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Random Priority Item Allocation
Random priority (RP), also called Random serial dictatorship (RSD), is a procedure for fair random assignment - dividing indivisible items fairly among people. Suppose n partners have to divide n (or fewer) different items among them. Since the items are indivisible, some partners will necessarily get the less-preferred items (or no items at all). RSD attempts to insert fairness into this situation in the following way. Draw a random permutation of the agents from the uniform distribution. Then, let them successively choose an object in that order (so the first agent in the ordering gets first pick and so on). Properties RSD is a truthful mechanism when the number of items is at most the number of agents, since you only have one opportunity to pick an item, and the obviously dominant strategy in this opportunity is to pick the best available item. RSD is ex-ante envy-free (EF), since each agent has the same chance to appear in each position in the ordering. Obviously, it is not e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Fair Random Assignment
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 problem'' or ''one-sided matching''), there ''m'' objects and they have to be allocated among ''n'' agents, such that each agent receives at most one object. Examples include the assignment of jobs to workers, rooms to housemates, dormitories to students, time-slots to users of a common machine, and so on. In general, a fair assignment may be impossible to attain. For example, if Alice and Batya both prefer the eastern room to the western room, only one of them will get it and the other will be envious. In the random assignment setting, fairness is attained using a lottery. So in the simple example above, Alice and Batya will toss a fair coin and the winner will get the eastern room. History Random assignment is mentioned already in the Bible: a lottery was used to allocate the lands of Canaan among the Tribes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Random Permutation
A random permutation is a random ordering of a set of objects, that is, a permutation-valued random variable. The use of random permutations is often fundamental to fields that use randomized algorithms such as coding theory, cryptography, and simulation. A good example of a random permutation is the shuffling of a deck of cards: this is ideally a random permutation of the 52 cards. Generating random permutations Entry-by-entry brute force method One method of generating a random permutation of a set of length ''n'' uniformly at random (i.e., each of the ''n''! permutations is equally likely to appear) is to generate a sequence by taking a random number between 1 and ''n'' sequentially, ensuring that there is no repetition, and interpreting this sequence (''x''1, ..., ''x''''n'') as the permutation : \begin 1 & 2 & 3 & \cdots & n \\ x_1 & x_2 & x_3 & \cdots & x_n \\ \end, shown here in two-line notation. This brute-force method will require occasional retries whenever the r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Truthful Mechanism
In game theory, an asymmetric game where players have private information is said to be strategy-proof or strategyproof (SP) if it is a weakly-dominant strategy for every player to reveal his/her private information, i.e. given no information about what the others do, you fare best or at least not worse by being truthful. SP is also called truthful or dominant-strategy-incentive-compatible (DSIC), to distinguish it from other kinds of incentive compatibility. An SP game is not always immune to collusion, but its robust variants are; with group strategyproofness no group of people can collude to misreport their preferences in a way that makes every member better off, and with strong group strategyproofness no group of people can collude to misreport their preferences in a way that makes at least one member of the group better off without making any of the remaining members worse off. Examples Typical examples of SP mechanisms are majority voting between two alternatives, secon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Envy-freeness
Envy-freeness, also known as no-envy, is a criterion for fair division. It says that, when resources are allocated among people with equal rights, each person should receive a share that is, in their eyes, at least as good as the share received by any other agent. In other words, no person should feel envy. General definitions Suppose a certain resource is divided among several agents, such that every agent i receives a share X_i. Every agent i has a personal preference relation \succeq_i over different possible shares. The division is called envy-free (EF) if for all i and j: :::X_i \succeq_i X_j Another term for envy-freeness is no-envy (NE). If the preference of the agents are represented by a value functions V_i, then this definition is equivalent to: :::V_i(X_i) \geq V_i(X_j) Put another way: we say that agent i ''envies'' agent j if i prefers the piece of j over his own piece, i.e.: :::X_i \prec_i X_j :::V_i(X_i) 2 the problem is much harder. See envy-free cake-cutting. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Pareto Efficient
Pareto efficiency or Pareto optimality is a situation where no action or allocation is available that makes one individual better off without making another worse off. The concept is named after Vilfredo Pareto (1848–1923), Italian civil engineer and economist, who used the concept in his studies of economic efficiency and income distribution. The following three concepts are closely related: * Given an initial situation, a Pareto improvement is a new situation where some agents will gain, and no agents will lose. * A situation is called Pareto-dominated if there exists a possible Pareto improvement. * A situation is called Pareto-optimal or Pareto-efficient if no change could lead to improved satisfaction for some agent without some other agent losing or, equivalently, if there is no scope for further Pareto improvement. The Pareto front (also called Pareto frontier or Pareto set) is the set of all Pareto-efficient situations. Pareto originally used the word "optimal" for th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Von Neumann-Morgenstern Utilities
The term ''von'' () is used in German language surnames either as a nobiliary particle indicating a noble patrilineality, or as a simple preposition used by commoners that means ''of'' or ''from''. Nobility directories like the ''Almanach de Gotha'' often abbreviate the noble term ''von'' to ''v.'' In medieval or early modern names, the ''von'' particle was at times added to commoners' names; thus, ''Hans von Duisburg'' meant "Hans from he city ofDuisburg". This meaning is preserved in Swiss toponymic surnames and in the Dutch or Afrikaans ''van'', which is a cognate of ''von'' but does not indicate nobility. Usage Germany and Austria The abolition of the monarchies in Germany and Austria in 1919 meant that neither state has a privileged nobility, and both have exclusively republican governments. In Germany, this means that legally ''von'' simply became an ordinary part of the surnames of the people who used it. There are no longer any legal privileges or constraints as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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SD-efficiency
Ordinal Pareto efficiency refers to several adaptations of the concept of Pareto-efficiency to settings in which the agents only express ordinal utilities over items, but not over bundles. That is, agents rank the items from best to worst, but they do not rank the subsets of items. In particular, they 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, consider an economy with three items and two agents, with the following rankings: * Alice: x > y > z. * George: x > z > y. Consider the allocation lice: x, George: y,z Whether or not this allocation is Pareto-efficient depends on the agents' numeric valuations. For example: * It is possible that Alice prefers to and George prefers to (for example: Alice's valuations for x,y,z are 8,7,6 and George's valuations are 7,1,2, so the utility profile is 8,3). Then the allocation is not Pareto-efficient, since both Alice and George wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Probabilistic-serial Rule
A simultaneous eating algorithm (SE) is an algorithm for allocating divisible objects among agents with ordinal preferences. "Ordinal preferences" means that each 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 - a weak ordinal variant of Pareto-efficiency (it means that the allocation is Pareto-efficient for ''at least one'' vector of additive utility functions consistent with the agents' item rankings). SE is parametrized by the "eating speed" of each agent. If all agents are given the same eating speed, then the SE allocation satisfies SD-envy-freeness - a strong ordinal variant of envy-freeness (it means that the allocation is envy-free for ''all'' vectors of additive utility functions consistent with the agents' item rankings). This particular variant of SE is called the Probabilistic Serial rule (PS). SE was developed by Hervé Moulin and Anna Bogomolnaia as a soluti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Ordinal Utility
In economics, an ordinal utility function is a function representing the preferences of an agent on an ordinal scale. Ordinal utility theory claims that it is only meaningful to ask which option is better than the other, but it is meaningless to ask ''how much'' better it is or how good it is. All of the theory of consumer decision-making under conditions of certainty can be, and typically is, expressed in terms of ordinal utility. For example, suppose George tells us that "I prefer A to B and B to C". George's preferences can be represented by a function ''u'' such that: :u(A)=9, u(B)=8, u(C)=1 But critics of cardinal utility claim the only meaningful message of this function is the order u(A)>u(B)>u(C); the actual numbers are meaningless. Hence, George's preferences can also be represented by the following function ''v'': :v(A)=9, v(B)=2, v(C)=1 The functions ''u'' and ''v'' are ordinally equivalent – they represent George's preferences equally well. Ordinal utility contrasts ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Strategyproof
In game theory, an asymmetric game where players have private information is said to be strategy-proof or strategyproof (SP) if it is a weakly-dominant strategy for every player to reveal his/her private information, i.e. given no information about what the others do, you fare best or at least not worse by being truthful. SP is also called truthful or dominant-strategy-incentive-compatible (DSIC), to distinguish it from other kinds of incentive compatibility. An SP game is not always immune to collusion, but its robust variants are; with group strategyproofness no group of people can collude to misreport their preferences in a way that makes every member better off, and with strong group strategyproofness no group of people can collude to misreport their preferences in a way that makes at least one member of the group better off without making any of the remaining members worse off. Examples Typical examples of SP mechanisms are majority voting between two alternatives, second ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Round-robin Item Allocation
Round robin is a 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: each agent believes that the bundle he received is at least as good as the bundle of any other agent, when at most one item is removed from the other bundle. In sports, the round-robin procedure is called a draft. Setting There are ''m'' objects to allocate, and ''n'' people ("agents") with equal rights to these objects. Each person has different preferences over the objects. The preferences of an agent are given by a vector of values - a value for each object. It is assumed that the value of a bundle for an agent is the sum of the values of the objects in the bundle (in other words, the agents' valuations are an additive set function on the set of objects). Description The protocol proceeds as follows: # Number the people arbitrarily from 1 to n; # While there are unassigned objects: #* Let each p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Strategyproofness
In game theory, an asymmetric game where players have private information is said to be strategy-proof or strategyproof (SP) if it is a weakly-dominant strategy for every player to reveal his/her private information, i.e. given no information about what the others do, you fare best or at least not worse by being truthful. SP is also called truthful or dominant-strategy-incentive-compatible (DSIC), to distinguish it from other kinds of incentive compatibility. An SP game is not always immune to collusion, but its robust variants are; with group strategyproofness no group of people can collude to misreport their preferences in a way that makes every member better off, and with strong group strategyproofness no group of people can collude to misreport their preferences in a way that makes at least one member of the group better off without making any of the remaining members worse off. Examples Typical examples of SP mechanisms are majority voting between two alternatives, secon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |