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Landau Set
In voting systems, the Landau set (or uncovered set, or Fishburn set) is the set of candidates x such that for every other candidate z, there is some candidate y (possibly the same as x or z) such that y is not preferred to x and z is not preferred to y. In notation, x is in the Landau set if \forall \,z, \exists \,y, x \ge y \ge z. The Landau set is a nonempty subset of the Smith set In voting systems, the Smith set, named after John H. Smith, but also known as the top cycle, or as Generalized Top-Choice Assumption (GETCHA), is the smallest non-empty set of candidates in a particular election such that each member defeats ever .... It was discovered by Nicholas Miller. References *Nicholas R. Miller, "Graph-theoretical approaches to the theory of voting", ''American Journal of Political Science'', Vol. 21 (1977), pp. 769–803. . . *Nicholas R. Miller, "A new solution set for tournaments and majority voting: further graph-theoretic approaches to majority voting", ''Ame ... [...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] |
Peter Fishburn
Peter Clingerman Fishburn (September 2, 1936 – June 10, 2021) was an American mathematician, known as a pioneer in the field of decision theory. In collaboration with Steven Brams, Fishburn published a paper about approval voting in 1978. Biography Intellectual Fishburn received his B.S. in industrial engineering from Pennsylvania State University in 1958, his M.S. in operations research in 1961, and a Ph.D. in operations research in 1962, the latter two from the Case Institute of Technology. In collaboration with Steven Brams, Fishburn published a paper about approval voting in 1978. In 1996, he won the John von Neumann Theory Prize. He also won the Decision Analysis Publication Award in 1991 and the Frank P. Ramsey Medal in 1987. He was elected to the 2002 class of Fellows of the Institute for Operations Research and the Management Sciences. Personal Fishburn retired after many years of research at AT&T Bell Laboratories in the state of New Jersey, United States. He was mar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smith Set
In voting systems, the Smith set, named after John H. Smith, but also known as the top cycle, or as Generalized Top-Choice Assumption (GETCHA), is the smallest non-empty set of candidates in a particular election such that each member defeats every candidate outside the set in a pairwise election. The Smith set provides one standard of optimal choice for an election outcome. Voting systems that always elect a candidate from the Smith set pass the Smith criterion and are said to be 'Smith-efficient' or to satisfy the Smith criterion. A set of candidates each of whose members pairwise defeats every candidate outside the set is known as a dominating set. The Smith set can be seen as defining a voting method (Smith's method) which is most often encountered when extended by an IRV tie-break as Smith/IRV or as Tideman's Alternative, or by minimax as Smith/minimax. Properties of Smith sets *The Smith set always exists and is well defined (see next section). *The Smith set can have mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
