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Tournament Solution
A tournament solution is a function that maps an oriented complete graph to a nonempty subset of its vertices. It can informally be thought of as a way to find the "best" alternatives among all of the alternatives that are "competing" against each other in the tournament. Tournament solutions originate from social choice theory, but have also been considered in sports competition, game theory, multi-criteria decision analysis, biology, webpage ranking, and dueling bandit problems. In the context of social choice theory, tournament solutions are closely related to Fishburn's C1 social choice functions, and thus seek to show who the best candidates are among all candidates. Definition A tournament (graph) T is a tuple (A,\succ) where A is a set of vertices (called ''alternatives'') and \succ is a connex and asymmetric binary relation over the vertices. In social choice theory, the binary relation typically represents the pairwise majority comparison between alternatives. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the function and the set is called the codomain of the function.Codomain ''Encyclopedia of Mathematics'Codomain. ''Encyclopedia of Mathematics''/ref> The earliest known approach to the notion of function can be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Web Search Engine
A search engine is a software system designed to carry out web searches. They search the World Wide Web in a systematic way for particular information specified in a textual web search query. The search results are generally presented in a line of results, often referred to as search engine results pages (SERPs). When a user enters a query into a search engine, the engine scans its index of web pages to find those that are relevant to the user's query. The results are then ranked by relevancy and displayed to the user. The information may be a mix of links to web pages, images, videos, infographics, articles, research papers, and other types of files. Some search engines also mine data available in databases or open directories. Unlike web directories and social bookmarking sites, which are maintained by human editors, search engines also maintain real-time information by running an algorithm on a web crawler. Any internet-based content that can't be indexed and searched ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Top Cycle
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 more ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
