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Jury Theorem
A jury theorem is a mathematical theorem proving that, under certain assumptions, a decision attained using majority voting in a large group is more likely to be correct than a decision attained by a single expert. It serves as a formal argument for the idea of wisdom of the crowd, for decision of questions of fact by jury trial, and for democracy in general. The first and most famous jury theorem is Condorcet's jury theorem. It assumes that all voters have independent probabilities to vote for the correct alternative, these probabilities are larger than 1/2, and are the same for all voters. Under these assumptions, the probability that the majority decision is correct is strictly larger when the group is larger; and when the group size tends to infinity, the probability that the majority decision is correct tends to 1. There are many other jury theorems, relaxing some or all of these assumptions. Setting The premise of all jury theorems is that there is an ''objective truth'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Theorem
In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In the mainstream of mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice, or of a less powerful theory, such as Peano arithmetic. A notable exception is Wiles's proof of Fermat's Last Theorem, which involves the Grothendieck universes whose existence requires the addition of a new axiom to the set theory. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as ''theorems'' only the most important results, and use the terms ''lemma'', ''proposition'' and '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bahadur Representation
Bahadur may refer to: * Bahadur, a form of Baghatur, an honorific title * Bahadur Fort, in Ahmednagar district, Maharashtra, India * Bahadur (comics), an Indian comic book superhero * ''Bahadur'' (film), a 1953 Indian film * Bahadur (character), a character type in Hindi literature and media * Bahadur, the Indian Air Force's designation for the Mikoyan MiG-27 ground-attack aircraft * Bahadur Group, an Indian Special Forces unit See also * Bahadur Shah (other) * Bahadur Singh (other) * Nawab Bahadur (other) * Bahadır, a Turkish forename and surname * Rao Bahadur, a title of honour bestowed during British rule in India * Khan Bahadur, a formal title of respect and honour conferred on non-Hindu natives of British India * Dewan Bahadur Dewan Bahadur or Diwan Bahadur was a title of honour awarded during British Raj, British rule in India. It was awarded to individuals who had performed faithful service or acts of public welfare to the nation. From 1911 th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Condorcet's Paradox
The Condorcet paradox (also known as the voting paradox or the paradox of voting) in social choice theory is a situation noted by the Marquis de Condorcet in the late 18th century, in which collective preferences can be cyclic, even if the preferences of individual voters are not cyclic. This is paradoxical, because it means that majority wishes can be in conflict with each other: Suppose majorities prefer, for example, candidate A over B, B over C, and yet C over A. When this occurs, it is because the conflicting majorities are each made up of different groups of individuals. Thus an expectation that transitivity on the part of all individuals' preferences should result in transitivity of societal preferences is an example of a fallacy of composition. The paradox was independently discovered by Lewis Carroll and Edward J. Nanson, but its significance was not recognized until popularized by Duncan Black in the 1940s. Example Suppose we have three candidates, A, B, and C, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Learning Theory
Statistical learning theory is a framework for machine learning drawing from the fields of statistics and functional analysis. Statistical learning theory deals with the statistical inference problem of finding a predictive function based on data. Statistical learning theory has led to successful applications in fields such as computer vision, speech recognition, and bioinformatics. Introduction The goals of learning are understanding and prediction. Learning falls into many categories, including supervised learning, unsupervised learning, online learning, and reinforcement learning. From the perspective of statistical learning theory, supervised learning is best understood. Supervised learning involves learning from a training set of data. Every point in the training is an input-output pair, where the input maps to an output. The learning problem consists of inferring the function that maps between the input and the output, such that the learned function can be used to predict t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moshe Koppel
Moshe Koppel is an American-Israeli computer scientist, Talmud scholar and political activist. Koppel was born and raised in New York, where he received a traditional Jewish education. He studied at Yeshivat Har Etzion, received a B.A. from Yeshiva University and in 1979 completed his doctorate in mathematics under the supervision of Martin Davis at the Courant Institute of New York University. He spent a post-doctoral year at the Institute for Advanced Study in Princeton before moving to Israel in 1980. He has been a member of the Department of Computer Science in Bar-Ilan University since then. Computer science Koppel is best known for his research on authorship attribution. Together with Shlomo Engelson Argamon and Jonathan Schler, he has shown that statistical analysis of word usage in a document can be used to determine an author's gender, age, native language and personality type. The findings regarding gender generated considerable controversy. In a string of papers, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Utility Hypothesis
The expected utility hypothesis is a popular concept in economics that serves as a reference guide for decisions when the payoff is uncertain. The theory recommends which option rational individuals should choose in a complex situation, based on their risk appetite and Preference, preferences. The expected utility hypothesis states an agent chooses between risky prospects by comparing expected utility values (i.e. the weighted sum of adding the respective utility values of payoffs multiplied by their probabilities). The summarised formula for expected utility is U(p)=\sum u(x_k)p_k where p_k is the probability that outcome indexed by k with payoff x_k is realized, and function ''u'' expresses the utility of each respective payoff. On a graph, the curvature of u will explain the agent's risk attitude. For example, if an agent derives 0 utils from 0 apples, 2 utils from one apple, and 3 utils from two apples, their expected utility for a 50–50 gamble between zero apples and two is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sortition
In governance, sortition (also known as selection by lottery, selection by lot, allotment, demarchy, stochocracy, aleatoric democracy, democratic lottery, and lottocracy) is the selection of political officials as a random sample from a larger pool of candidates. The system intends to ensure that all competent and interested parties have an equal chance of holding public office. It also minimizes factionalism, since there would be no point making promises to win over key constituencies if one was to be chosen by lot, while elections An election is a formal group decision-making process by which a population chooses an individual or multiple individuals to hold Public administration, public office. Elections have been the usual mechanism by which modern representative ..., by contrast, foster it. In ancient Athenian democracy, sortition was the traditional and primary method for appointing political officials, and its use was regarded as a principal characteristic of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Causal Network
A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). Bayesian networks are ideal for taking an event that occurred and predicting the likelihood that any one of several possible known causes was the contributing factor. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. Efficient algorithms can perform inference and learning in Bayesian networks. Bayesian networks that model sequences of variables (''e.g.'' speech signals or protein sequences) are called dynamic Bayesian networks. Generalizations of Bayesian networks that can represent and solve decision problems under uncertainty are called influence diagrams. Graphical mode ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peer Pressure
Peer pressure is the direct or indirect influence on peers, i.e., members of social groups with similar interests, experiences, or social statuses. Members of a peer group are more likely to influence a person's beliefs, values, and behavior. A group or individual may be encouraged and want to follow their peers by changing their attitudes, values or behaviors to conform to those of the influencing group or individual. For the individual affected by peer pressure, this can have both a positive or negative influence on them. Social groups include both ''membership groups'' in which individuals hold "formal" membership (e.g. political parties, trade unions, schools) and cliques in which membership is less clearly defined. However, a person does not need to be a member or be seeking membership of a group to be affected by peer pressure. An individual can be in a crowd, a group of many cliques, and still be affected by peer pressure. Research suggests that organizations as well ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deliberation
Deliberation is a process of thoughtfully weighing options, usually prior to voting. Deliberation emphasizes the use of logic and reason as opposed to power-struggle, creativity, or dialogue. Group decisions are generally made after deliberation through a vote or consensus of those involved. In legal settings a jury famously uses deliberation because it is given specific options, like guilty or not guilty, along with information and arguments to evaluate. In " deliberative democracy", the aim is for both elected officials and the general public to use deliberation rather than power-struggle as the basis for their vote. Trial juries In countries with a jury system, the jury's deliberation in criminal matters can involve both rendering a verdict and determining the appropriate sentence. In civil cases, the jury decision is whether to agree with the plaintiff or the defendant and rendering a resolution binding actions by the parties based on the results of the trial. Typically ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Opinion Leadership
Opinion leadership is leadership by an active media user who interprets the meaning of media messages or content for lower-end media users. Typically opinion leaders are held in high esteem by those who accept their opinions. Opinion leadership comes from the theory of two-step flow of communication propounded by Paul Lazarsfeld and Elihu Katz. Significant developers of the opinion leader concept have been Robert K. Merton, C. Wright Mills and Bernard Berelson. This theory is one of several models that try to explain the diffusion of innovations, ideas, or commercial products. Opinion leaders play an important role in information flow, because we tend to seek advice from others in the social environment. Information from the mass media does not directly flow to the target audiences, but through a mediation process, in which influential people digest the information and spread it to the public. Opinion leaders have certain characteristics that make them influential in the decision- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Correlation And Dependence
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are ''linearly'' related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve. Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling. However ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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