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Von Neumann–Morgenstern Utility Theorem
In decision theory, the von Neumann–Morgenstern (VNM) utility theorem shows that, under certain axioms of rational behavior, a decision-maker faced with risky (probabilistic) outcomes of different choices will behave as if he or she is maximizing the expected value of some function defined over the potential outcomes at some specified point in the future. This function is known as the von Neumann–Morgenstern utility function. The theorem is the basis for expected utility theory. In 1947, John von Neumann and Oskar Morgenstern proved that any individual whose preferences satisfied four axioms has a utility function; Neumann, John von and Morgenstern, Oskar, '' Theory of Games and Economic Behavior''. Princeton, NJ. Princeton University Press, 1953. such an individual's preferences can be represented on an interval scale and the individual will always prefer actions that maximize expected utility. That is, they proved that an agent is (VNM-)rational ''if and only if'' there exis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decision Theory
Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical consequences to the outcome. There are three branches of decision theory: # Normative decision theory: Concerned with the identification of optimal decisions, where optimality is often determined by considering an ideal decision-maker who is able to calculate with perfect accuracy and is in some sense fully rational. # Prescriptive decision theory: Concerned with describing observed behaviors through the use of conceptual models, under the assumption that those making the decisions are behaving under some consistent rules. # Descriptive decision theory: Analyzes how individuals actually make the decisions that they do. Decision theory is closely related to the field of game theory and is an interdisciplinary topic, studied by econom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mutually Exclusive
In logic and probability theory, two events (or propositions) are mutually exclusive or disjoint if they cannot both occur at the same time. A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both. In the coin-tossing example, both outcomes are, in theory, collectively exhaustive, which means that at least one of the outcomes must happen, so these two possibilities together exhaust all the possibilities. However, not all mutually exclusive events are collectively exhaustive. For example, the outcomes 1 and 4 of a single roll of a six-sided die are mutually exclusive (both cannot happen at the same time) but not collectively exhaustive (there are other possible outcomes; 2,3,5,6). Logic In logic, two mutually exclusive propositions are propositions that logically cannot be true in the same sense at the same time. To say that more than two propositions are mutually exclusive, depending on the context, means that one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Utilitarianism
In ethical philosophy, utilitarianism is a family of normative ethical theories that prescribe actions that maximize happiness and well-being for all affected individuals. Although different varieties of utilitarianism admit different characterizations, the basic idea behind all of them is, in some sense, to maximize utility, which is often defined in terms of well-being or related concepts. For instance, Jeremy Bentham, the founder of utilitarianism, described ''utility'' as: That property in any object, whereby it tends to produce benefit, advantage, pleasure, good, or happiness ... rto prevent the happening of mischief, pain, evil, or unhappiness to the party whose interest is considered. Utilitarianism is a version of consequentialism, which states that the consequences of any action are the only standard of right and wrong. Unlike other forms of consequentialism, such as egoism and altruism, utilitarianism considers the interests of all sentient beings equally. Pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Consequentialism
In ethical philosophy, consequentialism is a class of normative, teleological ethical theories that holds that the consequences of one's conduct are the ultimate basis for judgment about the rightness or wrongness of that conduct. Thus, from a consequentialist standpoint, a morally right act (or omission from acting) is one that will produce a good outcome. Consequentialism, along with eudaimonism, falls under the broader category of teleological ethics, a group of views which claim that the moral value of any act consists in its tendency to produce things of intrinsic value.Teleological Ethics " ''''. via ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Expected Utility
Generalized expected utility is a decision-making metric based on any of a variety of theories that attempt to resolve some discrepancies between expected utility theory and empirical observations, concerning choice under risky (probabilistic) circumstances. Given its motivations and approach, generalized expected utility theory may properly be regarded as a subfield of behavioral economics, but it is more frequently located within mainstream economic theory. The expected utility model developed by John von Neumann and Oskar Morgenstern dominated decision theory from its formulation in 1944 until the late 1970s, not only as a prescriptive, but also as a descriptive model, despite powerful criticism from Maurice Allais and Daniel Ellsberg who showed that, in certain choice problems, decisions were usually inconsistent with the axioms of expected utility theory. These problems are usually referred to as the Allais paradox and Ellsberg paradox. Beginning in 1979 with the publicati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel Bernoulli
Daniel Bernoulli FRS (; – 27 March 1782) was a Swiss mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family from Basel. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics. His name is commemorated in the Bernoulli's principle, a particular example of the conservation of energy, which describes the mathematics of the mechanism underlying the operation of two important technologies of the 20th century: the carburetor and the airplane wing. Early life Daniel Bernoulli was born in Groningen, in the Netherlands, into a family of distinguished mathematicians. Rothbard, MurrayDaniel Bernoulli and the Founding of Mathematical Economics ''Mises Institute'' (excerpted from ''An Austrian Perspective on the History of Economic Thought'') The Bernoulli family came originally from Antwerp, at that time in the Spanish Netherlands, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Risk Aversion
In economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to or higher in monetary value than the more certain outcome. Risk aversion explains the inclination to agree to a situation with a more predictable, but possibly lower payoff, rather than another situation with a highly unpredictable, but possibly higher payoff. For example, a risk-averse investor might choose to put their money into a bank account with a low but guaranteed interest rate, rather than into a stock that may have high expected returns, but also involves a chance of losing value. Example A person is given the choice between two scenarios: one with a guaranteed payoff, and one with a risky payoff with same average value. In the former scenario, the person receives $50. In the uncertain scenario, a coin is flipped to decide whether the person receives $100 or nothing. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Value Theory
In ethics and the social sciences, value theory involves various approaches that examine how, why, and to what degree humans value things and whether the object or subject of valuing is a person, idea, object, or anything else. Within philosophy, it is also known as ethics or axiology. Traditionally, philosophical investigations in value theory have sought to understand the concept of "the good". Today, some work in value theory has trended more towards empirical sciences, recording what people do value and attempting to understand why they value it in the context of psychology, sociology, and economics. In ecological economics, value theory is separated into two types: donor-type value and receiver-type value. Ecological economists tend to believe that 'real wealth' needs an accrual-determined value as a measure of what things were needed to make an item or generate a service ( H. T. Odum, ''Environmental Accounting: Emergy and environmental decision-making'', 1996). In othe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gamble
Gambling (also known as betting or gaming) is the wagering of something of value ("the stakes") on a random event with the intent of winning something else of value, where instances of strategy are discounted. Gambling thus requires three elements to be present: consideration (an amount wagered), risk (chance), and a prize. The outcome of the wager is often immediate, such as a single roll of dice, a spin of a roulette wheel, or a horse crossing the finish line, but longer time frames are also common, allowing wagers on the outcome of a future sports contest or even an entire sports season. The term "gaming" in this context typically refers to instances in which the activity has been specifically permitted by law. The two words are not mutually exclusive; ''i.e.'', a "gaming" company offers (legal) "gambling" activities to the public and may be regulated by one of many gaming control boards, for example, the Nevada Gaming Control Board. However, this distinction is not univ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence Of Irrelevant Alternatives
The independence of irrelevant alternatives (IIA), also known as binary independence or the independence axiom, is an axiom of decision theory and various social sciences. The term is used in different connotation in several contexts. Although it always attempts to provide an account of rational individual behavior or aggregation of individual preferences, the exact formulation differs widely in both language and exact content. Perhaps the easiest way to understand the axiom is how it pertains to casting a ballot. There the axiom says that if Charlie (the irrelevant alternative) enters a race between Alice and Bob, with Alice (leader) liked better than Bob (runner-up), then the individual voter who likes Charlie less than Alice will not switch his vote from Alice to Bob. Because of this, a violation of IIA is commonly referred to as the "spoiler effect": support for Charlie "spoils" the election for Alice, while it "logically" should not have. After all, Alice ''was'' liked better t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedean Property
In abstract algebra and analysis, the Archimedean property, named after the ancient Greek mathematician Archimedes of Syracuse, is a property held by some algebraic structures, such as ordered or normed groups, and fields. The property, typically construed, states that given two positive numbers ''x'' and ''y'', there is an integer ''n'' such that ''nx'' > ''y''. It also means that the set of natural numbers is not bounded above. Roughly speaking, it is the property of having no ''infinitely large'' or ''infinitely small'' elements. It was Otto Stolz who gave the axiom of Archimedes its name because it appears as Axiom V of Archimedes’ ''On the Sphere and Cylinder''. The notion arose from the theory of magnitudes of Ancient Greece; it still plays an important role in modern mathematics such as David Hilbert's axioms for geometry, and the theories of ordered groups, ordered fields, and local fields. An algebraic structure in which any two non-zero elements are ''comparabl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transitive Relation
In mathematics, a relation on a set is transitive if, for all elements , , in , whenever relates to and to , then also relates to . Each partial order as well as each equivalence relation needs to be transitive. Definition A homogeneous relation on the set is a ''transitive relation'' if, :for all , if and , then . Or in terms of first-order logic: :\forall a,b,c \in X: (aRb \wedge bRc) \Rightarrow aRc, where is the infix notation for . Examples As a non-mathematical example, the relation "is an ancestor of" is transitive. For example, if Amy is an ancestor of Becky, and Becky is an ancestor of Carrie, then Amy, too, is an ancestor of Carrie. On the other hand, "is the birth parent of" is not a transitive relation, because if Alice is the birth parent of Brenda, and Brenda is the birth parent of Claire, then this does not imply that Alice is the birth parent of Claire. What is more, it is antitransitive: Alice can ''never'' be the birth parent of Claire. "Is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
