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Seat Bias
Seat bias is a property describing methods of apportionment. These are methods used to allocate seats in a parliament among federal states or among political parties. A method is ''biased'' if it systematically favors small parties over large parties, or vice versa. There are various ways to compute the bias of apportionment methods. When the agents are federal states, it is particularly important to avoid bias between large states and small states. There are several ways to measure this bias formally. Notation There is a positive integer h (=house size), representing the total number of seats to allocate. There is a positive integer n representing the number of parties to which seats should be allocated. There is a vector of fractions (t_1,\ldots,t_n) with \sum_^n t_i = 1, representing ''entitlements'' - t_i represents the entitlement of party i, that is, the fraction of seats to which i is entitled (out of the total of h). This is usually the fraction of votes that this party ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Of Apportionment
Mathematics of apportionment describes mathematical principles and algorithms for fair allocation of identical items among parties with different entitlements. Such principles are used to apportion seats in parliaments among federal states or political parties. See apportionment (politics) for the more concrete principles and issues related to apportionment, and apportionment by country for practical methods used around the world. Mathematically, an apportionment method is just a method of rounding fractions to integers. As simple as it may sound, each and every method for rounding suffers from one or more paradoxes. The mathematical theory of apportionment aims to decide what paradoxes can be avoided, or in other words, what properties can be expected from an apportionment method. The mathematical theory of apportionment was studied as early as 1907 by the mathematician Agner Krarup Erlang. It was later developed to a great detail by the mathematician Michel Balinsky and the econo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Federal States
A federation (also known as a federal state) is a political entity characterized by a union of partially self-governing provinces, states, or other regions under a central federal government (federalism). In a federation, the self-governing status of the component states, as well as the division of power between them and the central government, is typically constitutionally entrenched and may not be altered by a unilateral decision, neither by the component states nor the federal political body. Alternatively, a federation is a form of government in which sovereign power is formally divided between a central authority and a number of constituent regions so that each region retains some degree of control over its internal affairs. It is often argued that federal states where the central government has overriding powers are not truly federal states. For example, such overriding powers may include: the constitutional authority to suspend a constituent state's government by i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Political Parties
A political party is an organization that coordinates candidates to compete in a particular country's elections. It is common for the members of a party to hold similar ideas about politics, and parties may promote specific ideological or policy goals. Political parties have become a major part of the politics of almost every country, as modern party organizations developed and spread around the world over the last few centuries. It is extremely rare for a country to have no political parties. Some countries have only one political party while others have several. Parties are important in the politics of autocracies as well as democracies, though usually democracies have more political parties than autocracies. Autocracies often have a single party that governs the country, and some political scientists consider competition between two or more parties to be an essential part of democracy. Parties can develop from existing divisions in society, like the divisions betwe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entitlement (fair Division)
Entitlement in fair division describes that proportion of the resources or goods to be divided that a player can expect to receive. In many fair division settings, all agents have ''equal entitlements'', which means that each agent is entitled to 1/''n'' of the resource. But there are practical settings in which agents have ''different entitlements''. Some examples are: * In partnership resolution settings, each partner is entitled to a fraction of the common assets in proportion to his/her investment in the partnership. * In inheritance settings, the law in some jurisdictions prescribes a different share to each heir according to his/her proximity to the deceased person. For example, according to the Bible, the firstborn son must receive twice as much as every other son. In contrast, according to the Italian law, when there are three heirs - parent, brother and spouse - they are entitled to 1/4, 1/12 and 2/3 respectively. * In parliamentary democracies, each party is entitled to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divisor Method
A highest-averages method, also called a divisor method, is a class of methods for allocating seats in a parliament among agents such as political parties or federal states. A divisor method is an iterative method: at each iteration, the number of votes of each party is divided by its ''divisor'', which is a function of the number of seats (initially 0) currently allocated to that party. The next seat is allocated to the party whose resulting ratio is largest. Definitions The inputs to a divisor method are the number of seats to allocate, denoted by ''h'', and the vector of parties' entitlements, where the entitlement of party i is denoted by t_i (a number between 0 and 1 determining the fraction of seats to which i is entitled). Assuming all votes are counted, t_i is simply the number of votes received by i, divided by the total number of votes. Procedural definition A divisor method is parametrized by a function d(k), mapping each integer k to a real number (usually in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Majorization
In mathematics, majorization is a preorder on vectors of real numbers. Let ^_,\ i=1,\,\ldots,\,n denote the i-th largest element of the vector \mathbf\in\mathbb^n. Given \mathbf,\ \mathbf \in \mathbb^n, we say that \mathbf weakly majorizes (or dominates) \mathbf from below (or equivalently, we say that \mathbf is weakly majorized (or dominated) by \mathbf from below) denoted as \mathbf \succ_w \mathbf if \sum_^k x_^ \geq \sum_^k y_^ for all k=1,\,\dots,\,d. If in addition \sum_^d x_i^ = \sum_^d y_i^, we say that \mathbf majorizes (or dominates) \mathbf , written as \mathbf \succ \mathbf , or equivalently, we say that \mathbf is majorized (or dominated) by \mathbf. The order of the entries of the vectors \mathbf or \mathbf does not affect the majorization, e.g., the statement (1,2)\prec (0,3) is simply equivalent to (2,1)\prec (3,0). As a consequence, majorization is not a partial order, since \mathbf \succ \mathbf and \mathbf \succ \mathbf do not imply \mathbf = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Largest Remainder Method
The largest remainder method (also known as Hare–Niemeyer method, Hamilton method or as Vinton's method) is one way of allocating seats proportionally for representative assemblies with party list voting systems. It contrasts with various highest averages methods (also known as divisor methods). Method The ''largest remainder method'' requires the numbers of votes for each party to be divided by a quota representing the number of votes ''required'' for a seat (i.e. usually the total number of votes cast divided by the number of seats, or some similar formula). The result for each party will usually consist of an integer part plus a fractional remainder. Each party is first allocated a number of seats equal to their integer. This will generally leave some remainder seats unallocated: the parties are then ranked on the basis of the fractional remainders, and the parties with the largest remainders are each allocated one additional seat until all the seats have been alloca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Webster/Sainte-Laguë Method
The Webster method, also called the Sainte-Laguë method () or the major fractions method, is a method for allocating seats in a parliament among federal states, or among parties in a party-list proportional representation system. The method was first described in 1832 by the American statesman and senator Daniel Webster. In 1842 the method was adopted for proportional allocation of seats in United States congressional apportionment (Act of 25 June 1842, ch 46, 5 Stat. 491). It was then replaced by Hamilton method and in 1911 the Webster method was reintroduced. The method was again replaced in 1940, this time by the Huntington–Hill method. The same method was independently invented in 1910 by the French mathematician André Sainte-Laguë. It seems that French and European literature was unaware of Webster until after World War II. This is the reason for the double name. Description After all the votes have been tallied, successive quotients are calculated for each p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. For example, * a 0-dimensional simplex is a point, * a 1-dimensional simplex is a line segment, * a 2-dimensional simplex is a triangle, * a 3-dimensional simplex is a tetrahedron, and * a 4-dimensional simplex is a 5-cell. Specifically, a ''k''-simplex is a ''k''-dimensional polytope which is the convex hull of its ''k'' + 1 vertices. More formally, suppose the ''k'' + 1 points u_0, \dots, u_k \in \mathbb^ are affinely independent, which means u_1 - u_0,\dots, u_k-u_0 are linearly independent. Then, the simplex determined by them is the set of points : C = \left\ This representation in terms of weighted vertices is known as the barycentric coordinate system. A regular simplex is a simplex that is also a regular polytop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electoral Threshold
The electoral threshold, or election threshold, is the minimum share of the primary vote that a candidate or political party requires to achieve before they become entitled to representation or additional seats in a legislature. This limit can operate in various ways, e.g. in party-list proportional representation systems where an electoral threshold requires that a party must receive a specified minimum percentage of votes (e.g. 5%), either nationally or in a particular electoral district, to obtain seats in the legislature. In Single transferable voting the election threshold is called the quota and not only the first choice but also the next-indicated choices are used to determine whether or not a party passes the electoral threshold (and it is possible to be elected under STV even if a candidate does not pass the election threshold). In MMP systems the election threshold determines which parties are eligible for the top-up seats. The effect of an electoral threshold is to d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Political Alliance
A political group is a group consisting of political parties or legislators of aligned ideologies. A technical group is similar to a political group, but with members of differing ideologies. International terms Equivalent terms are used different countries, including: Argentina (''bloque'' and ''interbloque''), Australia (party room); Austria (''Club''); Belgium (''fractie''/''fraction''/''Fraktion''); Brazil and Portugal ("grupo parlamentar" or, informally, "bancadas"); Germany (''Fraktion''); Italy (''gruppo''), Finland (eduskuntaryhmä/''riksdagsgrupp''); the Netherlands (''fractie''); Poland (''frakcja''), Switzerland (''fraction''/''Fraktion''/''frazione''); and Romania (''grup parlamentar''). A political group in Swiss Federal Assembly is called a ''parliamentary group'', which differs from a parliamentary group in the UK. Examples Armenia In Armenia, political parties often form political groups before running in elections. Prior to the 2021 Armenian parliame ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
