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Entitlement (fair Division)
In fair division, a person's entitlement is the value of the goods they are owed or deserve, i.e. the total value of the goods or resources that a player would ideally receive. For example, in party-list proportional representation, a party's seat entitlement (sometimes called its seat quota) is equal to its share of the vote, times the number of seats in the legislature. Dividing money Even when only money is to be divided and some fixed amount has been specified for each recipient, the problem can be complex. The amounts specified may be more or less than the amount of money, and the profit or loss will then need to be shared out. The proportional rule is normally used in law nowadays, and is the default assumption in the theory of bankruptcy. However, other rules can also be used. For example: * The Shapley value is one common method of deciding bargaining power, as can be seen in the airport problem. * Welfare economics on the other hand tries to determine allocations de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fair Division
Fair division is the problem in game theory of dividing a set of resources among several people who have an Entitlement (fair division), entitlement to them so that each person receives their due share. The central tenet of fair division is that such a division should be performed by the players themselves, without the need for external arbitration, as only the players themselves really know how they value the goods. There are many different kinds of fair division problems, depending on the nature of goods to divide, the criteria for fairness, the nature of the players and their preferences, and other criteria for evaluating the quality of the division. The archetypal fair division algorithm is divide and choose. The research in fair division can be seen as an extension of this procedure to various more complex settings. Description In game theory, fair division is the problem of dividing a set of resources among several people who have an Entitlement (fair division), entitlem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Maschler
Michael Bahir Maschler (; July 22, 1927 – July 20, 2008) was an Israeli mathematician well known for his contributions to the field of game theory. He was a professor in the Einstein Institute of Mathematics and the Center for the Study of Rationality at the Hebrew University of Jerusalem. In 2012, the Israeli Chapter of the Game Theory Society founded the Maschler Prize, an annual prize awarded to an outstanding research student in game theory and related topics in Israel. Biography Michael B. Maschler was born in Jerusalem Jerusalem is a city in the Southern Levant, on a plateau in the Judaean Mountains between the Mediterranean Sea, Mediterranean and the Dead Sea. It is one of the List of oldest continuously inhabited cities, oldest cities in the world, and ... on July 22, 1927. Selected publications For a complete list of English and Hebrew publications, see Michael Maschler: In Memoriam, above. * "The Bargaining Set for Cooperative Games", with R.J. Aumann ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fair Item Allocation
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 among several partners who potentially value them differently, and each item has to be given as a whole to a single person. This situation arises in various real-life scenarios: * Several heirs want to divide the inherited property, which contains e.g. a house, a car, a piano and several paintings. * Several lecturers want to divide the courses given in their faculty. Each lecturer can teach one or more whole courses. *White elephant gift exchange parties The indivisibility of the items implies that a fair division may not be possible. As an extreme example, if there is only a single item (e.g. a house), it must be given to a single partner, but this is not fair to the other partners. This is in contrast to the fair cake-cutting problem, where the dividend is divisible and a fair division always exists. In some cases, the ind ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Penrose Method
The Penrose method (or square-root method) is a method devised in 1946 by Professor Lionel Penrose for allocating the voting weights of delegations (possibly a single representative) in decision-making bodies proportional to the square root of the population represented by this delegation. This is justified by the fact that, due to the square root law of Penrose, the ''a priori'' voting power (as defined by the Penrose–Banzhaf index) of a member of a voting body is inversely proportional to the square root of its size. Under certain conditions, this allocation achieves equal voting powers for all people represented, independent of the size of their constituency. Proportional allocation would result in excessive voting powers for the electorates of larger constituencies. A precondition for the appropriateness of the method is ''en bloc'' voting of the delegations in the decision-making body: a delegation cannot split its votes; rather, each delegation has just a single vote to wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Banzhaf Power Index
The Banzhaf power index, named after John Banzhaf (originally invented by Lionel Penrose in 1946 and sometimes called Penrose–Banzhaf index; also known as the Banzhaf–Coleman index after James Samuel Coleman), is a power index defined by the probability of changing an outcome of a vote where voting rights are not necessarily equally divided among the voters or shareholders. To calculate the power of a voter using the Banzhaf index, list all the winning coalitions, then count the critical voters. A ''critical voter'' is a voter who, if he changed his vote from yes to no, would cause the measure to fail. A voter's power is measured as the fraction of all swing votes that he could cast. There are some algorithms for calculating the power index, e.g., dynamic programming techniques, enumeration methods and Monte Carlo methods. Examples Voting game Simple voting game A simple voting game, taken from ''Game Theory and Strategy'' by Philip D. Straffin: ; 4, 3, 2, 1 The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shapley–Shubik Power Index
The Shapley–Shubik power index was formulated by Lloyd Shapley and Martin Shubik in 1954 to measure the powers of players in a voting game. The constituents of a voting system, such as legislative bodies, executives, shareholders, individual legislators, and so forth, can be viewed as players in an ''n''-player game. Players with the same preferences form coalitions. Any coalition that has enough votes to pass a bill or elect a candidate is called winning. The power of a coalition (or a player) is measured by the fraction of the possible voting sequences in which that coalition casts the deciding vote, that is, the vote that first guarantees passage or failure. The power index is normalized between 0 and 1. A power of 0 means that a coalition has no effect at all on the outcome of the game; and a power of 1 means a coalition determines the outcome by its vote. Also the sum of the powers of all the players is always equal to 1. There are some algorithms for calculating the power ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States
The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 contiguous states border Canada to the north and Mexico to the south, with the semi-exclave of Alaska in the northwest and the archipelago of Hawaii in the Pacific Ocean. The United States asserts sovereignty over five Territories of the United States, major island territories and United States Minor Outlying Islands, various uninhabited islands in Oceania and the Caribbean. It is a megadiverse country, with the world's List of countries and dependencies by area, third-largest land area and List of countries and dependencies by population, third-largest population, exceeding 340 million. Its three Metropolitan statistical areas by population, largest metropolitan areas are New York metropolitan area, New York, Greater Los Angeles, Los Angel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
European Union
The European Union (EU) is a supranational union, supranational political union, political and economic union of Member state of the European Union, member states that are Geography of the European Union, located primarily in Europe. The union has a total area of and an estimated population of over 449million as of 2024. The EU is often described as a ''sui generis'' political entity combining characteristics of both a federation and a confederation. Containing 5.5% of the world population in 2023, EU member states generated a nominal gross domestic product (GDP) of around €17.935 trillion in 2024, accounting for approximately one sixth of global economic output. Its cornerstone, the European Union Customs Union, Customs Union, paved the way to establishing European Single Market, an internal single market based on standardised European Union law, legal framework and legislation that applies in all member states in those matters, and only those matters, where the states ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apportionment (politics)
Apportionment is the process by which seats in a Legislature, legislative body are distributed among administrative divisions, such as states or parties, entitled to Representation (politics), representation. This page presents the general principles and issues related to apportionment. The apportionment by country page describes the specific practices used around the world. The Mathematics of apportionment page describes mathematical formulations and properties of apportionment rules. The simplest and most universal principle is that elections should One man, one vote, give each vote an equal weight. This is both intuitive and stated in laws such as the Fourteenth Amendment to the United States Constitution (the Equal Protection Clause). One example of deliberate malapportionment is seen in bicameral legislatures: while one house, often called a house of commons or representatives, is based on proportional representation, the other is based on regional representation. This is mod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proportional Representation
Proportional representation (PR) refers to any electoral system under which subgroups of an electorate are reflected proportionately in the elected body. The concept applies mainly to political divisions (Political party, political parties) among voters. The aim of such systems is that all votes cast contribute to the result so that each representative in an assembly is mandated by a roughly equal number of voters, and therefore all votes have equal weight. Under other election systems, a bare Plurality (voting), plurality or a scant majority in a district are all that are used to elect a member or group of members. PR systems provide balanced representation to different factions, usually defined by parties, reflecting how votes were cast. Where only a choice of parties is allowed, the seats are allocated to parties in proportion to the vote tally or ''vote share'' each party receives. Exact proportionality is never achieved under PR systems, except by chance. The use of elector ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cloud Computing
Cloud computing is "a paradigm for enabling network access to a scalable and elastic pool of shareable physical or virtual resources with self-service provisioning and administration on-demand," according to International Organization for Standardization, ISO. Essential characteristics In 2011, the National Institute of Standards and Technology (NIST) identified five "essential characteristics" for cloud systems. Below are the exact definitions according to NIST: * On-demand self-service: "A consumer can unilaterally provision computing capabilities, such as server time and network storage, as needed automatically without requiring human interaction with each service provider." * Broad network access: "Capabilities are available over the network and accessed through standard mechanisms that promote use by heterogeneous thin or thick client platforms (e.g., mobile phones, tablets, laptops, and workstations)." * Pooling (resource management), Resource pooling: " The provider' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Envy-free Cake-cutting With Different Entitlements
An envy-free cake-cutting is a kind of fair cake-cutting. It is a division of a heterogeneous resource ("cake") that satisfies the envy-free criterion, namely, that every partner feels that their allocated share is at least as good as any other share, according to their own subjective valuation. When there are only two partners, the problem is easy and was solved in antiquity by the divide and choose protocol. When there are three or more partners, the problem becomes much more challenging. Two major variants of the problem have been studied: * Connected pieces, e.g. if the cake is a 1-dimensional interval then each partner must receive a single sub-interval. If there are n partners, only n-1 cuts are needed. * General pieces, e.g. if the cake is a 1-dimensional interval then each partner can receive a union of disjoint sub-intervals. Short history Modern research into the fair cake-cutting problem started in the 1940s. The first fairness criterion studied was proportional div ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
