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Proportionality For Solid Coalitions
Proportionality for Solid Coalitions (PSC) is a voting system criterion relating to ranked voting systems. It's the essential requirementD. R. Woodall: ''Monotonicity of single-seat preferential election rules''. Discrete Applied Mathematics 77 (1997), p. 83–84. to guarantee a proportional representation of voters in multiple winner ranked voting systems. Solid coalitions Informally speaking, a solid coalition is a group of voters who prefer any candidate within a certain set of candidates over any candidate not in the set. A set of voters V is a ''solid coalition'' for a set of candidates C, if every voter in V ranks every candidate in C ahead of every candidate that is not in C. * When a voter is part of a solid coalition that prefers some set of candidates, they are said to be "solidly supporting" or "solidly committed to" that set of candidates. Any voter who ranks a single candidate as their 1st choice solidly supports that candidate. Note that a solid coalition may be "n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voting System
An electoral system or voting system is a set of rules that determine how elections and referendums are conducted and how their results are determined. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, non-profit organisations and informal organisations. These rules govern all aspects of the voting process: when elections occur, who is allowed to vote, who can stand as a candidate, how ballots are marked and cast, how the ballots are counted, how votes translate into the election outcome, limits on campaign spending, and other factors that can affect the result. Political electoral systems are defined by constitutions and electoral laws, are typically conducted by election commissions, and can use multiple types of elections for different offices. Some electoral systems elect a single winner to a unique position, such as prime minister, president or governor, while others elect multiple winners, such as memb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ranked Voting System
A ranking is a relationship between a set of items such that, for any two items, the first is either "ranked higher than", "ranked lower than" or "ranked equal to" the second. In mathematics, this is known as a weak order or total preorder of objects. It is not necessarily a total order of objects because two different objects can have the same ranking. The rankings themselves are totally ordered. For example, materials are totally preordered by hardness, while degrees of hardness are totally ordered. If two items are the same in rank it is considered a tie. By reducing detailed measures to a sequence of ordinal numbers, rankings make it possible to evaluate complex information according to certain criteria. Thus, for example, an Internet search engine may rank the pages it finds according to an estimation of their relevance, making it possible for the user quickly to select the pages they are likely to want to see. Analysis of data obtained by ranking commonly requires non-par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proportional Representation
Proportional representation (PR) refers to a type of electoral system under which subgroups of an electorate are reflected proportionately in the elected body. The concept applies mainly to geographical (e.g. states, regions) and political divisions (political parties) of the electorate. The essence of such systems is that all votes cast - or almost all votes cast - contribute to the result and are actually used to help elect someone—not just a plurality, or a bare majority—and that the system produces mixed, balanced representation reflecting how votes are cast. "Proportional" electoral systems mean proportional to ''vote share'' and ''not'' proportional to population size. For example, the US House of Representatives has 435 districts which are drawn so roughly equal or "proportional" numbers of people live within each district, yet members of the House are elected in first-past-the-post elections: first-past-the-post is ''not'' proportional by vote share. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hare Quota
The Hare quota (also known as the simple quota) is a formula used under some forms of proportional representation. In these voting systems the quota is the number of votes that guarantees a candidate, or a party in some cases, captures a seat. The Hare quota is the total number of votes divided by the number of seats to be filled. This is the simplest quota, but the Droop quota is mostly used currently. The Hare quota can be used in the single transferable vote (STV-Hare) system and the largest remainder method (LR-Hare) and other quota rule compatible methods of party-list proportional representation. Both versions are named after the political scientist Thomas Hare, but the largest remainder method in which it is used is also sometimes called the Hare–Niemeyer method (after Horst Niemeyer) or the Hamilton method (after Alexander Hamilton). Formula The Hare quota may be given as: :\frac where *Total votes = the total valid poll; that is, the number of valid (unspoilt) vo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Dummett
Sir Michael Anthony Eardley Dummett (27 June 1925 – 27 December 2011) was an English academic described as "among the most significant British philosophers of the last century and a leading campaigner for racial tolerance and equality." He was, until 1992, Wykeham Professor of Logic at the University of Oxford. He wrote on the history of analytic philosophy, notably as an interpreter of Frege, and made original contributions particularly in the philosophies of mathematics, logic, language and metaphysics. He was known for his work on truth and meaning and their implications to debates between realism and anti-realism, a term he helped to popularize. He devised the Quota Borda system of proportional voting, based on the Borda count. In mathematical logic, he developed an intermediate logic, already studied by Kurt Gödel: the Gödel–Dummett logic. Education and army service Born 27 June 1925, Dummett was the son of George Herbert Dummett (1880–1970), a silk merchant, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unanimity Criterion
Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem in social choice theory that states that when voters have three or more distinct alternatives (options), no ranked voting electoral system can convert the ranked preferences of individuals into a community-wide (complete and transitive) ranking while also meeting the specified set of criteria: ''unrestricted domain'', ''non-dictatorship'', ''Pareto efficiency'', and ''independence of irrelevant alternatives''. The theorem is often cited in discussions of voting theory as it is further interpreted by the Gibbard–Satterthwaite theorem. The theorem is named after economist and Nobel laureate Kenneth Arrow, who demonstrated the theorem in his doctoral thesis and popularized it in his 1951 book ''Social Choice and Individual Values''. The original paper was titled "A Difficulty in the Concept of Social Welfare". In short, the theorem states that no rank-order electoral system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hagenbach-Bischoff Quota
The Hagenbach-Bischoff quota (also known as the Newland-Britton quota or the exact Droop quota, as opposed to the more common rounded Droop quota) is a formula used in some voting systems based on proportional representation (PR). It is used in some elections held under the largest remainder method of party-list proportional representation as well as in a variant of the D'Hondt method known as the Hagenbach-Bischoff system. The Hagenbach-Bischoff quota is named for its inventor, Swiss professor of physics and mathematics Eduard Hagenbach-Bischoff (1833–1910) The Hagenbach-Bischoff quota is sometimes referred to as the 'Droop quota' and vice versa (especially in connection with the largest remainder method) because the two are very similar. However, under the Hagenbach-Bischoff and any smaller (e.g. the Imperiali) quota it is theoretically possible for more candidates to reach the quota than there are seats, whereas under the slightly larger Droop quota, this is mathematically ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Majority Criterion
The majority criterion is a single-winner voting system criterion, used to compare such systems. The criterion states that "if one candidate is ranked first by a majority (more than 50%) of voters, then that candidate must win". Some methods that comply with this criterion include any Condorcet method, Instant-runoff voting, Bucklin voting, and Plurality voting. The criterion was originally defined in relation to methods which rely only on ranked ballots (voted preference orders of the candidates), so while ranked methods such as the Borda count fail the criterion under any definition, its application to methods which give weight to preference strength is disputed. For these methods, such as STAR voting, Score (Range) voting, Approval voting and Majority Judgment, the system may pass or fail depending on the definition of the criterion which is used. Advocates of other voting systems contend that the majority criterion is actually a ''flaw'' of a voting system, and not a featur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Droop Quota
The Droop quota is the quota most commonly used in elections held under the single transferable vote (STV) system. It is also sometimes used in elections held under the largest remainder method of party-list proportional representation (list PR). In an STV election the quota is the minimum number of votes a candidate must receive in order to be elected. Any votes a candidate receives above the quota are transferred to another candidate. The Droop quota was devised in 1868 by the English lawyer and mathematician Henry Richmond Droop (1831–1884) as a replacement for the earlier Hare quota. Today the Droop quota is used in almost all STV elections, including the forms of STV used in India, the Republic of Ireland, Northern Ireland, Malta and Australia, among other places, and is also used to allocate seats via the largest remainder model in South Africa. The Droop quota is very similar to the simpler Hagenbach-Bischoff quota, which is also sometimes loosely referred to as the 'Dro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expanding Approvals Rule
Expansion may refer to: Arts, entertainment and media * ''L'Expansion'', a French monthly business magazine * ''Expansion'' (album), by American jazz pianist Dave Burrell, released in 2004 * ''Expansions'' (McCoy Tyner album), 1970 * ''Expansions'' (Lonnie Liston Smith album), 1975 * ''Expansión'' (Mexico), a Mexican news portal linked to CNN * Expansion (sculpture) (2004) Bronze sculpture illuminated from within * ''Expansión'' (Spanish newspaper), a Spanish economic daily newspaper published in Spain * Expansion pack in gaming, extra content for games, often simply "expansion" Science, technology, and mathematics * Expansion (geometry), stretching of geometric objects with flat sides * Expansion (model theory), in mathematical logic, a mutual converse of a reduct * Expansion card, in computing, a printed circuit board that can be inserted into an expansion slot * Expansion chamber, on a two-stroke engine, a tuned exhaust system that enhances power output * Expansion joint, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bucklin Voting
Bucklin voting is a class of voting methods that can be used for single-member and multi-member districts. As in highest median rules like the majority judgment, the Bucklin winner will be one of the candidates with the highest median ranking or rating. It is named after its original promoter, the Georgist politician James W. Bucklin of Grand Junction, Colorado, and is also known as the Grand Junction system. Voting process Bucklin rules varied, but here is a typical example: Voters are allowed rank preference ballots (first, second, third, etc.). First choice votes are first counted. If one candidate has a majority, that candidate wins. Otherwise the second choices are added to the first choices. Again, if a candidate with a majority vote is found, the winner is the candidate with the most votes accumulated. Lower rankings are added as needed. A majority is determined based on the number of valid ballots. Since, after the first round, there may be more votes cast than vo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mutual Majority Criterion
The mutual majority criterion is a criterion used to compare voting systems. It is also known as the majority criterion for solid coalitions and the generalized majority criterion. The criterion states that if there is a subset S of the candidates, such that more than half of the voters strictly prefer every member of S to every candidate outside of S, this majority voting sincerely, the winner must come from S. This is similar to but stricter than the majority criterion, where the requirement applies only to the case that ''S'' contains a single candidate. This is also stricter than the majority loser criterion, where the requirement applies only to the case that ''S'' contains all but one candidate. The mutual majority criterion is the single-winner case of the Droop proportionality criterion. The Schulze method, ranked pairs, instant-runoff voting, Nanson's method, and Bucklin voting pass this criterion. All Smith-efficient Condorcet methods pass the mutual majority criterion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
