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Vote-ratio Monotonicity
Vote-ratio, weight-ratio, or population-ratio monotonicity is a property of some apportionment methods. It says that if the entitlement for A grows at a faster rate than B (i.e. A grows proportionally more than B), A should not lose a seat to B. More formally, if the ratio of votes or populations A / B increases, then A should not lose a seat while B gains a seat. An apportionment method violating this rule may encounter population paradoxes. A particularly severe variant, where voting ''for'' a party causes it to ''lose'' seats, is called a no-show paradox. The largest remainders method exhibits both population and no-show paradoxes. Population-pair monotonicity Pairwise monotonicity says that if the ''ratio'' between the entitlements of two states i, j increases, then state j should not gain seats at the expense of state i. In other words, a shrinking state should not "steal" a seat from a growing state. Some earlier apportionment rules, such as Hamilton's method, do not s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Of Apportionment
In mathematics and fair division, apportionment problems involve dividing (''apportioning'') a whole number of identical goods fairly across several parties with real-valued entitlements. The original, and best-known, example of an apportionment problem involves distributing seats in a legislature between different federal states or political parties. However, apportionment methods can be applied to other situations as well, including bankruptcy problems, inheritance law (e.g. dividing animals), manpower planning (e.g. demographic quotas), and rounding percentages. Mathematically, an apportionment method is just a method of rounding real numbers to natural numbers. Despite the simplicity of this problem, every method of rounding suffers one or more paradoxes, as proven by the Balinski–Young theorem. The mathematical theory of apportionment identifies what properties can be expected from an apportionment method. The mathematical theory of apportionment was studied as early ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Highest Averages Method
The highest averages, divisor, or divide-and-round methods are a family of Apportionment (politics), apportionment rules, i.e. algorithms for fair division of seats in a legislature between several groups (like Political party, political parties or State (sub-national), states). More generally, divisor methods are used to round shares of a total to a Ratio, fraction with a fixed denominator (e.g. percentage points, which must add up to 100). The methods aim to treat voters equally by ensuring legislators One man, one vote, represent an equal number of voters by ensuring every party has the same seats-to-votes ratio (or ''divisor''). Such methods divide the number of votes by the number of votes needed to win a seat. The final apportionment. In doing so, the method approximately maintains proportional representation, meaning that a party with e.g. twice as many votes will win about twice as many seats. The divisor methods are generally preferred by Social choice theory, social ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apportionment Paradox
An apportionment paradox is a situation where an apportionment—a rule for dividing discrete objects according to some proportional relationship—produces results that violate notions of common sense or fairness. Certain quantities, like milk, can be divided in any proportion whatsoever; others, such as horses, cannot—only whole numbers will do. In the latter case, there is an inherent tension between the desire to obey the rule of proportion as closely as possible and the constraint restricting the size of each portion to discrete values. Several paradoxes related to apportionment and fair division have been identified. In some cases, simple adjustments to an apportionment methodology can resolve observed paradoxes. However, as shown by the Balinski–Young theorem, it is not always possible to provide a perfectly fair resolution that satisfies all competing fairness criteria. History An example of the apportionment paradox known as "the Alabama paradox" was discovered in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coherency (apportionment)
Coherence, also called uniformity or consistency, is a 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 also for each sub-problem. Every part of a fair division should be fair. The coherence requirement was first studied in the context of apportionment. In this context, failure to satisfy coherence is called the new states paradox: when a new U.S. state enters the union, and the number of seats in the House of Representatives is enlarged to accommodate the number of seats allocated to this new state, some other unrelated states are affected. Coherence is also relevant to other fair division problems, such as bankruptcy problems. Definition There is a ''resource'' to allocate, denoted by h. For example, it can be an integer representing the number of seats in a ''h''ouse of representatives. The resource should be allocated between some n ''agents''. For example, these can be f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogeneous Function
In mathematics, a homogeneous function is a function of several variables such that the following holds: If each of the function's arguments is multiplied by the same scalar (mathematics), scalar, then the function's value is multiplied by some power of this scalar; the power is called the degree of homogeneity, or simply the ''degree''. That is, if is an integer, a function of variables is homogeneous of degree if :f(sx_1,\ldots, sx_n)=s^k f(x_1,\ldots, x_n) for every x_1, \ldots, x_n, and s\ne 0. This is also referred to a ''th-degree'' or ''th-order'' homogeneous function. For example, a homogeneous polynomial of degree defines a homogeneous function of degree . The above definition extends to functions whose domain of a function, domain and codomain are vector spaces over a Field (mathematics), field : a function f : V \to W between two -vector spaces is ''homogeneous'' of degree k if for all nonzero s \in F and v \in V. This definition is often further generalized to f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concordance (apportionment)
Static population-monotonicity, also called concordance, says that a party with more votes should not receive a smaller apportionment The legal term apportionment (; Mediaeval Latin: , derived from , share), also called delimitation, is in general the distribution or allotment of proper shares, though may have different meanings in different contexts. Apportionment can refer ... of seats. Failures of concordance are often called electoral inversions or majority reversals. References {{Economics-stub Apportionment (politics) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Balance (apportionment)
Balance or balancedness is a property of apportionment methods, which are methods of allocating identical items among agents, such as dividing seats in a parliament among political parties or federal states. The property says that, if two agents have exactly the same entitlements, then the number of items they receive should differ by at most one. So if two parties win the same number of votes, or two states have the same populations, then the number of seats they receive should differ by at most one. Ideally, agents with identical entitlements should receive an identical number of items, but this may be impossible due to the indivisibility of the items. Balancedness requires that the difference between identical-entitlement agents should be the smallest difference allowed by the indivisibility, which is 1. For example, if there are 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 diffe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anonymity (social Choice)
In economics and social choice, a function satisfies anonymity, neutrality, or symmetry if the rule does not discriminate between different participants ahead of time. For example, in an election, a voter-anonymous function is one where it does not matter who casts which vote, i.e. all voters' ballots are equal ahead of time. Formally, this is defined by saying the rule returns the same outcome (whatever this may be) if the votes are "relabeled" arbitrarily, e.g. by swapping votes #1 and #2. Similarly, outcome-neutrality says the rule does not discriminate between different outcomes (e.g. candidates) ahead of time. Formally, if the labels assigned to each outcome are permuted arbitrarily, the returned result is permuted in the same way. Some authors reserve the term anonymity for agent symmetry and neutrality for outcome-symmetry, but this pattern is not perfectly consistent.{{Rp, 75 Examples Most voting rules are anonymous and neutral by design. For example, plurality voting i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peyton Young
Hobart Peyton Young (born March 9, 1945) is an American game theorist and economist known for his contributions to evolutionary game theory and its application to the study of institutional and technological change, as well as the theory of learning in games. He is currently centennial professor at the London School of Economics, James Meade Professor of Economics Emeritus at the University of Oxford, professorial fellow at Nuffield College Oxford, and research principal at the Office of Financial Research at the U.S. Department of the Treasury. Peyton Young was named a fellow of the Econometric Society in 1995, a fellow of the British Academy in 2007, and a fellow of the American Academy of Arts and Sciences in 2018. He served as president of the Game Theory Society from 2006 to 2008. He has published widely on learning in games, the evolution of social norms and institutions, cooperative game theory, bargaining and negotiation, taxation and cost allocation, political represe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Michel Balinski
Michel Louis Balinski (born Michał Ludwik Baliński; October 6, 1933 – February 4, 2019) was an American and French applied mathematician, economist, operations research analyst and political scientist. Educated in the United States, from 1980 he lived and worked in France. He was known for his work in optimisation (combinatorial, linear, nonlinear), convex polyhedra, stable matching, and the theory and practice of electoral systems, jury decision, and social choice. He was Directeur de Recherche de classe exceptionnelle (emeritus) of the C.N.R.S. at the École Polytechnique (Paris). He was awarded the John von Neumann Theory Prize by INFORMS in 2013. Michel Louis Balinski died in Bayonne, France. He maintained an active involvement in research and public appearances, his last public engagement took place in January 2019. Early life Michel Balinski was born in Geneva, Switzerland, the grandson of the Polish bacteriologist and founder of UNICEF, Ludwik Rajchman. Brought up ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maine
Maine ( ) is a U.S. state, state in the New England region of the United States, and the northeasternmost state in the Contiguous United States. It borders New Hampshire to the west, the Gulf of Maine to the southeast, and the Provinces and territories of Canada, Canadian provinces of New Brunswick and Quebec to the northeast and northwest, and shares a maritime border with Nova Scotia. Maine is the largest U.S. state, state in New England by total area, nearly larger than the combined area of the remaining five states. Of the List of states and territories of the United States, 50 U.S. states, it is the List of U.S. states and territories by area, 12th-smallest by area, the List of U.S. states and territories by population, 9th-least populous, the List of U.S. states by population density, 13th-least densely populated, and the most rural. Maine's List of capitals in the United States, capital is Augusta, Maine, Augusta, and List of municipalities in Maine, its most populous c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
