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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] [Amazon] |
Mathematical Theorem
In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. 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 mainstream 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 (ZFC), or of a less powerful theory, such as Peano arithmetic. 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 ''corollary'' for less important theorems. In mathematical logic, the concepts of theorems and proofs have been formalized in order to allow mathematical reason ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Bahadur Representation
Bahadur may refer to: * Bahadur, a form of Baghatur, an honorific title * Bahadoor, Indian actor * 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, a title of honour awarded during British rule in India * Lal Bahadur Shastri Lal Bahadur Shastri (; born Lal Bahadur Srivastava; 2 October 190411 January 1966) was an Indian politician and st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Condorcet's Paradox
In social choice theory, Condorcet's voting paradox is a fundamental discovery by the Marquis de Condorcet that majority rule is inherently self-contradictory. The result implies that it is logically impossible for any voting system to guarantee that a winner will have support from a majority of voters; for example, there can be rock-paper-scissors scenarios where a majority of voters will prefer A to B, B to C, and also C to A, even if every voter's individual preferences are rational and avoid self-contradiction. Examples of Condorcet's paradox are called Condorcet cycles or cyclic ties. In such a cycle, every possible choice is rejected by the electorate in favor of another alternative, who is preferred by more than half of all voters. Thus, any attempt to ground social decision-making in majoritarianism must accept such self-contradictions (commonly called spoiler effects). Systems that attempt to do so, while minimizing the rate of such self-contradictions, are called Condo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Moshe Koppel
Moshe Koppel (; born 1956) is an American-Israeli computer scientist, Talmud scholar, and political activist best known for his research on authorship attribution. Together with Shlomo 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. Biography Koppel was born and raised in New York, where he received a traditional Jewish education. He studied at Yeshivat Har Etzion in Israel, 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 Bar-Ilan University Department of Computer Science since then. Research Computer science Koppel is best known for his research on authorship attribut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Expected Utility Hypothesis
The expected utility hypothesis is a foundational assumption in mathematical economics concerning decision making under uncertainty. It postulates that rational agents maximize utility, meaning the subjective desirability of their actions. Rational choice theory, a cornerstone of microeconomics, builds this postulate to model aggregate social behaviour. 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. Graphically the curvature of the u function captures the agent's risk attitude. For example, imagine you’re offered a choice between receiving $50 for sure, or flipping a coin to win $100 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Sortition
In governance, sortition is the selection of public officer, officials or jurors at random, i.e. by Lottery (probability), lottery, in order to obtain a representative sample. 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 democracy. Sortition is often classified as a method for both direct democracy and deliberative democracy. Today sortition is commonly used to select prospective jurors in common law (legal system), common-law systems. What has changed in recent years is the increased number of citizens' assembly, citizen groups with political advisory power, along with calls for making sortition more consequential than elections, as it was in Athenian democracy, Athens, Republic of Venice, Venice, and Republic of Florence, Florence. History Ancient Athens Athenian democracy developed in the 6th century BC out of what was then called isonomia (equal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 dependence, conditional dependencies via a directed acyclic graph (DAG). While it is one of several forms of causal notation, causal networks are special cases of Bayesian networks. 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 machine learning, learning in Bayesian networks. Bayesian networks that model sequences of variables (''e.g.'' speech recognition, speech signals or peptide sequence, protein sequences) ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Peer Pressure
Peer pressure is a direct or indirect influence on peers, i.e., members of social groups with similar interests and experiences, or social statuses. Members of a peer group are more likely to influence a person's beliefs, values, religion and behavior. A group or individual may be encouraged and want to follow their peers by changing their Attitude (psychology), attitudes, Value (ethics), 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 effect 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 may be in a crowd, a group of many cliques, and still be affected by peer pressure. Resea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Deliberation
Deliberation is a process of thoughtfully weighing options, for example prior to voting. Deliberation emphasizes the use of logic and reason as opposed to power-struggle, creativity, or dialogue. Group decision-making, Group decisions are generally made after deliberation through a vote or Consensus decision-making, 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. Individual deliberation is also a description of day-to-day rationality, rational decision-making, and as such is an epistemic virtue. 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 (law), se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 people 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 decis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 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, in gen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
