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Fair division problem
Fair random assignment (also called probabilistic one-sided matching) is a kind of a fair division problem. In an assignment problem (also called house-allocation
Fair_random_assignment
Tool for working with matrices
applications. One such application is for the problem of fair random assignment: given a randomized allocation of items, Birkhoff's algorithm can decompose
Birkhoff_algorithm
Distribution procedure
Random priority (RP), also called random serial dictatorship (RSD), is a procedure for fair random assignment - dividing indivisible items fairly among
Random priority item allocation
Random_priority_item_allocation
Apparent lack of pattern or predictability in events
definitions of randomness, typically assuming that there is some 'objective' probability distribution. In statistics, a random variable is an assignment of a numerical
Randomness
produces distorted probabilities relative to the uniform-random matching. Fair random assignment - one-sided matching - allocating items to agents with
Random_two-sided_matching
Algorithm for allocating divisible objects
developed by Hervé Moulin and Anna Bogomolnaia as a solution for the fair random assignment problem, where the fraction that each agent receives of each item
Simultaneous_eating_algorithm
Criterion for fair division
envy-free matching. Using randomization to find allocations that are envy-free in expectation ("ex-ante"); see fair random assignment. Strong envy-freeness
Envy-freeness
Problem of sharing resources
apartment). Fair river sharing – dividing waters flowing in an international river among the countries along its stream. Fair random assignment – dividing
Fair_division
ex-ante; see fair random assignment for other randomized mechanisms which are ex-ante PE. When each agent already owns a house, fairness considerations
House_allocation_problem
Weakly optimal allocation of resources
profile is (3.5, 2). When the decision process is random, such as in fair random assignment or random social choice or fractional approval voting, there
Pareto_efficiency
Method of resource allocation
Bogomolnaia and Moulin present an efficiency notion for the setting of fair random assignment (where the bundle rankings are additive, the allocations are fractional
Ordinal_Pareto_efficiency
Fair division problem for discrete items
harmony - a fair division problem where indivisible items and a fixed total cost have to be divided simultaneously. Fair random assignment - a fair division
Fair_item_allocation
Theory in matching markets
problem and the fair random assignment problem. In that context, the term used is popular assignment. Finding a min-cost popular assignment can be done in
Popular_matching
Process of making something random
the larger population. Random Allocation in Experimental Design: Random assignment of experimental units to treatment or control conditions is fundamental
Randomization
Mathematical function for the probability a given outcome occurs in an experiment
a coin toss can be represented by a random variable X that equals 1 for heads and 0 for tails. If the coin is fair, this distribution assigns probability
Probability_distribution
Russian economist
and on randomized solutions to assignment problems. With Hervé Moulin she formulated the probabilistic-serial procedure for solving the fair random assignment
Anna_Bogomolnaia
computation and for the mechanism of Hylland and Zeckhauser for fair random assignment. Etessami and Yannakakis describe the relation succinctly by saying
FIXP
French mathematician (born 1950)
and assignment problems. In particular, jointly with Anna Bogomolnaia, he proposed the probabilistic-serial procedure as a solution to the fair random assignment
Hervé_Moulin
Problem of fair division
monetary transfers: Fair random assignment - each agent should get a single object; fairness is attained using randomization. House allocation problem
Rental_harmony
Form of scientific experiment
various psychological sources of bias.[citation needed] The randomness in the assignment of participants to treatments reduces selection bias and allocation
Randomized_controlled_trial
Additionally, the algorithm has no fairness guarantees. Other mechanisms for course allocation use fair random assignment. Kominers, Scott Duke; Ruberry,
Course_allocation
Variable representing a random phenomenon
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which
Random_variable
Uses of an apparent lack of pattern or predictability in events
Randomness has multiple uses in science, art, statistics, cryptography, gaming, gambling, and other fields. For example, random assignment in randomized
Applications_of_randomness
Statistical property
envy-freeness. Hosseini and Larson analyse the properties of rules for fair random assignment based on lexicographic dominance. Chakrabarty, Deeparnab; Swamy
Lexicographic_dominance
Extension of modal logic
but to exit via the test ¬ p ? {\displaystyle \neg p?\,\!} . The random-assignment statement x := ? {\displaystyle x\mathbin {:=} {?}\,\!} denotes the
Dynamic_logic_(modal_logic)
Collection of statistical models
the protocol that specifies the random assignment of treatments to subjects; the protocol's description of the assignment mechanism should include a specification
Analysis_of_variance
British-American journalist, author and filmmaker
Vanity Fair, author of a number of New York Times-bestselling books, and a screenwriter. He worked at the Times for 13 years, then at Vanity Fair for 10
Nick_Bilton
Selection of decision-makers by random sample
governance, sortition is the selection of public officials or jurors at random, i.e., by lottery, in order to obtain a representative sample. In ancient
Sortition
Statistical measure of how far values spread from their average
{1}{\lambda }}\right)^{2}={\frac {1}{\lambda ^{2}}}.} A fair six-sided die can be modeled as a discrete random variable, X {\displaystyle X} , with outcomes
Variance
Two-leveled set of preferences in economics
either "approve" or "reject" each alternative. In the context of fair item assignment, DP can be represented by a mathematical logic formula: for every
Dichotomous_preferences
Fundamental theorem in probability theory and statistics
{\displaystyle {\bar {X}}_{n}} denote the sample mean (which is itself a random variable). Then the limit as n → ∞ {\displaystyle n\to \infty } of the distribution
Central_limit_theorem
Procedure that can be infinitely repeated, with a well-defined set of outcomes
An experiment is said to be random if it has more than one possible outcome, and deterministic if it has only one. A random experiment that has exactly
Experiment (probability theory)
Experiment_(probability_theory)
Digital workload distribution techniques
even more efficient to calculate a random permutation in advance. This avoids communication costs for each assignment. There is no longer a need for a distribution
Load_balancing_(computing)
Branch of mathematics concerning probability
single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior
Probability_theory
Computer program for the Boolean satisfiability problem
k-SAT at all values of k. In the setting with many satisfying assignments the randomized algorithm by Schöning has a better bound. SAT solvers have been
SAT_solver
Scientific tests related to game theory
fair cake-cutting. He tested them using a computerized simulation: valuation functions for each agent were generated by dividing the cake into random
Fair_division_experiments
Range to estimate an unknown parameter
data from a random sample. Because the sample is random, the interval endpoints are random variables. Let X {\displaystyle X} be a random sample from
Confidence_interval
Number measuring the chance an event occurs
from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally
Probability
Statistical concept
data are in effect a random sample of all the participants assigned a particular intervention. With MCAR, the random assignment of treatments is assumed
Missing_data
Value that a party would ideally get
"Fair Allocation Without Trade". arXiv:1204.4286 [cs.GT]. Aziz, Haris; Gaspers, Serge; Mackenzie, Simon; Walsh, Toby (2015-10-01). "Fair assignment of
Entitlement_(fair_division)
Nine-digit number issued to U.S. citizens and permanent residents
2011, the SSA changed the SSN assignment process to "SSN randomization". SSN randomization affects the SSN assignment process. Among its changes, it
Social_Security_number
a random variable (a lottery), whose value equals each candidate x with probability p(x). It can also be interpreted as a deterministic assignment of
Fractional_social_choice
American writer, spy novelist and former CIA officer (born 1963)
began her next assignment under cover as an "energy consultant" for Brewster-Jennings. Beginning in 1997, Plame's primary assignment was shifted to the
Valerie_Plame
Fair item allocation problem
Haris; Gaspers, Serge; Mackenzie, Simon; Walsh, Toby (2015-10-01). "Fair assignment of indivisible objects under ordinal preferences". Artificial Intelligence
Envy-free_item_allocation
1990s American social experiment on low-income families
Moving to Opportunity for Fair Housing (MTO) was a randomized social experiment sponsored by the United States Department of Housing and Urban Development
Moving_to_Opportunity
American photographer (born 1949)
the first time: pictures of Vietnam War protesters in Israel, taken on assignment for Rolling Stone, one of which landed on the cover. Since then, she has
Annie_Leibovitz
Private men's club in California, United States
pp. 28–35. Shepard, Steve; Reynolds, Frank (July 23, 1981). "Special Assignment (Bohemian Grove) #72819". ABC Evening News. Vanderbilt Television News
Bohemian_Grove
Outlaw Motorcycle Gangs Random House, 1967, (Trade Cloth) Random House Publishing Group, 1975, ISBN 0-345-24825-2 (Mass Market) Random House Publishing Group
Hunter S. Thompson bibliography
Hunter_S._Thompson_bibliography
Function of the observed sample results
studied hypothesis is true, or the probability that the data were produced by random chance alone" and that "a p-value, or statistical significance, does not
P-value
Assignment of resources among possible uses
In economics, resource allocation is the assignment of available resources to various uses. In the context of an entire economy, resources can be allocated
Resource_allocation
United States proposed political reform
plans is to allow for entry of less-funded candidates early on. With random assignment to groups within each region, any given primary date could be as small
Interregional_Primary_Plan
Field of machine learning
1007/BF00114726. ISSN 1573-0565. Sutton, Richard S. (1984). Temporal Credit Assignment in Reinforcement Learning (PhD thesis). University of Massachusetts, Amherst
Reinforcement_learning
Statistical phenomenon
of a random variable is extreme, the next sampling of the same random variable is likely to be closer to its mean. Furthermore, when many random variables
Regression_toward_the_mean
Fair division problem
societal preferences for fairness or efficiency. Other probabilistic division mechanisms, such as random lotteries or assignment by chance, are also used
Fair_cake-cutting
Protocol for fair item assignment
A picking sequence is a protocol for fair item assignment. Suppose m items have to be divided among n agents. One way to allocate the items is to let one
Picking_sequence
Subfield of information theory and computer science
halt when its input is supplied by flips of a fair coin (sometimes thought of as the probability that a random computer program will eventually halt). Although
Algorithmic information theory
Algorithmic_information_theory
Principle in Bayesian statistics
found that the maximum entropy distribution is the most probable of all "fair" random distributions, in the limit as the probability levels go from discrete
Principle_of_maximum_entropy
Season of television series
who would also divide directing assignments on the remaining six episodes with Pizzolatto. The season was filmed by Random Productions LLC at various locations
True_Detective_season_3
Scientific procedure performed to validate a hypothesis
eliminated through scientific controls and/or, in randomized experiments, through random assignment.[citation needed] In engineering and the physical
Experiment
United States Navy component of JSOC
testing and are then interviewed to deem whether they are suitable for assignment to NSWDG. Those who pass the stringent recruitment process will attend
SEAL_Team_Six
Function related to statistics and probability theory
model. It is constructed from the joint probability distribution of the random variable that (presumably) generated the observations. When evaluated on
Likelihood_function
Grouping a set of objects by similarity
clustering), choosing the initial centers less randomly (k-means++) or allowing a fuzzy cluster assignment (fuzzy c-means). Most k-means-type algorithms
Cluster_analysis
American actor and filmmaker (born 1937)
Random House (2013) Title page Gilmour, David. The Film Club: A Memoir, Hachette Book Group (2008) e-book Shore Patrol scene in The Last Detail, fair
Jack_Nicholson
English actor (1903–1988)
(uncredited) Cat People (1942) as Doc Carver (uncredited) Random Harvest (1942) as Julian Assignment in Brittany (1943) as Sam Wells Appointment in Berlin
Alan_Napier
British and American journalist (born 1953)
Vanity Fair Diaries: 1983-1992 by Tina Brown". www.publishersweekly.com. 14 November 2017. Retrieved 14 April 2022. "Author spotlight". Random House.
Tina_Brown
American attorney and politician (born 1988)
inspectors to observe Harris County's 2022 general election and perform random checks of election records, Menefee joined Houston Mayor Sylvester Turner
Christian_Menefee
Soccer tournament in North America
run commercials during these pauses. The match schedule, without group assignments, was announced on February 4, 2024. On June 13, 2024, FIFA released an
2026_FIFA_World_Cup
Mathematical rule for inverting probabilities
{\displaystyle P(A|B)} . Suppose that, after the agent has made these probability assignments, event B {\displaystyle B} occurs. An agent who follows Bayesian updating
Bayes'_theorem
Chief Justice of the United States from 1986 to 2005
predecessor of the U.S. Air Force. He served from 1943 to 1946, mostly in assignments in the United States. He was put into a pre-meteorology program and assigned
William_Rehnquist
American writer (born 1932)
the Times' Albany Bureau to cover state politics. It was a short-lived assignment, however, as his exacting habits and meticulous style soon irritated his
Gay_Talese
Statistic measuring inter-rater agreement for categorical items
{a+d}{a+b+c+d}}={\frac {20+15}{50}}=0.7} To calculate pe (the probability of random agreement) we note that: Reader A said "Yes" to 25 applicants and "No" to
Cohen's_kappa
2010 film by Clint Eastwood
the London Book Fair was recreated inside the Alexandra Palace for a scene featuring George and Marie. Publishers including Random House had their stands
Hereafter_(film)
Concept in game theory
player (or null player) property, which are widely accepted as defining a fair distribution. This method is used in many fields, from dividing profits in
Shapley_value
1966 novel by Truman Capote
supposedly chose the Clutter story, believing it would be the easier assignment. Capote later wrote a piece about following a cleaning woman, which he
In_Cold_Blood
2024 game show hosted by Rob Lowe
episodes) has nine duels per episode. One contestant is chosen at random (via "The Randomizer") to be a challenger and shown the categories of all opponents
The Floor (American game show)
The_Floor_(American_game_show)
American basketball player (born 1984)
(February 5, 2010). "Cleveland Cavaliers star LeBron James glad point-guard assignment is temporary". cleveland.com. Archived from the original on December 22
LeBron_James
Fictional character from The Sopranos
to Silvio by a Russian mobster named Valery. Paulie botches the simple assignment after he needlessly provokes Valery and they get into a fight at his apartment
Paulie_Gualtieri
1988 nonfiction book by Neil Sheehan
Vietnam and America's involvement in the conflict. Book I tells of Vann's assignment to Vietnam in 1962. Book II "The Antecedents to a Confrontation" tells
A_Bright_Shining_Lie
1999 film by Robert Iscove
of George Bernard Shaw's play Pygmalion and George Cukor's 1964 film My Fair Lady. The film received mixed reviews from critics, who praised the performances
She's_All_That
1997 video game developed by Blizzard North
has been considered one of the greatest games of all time for its randomized assignment of quests and enemies on each playthrough, online multiplayer, and
Diablo_(video_game)
Bogomolnaia, Anna; Moulin, Hervé (2001). "A New Solution to the Random Assignment Problem". Journal of Economic Theory. 100 (2): 295. doi:10.1006/jeth
Truthful_resource_allocation
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
American journalist
Baruch. At the height of the Great Depression, she was an editor of Vanity Fair. She later became notorious for an article called "Latins Are Lousy Lovers"
Helen_Lawrenson
American politician (born 1969)
a mentor, Fetterman says he became "preoccupied with the concept of the random lottery of birth", and promised the boy's mother he would continue to look
John_Fetterman
American-British actress (1911–1979)
Screen Snapshots Series 16, No. 4 (1936) Hollywood Goes to Town (1938) Assignment Foreign Legion (1956-1957 25 episodes) List of Academy Award winners and
Merle_Oberon
Star Wars character also known as Baby Yoda
Herzog), who works for a remnant of the now-fallen Galactic Empire. The assignment is to track down and capture an unidentified fifty-year-old target. The
Grogu
American politician (born 1973)
forward". NBC News. Retrieved March 12, 2025. "U.S. Senate: Committee Assignments of the 119th Congress". www.senate.gov. Retrieved March 11, 2026. "Members
Chris_Murphy
American journalist and author (1937–2005)
and substance abuse, and he failed to complete several high-profile assignments for Rolling Stone.[citation needed] For much of the late 1980s and early
Hunter_S._Thompson
American pastor and politician (born 1969)
2023. Mitchell, Tia. "Ossoff, Warnock receive their Senate committee assignments". The Atlanta Journal-Constitution. Archived from the original on February
Raphael_Warnock
American animated drama television series
she acts as a timid and caring mother, Renee coldly sees Caspian as an assignment. Krystina Alabado as Rachel Brooks / Hannah (season 1), a new student
Pantheon_(TV_series)
O.T. (Biotronic Operational Telecommunicator) is a robot built as an assignment for a pair of troublemaking sociopaths, who enlisted science girl Elise
List of The Transformers characters
List_of_The_Transformers_characters
Unit of information
A solution to the problem of reproducibility is the attempt to require FAIR data, that is, data that is Findable, Accessible, Interoperable, and Reusable
Data
Evaluates how likely it is that any difference between data sets arose by chance
simple example is testing the hypothesis that an ordinary six-sided die is "fair" (i. e., all six outcomes are equally likely to occur). In this case, the
Pearson's_chi-squared_test
American socialite (1891–1948)
Roosevelt, Mrs. Rutherfurd, and the Other Remarkable Women in His Life. Random House. ISBN 9781400064427. Rowley, Hazel (2010). Franklin and Eleanor: An
Lucy_Mercer_Rutherfurd
1985 film by Sydney Pollack
not in the plains. Denys was away from Kenya for two years on military assignment in Egypt, which is not mentioned. Denys took up flying and began to lead
Out_of_Africa_(film)
British photographer and designer (1904–1980)
including two for Best Costume Design (Gigi, 1958; My Fair Lady, 1964) and one for Best Art Direction (My Fair Lady, 1964), and received several Tony Awards for
Cecil_Beaton
American TV executive and consultant (1940–2017)
Fox Television Stations Group on August 15, 2005. Following his newest assignment, one of his first acts was canceling A Current Affair in September 2005
Roger_Ailes
American actress (1923–2012)
irresistible invitation to an unforgettable evening." It began during a modeling assignment on the Today show, where she caught the eye and ear of one of the producers
Tedi_Thurman
set up someone frau Wife free lance A writer writing without advance assignment free-for-all A general fight; a battle royal freebie This offer can be
Glossary of early twentieth century slang in the United States
Glossary_of_early_twentieth_century_slang_in_the_United_States
Position that there is no relationship between two phenomena
A {\displaystyle H_{A}} . A statistical significance test starts with a random sample from a population. If the sample data are consistent with the null
Null_hypothesis
FAIR RANDOM-ASSIGNMENT
FAIR RANDOM-ASSIGNMENT
Surname or Lastname
English
English : patronymic from Rand 1.
Boy/Male
English American
Son of Rand.
Male
English
Medieval form of English Randolf, RANDAL means "shield-wolf."
Surname or Lastname
English
English : nickname meaning ‘handsome’, ‘beautiful’, ‘fair’, Middle English fair, fayr, Old English fæger. The word was also occasionally used as a personal name in Middle English, applied to both men and women.Irish : translation of Gaelic fionn ‘fair’, which Woulfe describes as ‘a descriptive epithet that supplanted the real surname’, or a reduced Anglicized form of Gaelic Mac F(h)inn, a variant of Mag Fhinn (see McGinn).
Surname or Lastname
English
English : variant of Rand 1, from the Old French oblique case.
Female
Welsh
Welsh form of Greek Maria, MAIR means "obstinacy, rebelliousness" or "their rebellion."
Surname or Lastname
English
English : unexplained; perhaps a variant of Francom.
Boy/Male
English
Son of Rand.
Male
Norwegian
 Norwegian form of Old Norse Arnþórr, ANDOR means "eagle of Thor." Compare with another form of Andor.
Male
English
Variant spelling of English Gare, GAIR means "spear."
Surname or Lastname
English
English : probably a variant of Crandon, a habitational name from Crandon in Somerset or Crandean in Falmer, Sussex. Compare Grandin.
Surname or Lastname
English
English : variant of Brandon.
Female
English
Variant spelling of English Randy, RANDI means "worthy of admiration."
Male
English
Pet form of English Randall and Randolph, both RANDY means "shield-wolf." Compare with feminine Randy.
Male
Scandinavian
 Scandinavian form of Old Norse Randolfr, RANDOLF means "shield-wolf." Compare with another form of Randolf.
Male
English
 Variant spelling of Middle English Randulf, RANDOLF means "shield-wolf." Compare with other forms of Randolf.
Surname or Lastname
English (chiefly East Anglia)
English (chiefly East Anglia) : patronymic from the Middle English personal name Rand(e) (see Rand 1).
Surname or Lastname
English
English : variant spelling of Randall.Americanized spelling of Randel.
Male
Hungarian
 Variant spelling of Hungarian András, ANDOR means "man; warrior." Compare with another form of Andor.
Surname or Lastname
English
English : variant of Ransom.
FAIR RANDOM-ASSIGNMENT
FAIR RANDOM-ASSIGNMENT
Girl/Female
Anglo, Australian, British, English, German, Swedish
Joyous; Prosperity; Battle; Strife for Wealth
Female
Hungarian
Hungarian name derived from the word tündér, TÜNDÉR means "fairy."
Girl/Female
Tamil
Rajabrata | ராஜாபà¯à®°à®¤à®¾
Female
Welsh
Welsh Arthurian legend name of the mother of Culhwch, the hero of the story Culhwch and Olwen, GOLEUDDYDD means "splendid day" or "splendid sun."
Girl/Female
Tamil
Soumika | ஸோஂமிகா
Kumbh
Male
Welsh
Middle Welsh form of Old Welsh Urbgen, URIEN means "privileged birth." Urien was an actual historical king of Rheged who came to be incorporated into Arthurian legend as a Knight of the Round Table who initially opposed Arthur, but later became an ally. He was the husband of Morgan le Fay, father of Morvydd, Ywain/Owain, and Ywain the Bastard. Some authors make him a brother to King Lot and King Auguselus.Â
Boy/Male
Australian, Danish, Norse
Son of Odd
Surname or Lastname
Swiss German
Swiss German : habitational name for someone from Bohlingen in Switzerland which was formerly named Bollingen (see Bollinger).English : occupational name for a baker, from Old French bolonger, boulengier.
Boy/Male
Arabic, Muslim
Lord; Master
Boy/Male
Indian, Traditional
Third Eye of Shiva
FAIR RANDOM-ASSIGNMENT
FAIR RANDOM-ASSIGNMENT
FAIR RANDOM-ASSIGNMENT
FAIR RANDOM-ASSIGNMENT
FAIR RANDOM-ASSIGNMENT
v. t.
To make fair or beautiful.
n.
A fair woman; a sweetheart.
superl.
Not overcast; cloudless; clear; pleasant; propitious; favorable; -- said of the sky, weather, or wind, etc.; as, a fair sky; a fair day.
superl.
Characterized by frankness, honesty, impartiality, or candor; open; upright; free from suspicion or bias; equitable; just; -- said of persons, character, or conduct; as, a fair man; fair dealing; a fair statement.
v. i.
To go or stray at random.
n.
The release of a captive, or of captured property, by payment of a consideration; redemption; as, prisoners hopeless of ransom.
adv.
In a random manner.
n.
To exact a ransom for, or a payment on.
superl.
Without a dark hue; light; clear; as, a fair skin.
superl.
Free from any marked characteristic; average; middling; as, a fair specimen.
n.
A competitive exhibition of wares, farm products, etc., not primarily for purposes of sale; as, the Mechanics' fair; an agricultural fair.
superl.
Distinct; legible; as, fair handwriting.
n.
Random.
n.
To redeem from captivity, servitude, punishment, or forfeit, by paying a price; to buy out of servitude or penalty; to rescue; to deliver; as, to ransom prisoners from an enemy.
a.
Going at random or by chance; done or made at hazard, or without settled direction, aim, or purpose; hazarded without previous calculation; left to chance; haphazard; as, a random guess.
superl.
Free from obstacles or hindrances; unobstructed; unincumbered; open; direct; -- said of a road, passage, etc.; as, a fair mark; in fair sight; a fair view.
n.
A roving motion; course without definite direction; want of direction, rule, or method; hazard; chance; -- commonly used in the phrase at random, that is, without a settled point of direction; at hazard.
n.
Distance to which a missile is cast; range; reach; as, the random of a rifle ball.
a.
Having fair or light-colored hair.