible Goods and Criteria of Justice". Econometrica. 59 (4):
Gabrielle_Demange
Prescribed regulation under the US Securities Act of 1933
Summary Item 904: Risk Factors and Other Considerations Item 905: Comparative Information Item 906: Allocation of Roll-up Consideration Item 907: Background
Regulation_S-K
Mathematical optimization of resource allocation
then the allocation is maximally fair. However, exact fairness is usually unattainable, since the quotas are not integers and the allocations must be integers
Optimal_apportionment
Comparison between vectors
particular applications of the leximin rule in fair division, see: Leximin cake-cutting Leximin item allocation In Multiple-criteria decision analysis a decision
Leximin_order
Provision in British tax law
assigned the item. Other items are advertised to museums who are invited to apply for their allocation. In cases where the value of an item exceeds the
Acceptance_in_lieu
Domestic agenda of U.S. President Harry S. Truman (1945–53)
controversial items passed that liberals could claim some success. The Korean War made military spending the nation's priority and killed almost the entire Fair Deal
Fair_Deal
Process of offering goods or services up for bids
them up for bids, taking bids, and then selling the item to the highest bidder or buying the item from the lowest bidder. Some exceptions to this definition
Auction
their monetary contributions, the fair market value of property the partner contributed, and undistributed allocations of partnership income. The basic
Partnership taxation in the United States
Partnership_taxation_in_the_United_States
Carrying value of goods sold during a particular period
make more than one of a particular item. Thus, costs are incurred for multiple items rather than a particular item sold. Determining how much of each
Cost_of_goods_sold
Semi-formal score-keeping system for massively multiplayer online games
efficient allocation of items to players willing to part with DKP, it presents the social consequence that perceived selfish bidding could result in an item being
Dragon_kill_points
AI whose outputs can be understood by humans
The payoff allocation for each sub-game is perceived as fair, so the Shapley-based payoff allocation for the given game should seem fair as well. An
Explainable artificial intelligence
Explainable_artificial_intelligence
Former authoritative body of the American Institute of Certified Public Accountants
Provides authoritative guidance on consolidated financial statements, tax allocation accounts, taxes payable, and activities related to stocks. December 1966
Accounting_Principles_Board
bundles. VSOE focuses on the fair market value of an item sold individually, as opposed to the assigned sales value of the item sold as part of a multiple-element
Vendor-specific objective evidence
Vendor-specific_objective_evidence
1998 U.S. court case
rather than a corporation or trust. The IRS regulations require a daily allocation of gains and losses to "partners" in the fund within the eight hours from
State Street Bank & Trust Co. v. Signature Financial Group, Inc.
State_Street_Bank_&_Trust_Co._v._Signature_Financial_Group,_Inc.
System to predict users' preferences
simply algorithm is a type of information filtering system that suggests items most relevant to a particular user. The value of these systems becomes particularly
Recommender_system
Means of achieving good corporate governance
administration. Principal among the issues is the fair funding for each service and the allocation system for scarce services. Institutionalizing internal
Service_governance
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