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Luce's Choice Axiom
In probability theory, Luce's choice axiom, formulated by R. Duncan Luce (1959), states that the relative odds of selecting one item over another from a pool of many items is not affected by the presence or absence of other items in the pool. Selection of this kind is said to have " independence from irrelevant alternatives" (IIA). Overview Consider a set X of possible outcomes, and consider a selection rule P, such that for any a\in A \subset X with A a finite set, the selector selects a from A with probability P(a \mid A). Luce proposed two choice axioms. The second one is usually meant by "Luce's choice axiom", as the first one is usually called " independence from irrelevant alternatives" (IIA). Luce's choice axiom 1 (IIA): if P(a\mid A) = 0, P(b\mid A) > 0, then for any a, b \in B \subset A, we still have P(a\mid B) = 0. Luce's choice axiom 2 ("path independence"): P(a \mid A) = P(a\mid B)\sum_P(b\mid A)for any a \in B \subset A. Luce's choice axiom 1 is implied by choice ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms of probability, axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure (mathematics), measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event (probability theory), event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of determinism, non-deterministic or uncertain processes or measured Quantity, quantities that may either be single occurrences or evolve over time in a random fashion). Although it is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Odds
In probability theory, odds provide a measure of the probability of a particular outcome. Odds are commonly used in gambling and statistics. For example for an event that is 40% probable, one could say that the odds are or When gambling, odds are often given as the ratio of the possible net profit ''to'' the possible net loss. However in many situations, you pay the possible loss ("stake" or "wager") up front and, if you win, you are paid the net win plus you also get your stake returned. So wagering 2 at , pays out , which is called When Moneyline odds are quoted as a positive number , it means that a wager pays When Moneyline odds are quoted as a negative number , it means that a wager pays Odds have a simple relationship with probability. When probability is expressed as a number between 0 and 1, the relationships between probability and odds are as follows. Note that if probability is to be expressed as a percentage these probability values should be multiplied ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence Of Irrelevant Alternatives
Independence of irrelevant alternatives (IIA) is an axiom of decision theory which codifies the intuition that a choice between A and B (which are both related) should not depend on the quality of a third, unrelated outcome C. There are several different variations of this axiom, which are generally equivalent under mild conditions. As a result of its importance, the axiom has been independently rediscovered in various forms across a wide variety of fields, including economics, cognitive science, social choice, fair division, rational choice, artificial intelligence, probability, and game theory. It is closely tied to many of the most important theorems in these fields, including Arrow's impossibility theorem, the Balinski–Young theorem, and the money pump arguments. In behavioral economics, failures of IIA (caused by irrationality) are called menu effects or menu dependence. Motivation This is sometimes explained with a short story by philosopher Sidney Morgenbesser:Mor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matching Law
In operant conditioning, the matching law is a quantitative relationship that holds between the relative rates of response and the relative rates of reinforcement in concurrent schedules of reinforcement. For example, if two response alternatives A and B are offered to an organism, the ratio of response rates to A and B equals the ratio of reinforcements yielded by each response.Poling, A., Edwards, T. L., Weeden, M., & Foster, T. (2011). The matching law. ''Psychological Record'', 61(2), 313-322. This law applies fairly well when non-human subjects are exposed to concurrent reinforcement, variable interval schedules (but see below); its applicability in other situations is less clear, depending on the assumptions made and the details of the experimental situation. The generality of applicability of the matching law is subject of current debate. The matching law can be applied to situations involving a single response maintained by a single schedule of reinforcement if one assumes t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Softmax Function
The softmax function, also known as softargmax or normalized exponential function, converts a tuple of real numbers into a probability distribution of possible outcomes. It is a generalization of the logistic function to multiple dimensions, and is used in multinomial logistic regression. The softmax function is often used as the last activation function of a neural network to normalize the output of a network to a probability distribution over predicted output classes. Definition The softmax function takes as input a tuple of real numbers, and normalizes it into a probability distribution consisting of probabilities proportional to the exponentials of the input numbers. That is, prior to applying softmax, some tuple components could be negative, or greater than one; and might not sum to 1; but after applying softmax, each component will be in the interval (0, 1), and the components will add up to 1, so that they can be interpreted as probabilities. Furthermore, the la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boltzmann Distribution
In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution Translated by J.B. Sykes and M.J. Kearsley. See section 28) is a probability distribution or probability measure that gives the probability that a system will be in a certain state as a function of that state's energy and the temperature of the system. The distribution is expressed in the form: :p_i \propto \exp\left(- \frac \right) where is the probability of the system being in state , is the exponential function, is the energy of that state, and a constant of the distribution is the product of the Boltzmann constant and thermodynamic temperature . The symbol \propto denotes proportionality (see for the proportionality constant). The term ''system'' here has a wide meaning; it can range from a collection of 'sufficient number' of atoms or a single atom to a macroscopic system such as a natural gas storage tank. Therefore, the Boltzmann distribution can be used to sol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economics
Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interactions of Agent (economics), economic agents and how economy, economies work. Microeconomics analyses what is viewed as basic elements within economy, economies, including individual agents and market (economics), markets, their interactions, and the outcomes of interactions. Individual agents may include, for example, households, firms, buyers, and sellers. Macroeconomics analyses economies as systems where production, distribution, consumption, savings, and Expenditure, investment expenditure interact; and the factors of production affecting them, such as: Labour (human activity), labour, Capital (economics), capital, Land (economics), land, and Entrepreneurship, enterprise, inflation, economic growth, and public policies that impact gloss ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Consumer
A consumer is a person or a group who intends to order, or use purchased goods, products, or services primarily for personal, social, family, household and similar needs, who is not directly related to entrepreneurial or business activities. The term most commonly refers to a person who purchases goods and services for personal use. Rights "Consumers, by definition, include us all", said President John F. Kennedy, offering his definition to the United States Congress on March 15, 1962. This speech became the basis for the creation of World Consumer Rights Day, now celebrated on March 15. In his speech, John Fitzgerald Kennedy outlined the integral responsibility to consumers from their respective governments to help exercise consumers' rights, including: *The right to safety: To be protected against the marketing of goods that are hazardous to health or life. *The right to be informed: To be protected against fraudulent, deceitful, or grossly misleading information, adverti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Behaviorism
Behaviorism is a systematic approach to understand the behavior of humans and other animals. It assumes that behavior is either a reflex elicited by the pairing of certain antecedent stimuli in the environment, or a consequence of that individual's history, including especially reinforcement and punishment contingencies, together with the individual's current motivational state and controlling stimuli. Although behaviorists generally accept the important role of heredity in determining behavior, deriving from Skinner's two levels of selection: phylogeny and ontogeny. they focus primarily on environmental events. The cognitive revolution of the late 20th century largely replaced behaviorism as an explanatory theory with cognitive psychology, which unlike behaviorism views internal mental states as explanations for observable behavior. Behaviorism emerged in the early 1900s as a reaction to depth psychology and other traditional forms of psychology, which often had diffic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cognitive Science
Cognitive science is the interdisciplinary, scientific study of the mind and its processes. It examines the nature, the tasks, and the functions of cognition (in a broad sense). Mental faculties of concern to cognitive scientists include perception, memory, attention, reasoning, language, and emotion. To understand these faculties, cognitive scientists borrow from fields such as psychology, economics, artificial intelligence, neuroscience, linguistics, and anthropology.Thagard, PaulCognitive Science, ''The Stanford Encyclopedia of Philosophy'' (Fall 2008 Edition), Edward N. Zalta (ed.). The typical analysis of cognitive science spans many levels of organization, from learning and decision-making to logic and planning; from neuron, neural circuitry to modular brain organization. One of the fundamental concepts of cognitive science is that "thinking can best be understood in terms of representational structures in the mind and computational procedures that operate on those structur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
