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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 always yields an ex-post Pareto efficient (PE) outcome. Moreover, in an assignment problem, every deterministic PE assignment is ... [...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 are ''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 Tri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Random Permutation
A random permutation is a sequence where any order of its items is equally likely at random, that is, it is a permutation-valued random variable of a set of objects. The use of random permutations is common in games of chance and in randomized algorithms in coding theory, cryptography, and simulation. A good example of a random permutation is the fair shuffling of a standard deck of cards: this is ideally a random permutation of the 52 cards. Computation of random permutations Entry-by-entry methods One algorithm for generating a random permutation of a set of size ''n'' uniformly at random, i.e., such that each of the ''n''! permutations is equally likely to appear, is to generate a sequence by uniformly randomly selecting an integer between 1 and ''n'' (inclusive), sequentially and without replacement ''n'' times, and then to interpret 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 h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Truthful Mechanism
In mechanism design, a strategyproof (SP) mechanism is a game form in which each player has a weakly- dominant strategy, so that no player can gain by "spying" over the other players to know what they are going to play. When the players have private information (e.g. their type or their value to some item), and the strategy space of each player consists of the possible information values (e.g. possible types or values), a truthful mechanism is a game in which revealing the true information is a weakly-dominant strategy for each player. An SP mechanism is also called dominant-strategy-incentive-compatible (DSIC), to distinguish it from other kinds of incentive compatibility. A SP mechanism is immune to manipulations by individual players (but not by coalitions). In contrast, in a group strategyproof mechanism, no group of people can collude to misreport their preferences in a way that makes every member better off. In a strong group strategyproof mechanism, no group of people can c ... [...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 (economics), 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 e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Pareto Efficient
In welfare economics, a Pareto improvement formalizes the idea of an outcome being "better in every possible way". A change is called a Pareto improvement if it leaves at least one person in society better off without leaving anyone else worse off than they were before. A situation is called Pareto efficient or Pareto optimal if all possible Pareto improvements have already been made; in other words, there are no longer any ways left to make one person better off without making some other person worse-off. In social choice theory, the same concept is sometimes called the unanimity principle, which says that if ''everyone'' in a society ( non-strictly) prefers A to B, society as a whole also non-strictly prefers A to B. The Pareto front consists of all Pareto-efficient situations. In addition to the context of efficiency in ''allocation'', the concept of Pareto efficiency also arises in the context of ''efficiency in production'' vs. '' x-inefficiency'': a set of outputs of go ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Von Neumann-Morgenstern Utilities
The term () is used in German surnames either as a nobiliary particle indicating a noble patrilineality, or as a simple preposition used by commoners that means or . Nobility directories like the often abbreviate the noble term to ''v.'' In medieval or early modern names, the particle was at times added to commoners' names; thus, meant . This meaning is preserved in Swiss toponymic surnames and in the Dutch , which is a cognate of but also does not necessarily 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 associated with this naming convention. According to German alphabetical sorting, people with ''von'' in their surnames – of nobl ... [...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 ... [...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 solut ... [...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 contrast ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Strategyproof
In mechanism design, a strategyproof (SP) mechanism is a game form in which each player has a weakly-dominant strategy, so that no player can gain by "spying" over the other players to know what they are going to play. When the players have private information (e.g. their type or their value to some item), and the strategy space of each player consists of the possible information values (e.g. possible types or values), a truthful mechanism is a game in which revealing the true information is a weakly-dominant strategy for each player. An SP mechanism is also called dominant-strategy-incentive-compatible (DSIC), to distinguish it from other kinds of incentive compatibility. A SP mechanism is immune to manipulations by individual players (but not by coalitions). In contrast, in a group strategyproof mechanism, no group of people can collude to misreport their preferences in a way that makes every member better off. In a strong group strategyproof mechanism, no group of people can col ... [...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 they 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 mechanism design, a strategyproof (SP) mechanism is a game form in which each player has a weakly- dominant strategy, so that no player can gain by "spying" over the other players to know what they are going to play. When the players have private information (e.g. their type or their value to some item), and the strategy space of each player consists of the possible information values (e.g. possible types or values), a truthful mechanism is a game in which revealing the true information is a weakly-dominant strategy for each player. An SP mechanism is also called dominant-strategy-incentive-compatible (DSIC), to distinguish it from other kinds of incentive compatibility. A SP mechanism is immune to manipulations by individual players (but not by coalitions). In contrast, in a group strategyproof mechanism, no group of people can collude to misreport their preferences in a way that makes every member better off. In a strong group strategyproof mechanism, no group of people can c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |