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Gibbard–Satterthwaite Theorem
In social choice theory, the Gibbard–Satterthwaite theorem is a result published independently by philosopher Allan Gibbard in 1973 and economist Mark Satterthwaite in 1975. It deals with deterministic ordinal electoral systems that choose a single winner. It states that for every voting rule, one of the following three things must hold: # The rule is dictatorial, i.e. there exists a distinguished voter who can choose the winner; or # The rule limits the possible outcomes to two alternatives only; or # The rule is susceptible to tactical voting: in certain conditions, a voter's sincere ballot may not best defend their opinion. While the scope of this theorem is limited to ordinal voting, Gibbard's theorem is more general, in that it deals with processes of collective decision that may not be ordinal: for example, voting systems where voters assign grades to candidates. Gibbard's 1978 theorem and Hylland's theorem are even more general and extend these results to non-determini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social Choice Theory
Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a ''collective decision'' or ''social welfare'' in some sense.Amartya Sen (2008). "Social Choice,". ''The New Palgrave Dictionary of Economics'', 2nd EditionAbstract & TOC./ref> Whereas choice theory is concerned with individuals making choices based on their preferences, social choice theory is concerned with how to translate the preferences of individuals into the preferences of a group. A non-theoretical example of a collective decision is enacting a law or set of laws under a constitution. Another example is voting, where individual preferences over candidates are collected to elect a person that best represents the group's preferences. Social choice blends elements of welfare economics and public choice theory. It is methodologically individualistic, in that it aggregates preferences and behaviors of individual member ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robin Farquharson
Reginald Robin Farquharson (3 October 1930 – 1 April 1973) was an academic whose interest in mathematics and politics led him to work on game theory. He wrote an influential analysis of voting systems in his doctoral thesis, later published as ''Theory of Voting''. Farquharson diagnosed himself as suffering from bipolar disorder (manic depression), and episodes of mania made it difficult for him to obtain a permanent university position and also resulted in him losing commercial employment. In later years, he dropped out of mainstream society, and became a prominent counter-cultural figure in late-1960s London. Farquharson wrote an account of his unconventional life in his 1968 book, ''Drop Out!'', in which he described a week of being homeless in London. In 1973 he died from burns associated with an arson, for which two persons were convicted of unlawful killing. Education Robin Farquharson was educated at Michaelhouse, Natal, South Africa, 1944–46. He earned a B.A. in S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economics Theorems
Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyzes what's viewed as basic elements in the economy, including individual agents and markets, their interactions, and the outcomes of interactions. Individual agents may include, for example, households, firms, buyers, and sellers. Macroeconomics analyzes the economy as a system where production, consumption, saving, and investment interact, and factors affecting it: employment of the resources of labour, capital, and land, currency inflation, economic growth, and public policies that have impact on these elements. Other broad distinctions within economics include those between positive economics, describing "what is", and normative economics, advocating "what ought to be"; between economic theory and applied economics; between rational and beh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voting Theory
Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a ''collective decision'' or ''social welfare'' in some sense.Amartya Sen (2008). "Social Choice,". ''The New Palgrave Dictionary of Economics'', 2nd EditionAbstract & TOC./ref> Whereas choice theory is concerned with individuals making choices based on their preferences, social choice theory is concerned with how to translate the preferences of individuals into the preferences of a group. A non-theoretical example of a collective decision is enacting a law or set of laws under a constitution. Another example is voting, where individual preferences over candidates are collected to elect a person that best represents the group's preferences. Social choice blends elements of welfare economics and public choice theory. It is methodologically individualistic, in that it aggregates preferences and behaviors of individual member ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vickrey–Clarke–Groves Auction
A Vickrey–Clarke–Groves (VCG) auction is a type of sealed-bid auction of multiple items. Bidders submit bids that report their valuations for the items, without knowing the bids of the other bidders. The auction system assigns the items in a socially optimal manner: it charges each individual the harm they cause to other bidders. It gives bidders an incentive to bid their true valuations, by ensuring that the optimal strategy for each bidder is to bid their true valuations of the items; it can be undermined by bidder collusion and in particular in some circumstances by a single bidder making multiple bids under different names. It is a generalization of a Vickrey auction for multiple items. The auction is named after William Vickrey, Edward H. Clarke, and Theodore Groves for their papers that successively generalized the idea. The VCG auction is a specific use of the more general VCG mechanism. While the VCG auction tries to make a socially optimal allocation of items, V ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Utility
As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosophers such as Jeremy Bentham and John Stuart Mill. The term has been adapted and reapplied within neoclassical economics, which dominates modern economic theory, as a utility function that represents a single consumer's preference ordering over a choice set but is not comparable across consumers. This concept of utility is personal and based on choice rather than on pleasure received, and so is specified more rigorously than the original concept but makes it less useful (and controversial) for ethical decisions. Utility function Consider a set of alternatives among which a person can make a preference ordering. The utility obtained from these alternatives is an unknown function of the utilities obtained from each alternative, not the sum of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasilinear Utility
In economics and consumer theory, quasilinear utility functions are linear in one argument, generally the numeraire. Quasilinear preferences can be represented by the utility function u(x_1, x_2, \ldots, x_n) = x_1 + \theta (x_2, \ldots, x_n) where \theta is strictly concave. A useful property of the quasilinear utility function is that the Marshallian/Walrasian demand for x_2, \ldots, x_n does not depend on wealth and is thus not subject to a wealth effect; The absence of a wealth effect simplifies analysis and makes quasilinear utility functions a common choice for modelling. Furthermore, when utility is quasilinear, compensating variation (CV), equivalent variation (EV), and consumer surplus are algebraically equivalent. In mechanism design, quasilinear utility ensures that agents can compensate each other with side payments. Definition in terms of preferences A preference relation \succsim is quasilinear with respect to commodity 1 (called, in this case, the ''numeraire'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noam Nisan
Noam Nisan ( he, נעם ניסן; born June 20, 1961) is an Israeli computer scientist, a professor of computer science at the Hebrew University of Jerusalem. He is known for his research in computational complexity theory and algorithmic game theory. Biography Nisan did his undergraduate studies at the Hebrew University, graduating in 1984. He went to the University of California, Berkeley for graduate school, and received a Ph.D. in 1988 under the supervision of Richard Karp. After postdoctoral studies at the Massachusetts Institute of Technology he joined the Hebrew University faculty in 1990.Curriculum vitae retrieved 2012-03-01. Selected publications Nisan is the author of[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanism Design
Mechanism design is a field in economics and game theory that takes an objectives-first approach to designing economic mechanisms or incentives, toward desired objectives, in strategic settings, where players act rationally. Because it starts at the end of the game, then goes backwards, it is also called reverse game theory. It has broad applications, from economics and politics in such fields as market design, auction theory and social choice theory to networked-systems (internet interdomain routing, sponsored search auctions). Mechanism design studies solution concepts for a class of private-information games. Leonid Hurwicz explains that 'in a design problem, the goal function is the main "given", while the mechanism is the unknown. Therefore, the design problem is the "inverse" of traditional economic theory, which is typically devoted to the analysis of the performance of a given mechanism.' So, two distinguishing features of these games are: * that a game "designer" choos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duggan–Schwartz Theorem
The Duggan–Schwartz theorem (named after John Duggan and Thomas Schwartz) is a result about voting systems designed to choose a nonempty set of winners from the preferences of certain individuals, where each individual ranks all candidates in order of preference. It states that for three or more candidates, at least one of the following must hold: #The system is not anonymous (some voters are treated differently from others). #The system is imposed (some candidates can never win). #Every voter's top preference is in the set of winners. #The system can be manipulated by either an optimistic voter, one who can cast a ballot that would elect some candidate to a higher rank than all of those candidates who would have been elected if that voter had voted honestly; or by a pessimistic voter, one who can cast a ballot that would exclude some candidate to a lower rank than all of those candidates who were elected due that voter voting strategically. The first two conditions are consider ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. In this the ''American Mathematical Monthly'' fulfills a different role from that of typical mathematical research journals. The ''American Mathematical Monthly'' is the most widely read mathematics journal in the world according to records on JSTOR. Tables of contents with article abstracts from 1997–2010 are availablonline The MAA gives the Lester R. Ford Awards annually to "authors of articles of expository excellence" published in the ''American Mathematical Monthly''. Editors *2022– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Dummett
Sir Michael Anthony Eardley Dummett (27 June 1925 – 27 December 2011) was an English academic described as "among the most significant British philosophers of the last century and a leading campaigner for racial tolerance and equality." He was, until 1992, Wykeham Professor of Logic at the University of Oxford. He wrote on the history of analytic philosophy, notably as an interpreter of Frege, and made original contributions particularly in the philosophies of mathematics, logic, language and metaphysics. He was known for his work on truth and meaning and their implications to debates between realism and anti-realism, a term he helped to popularize. He devised the Quota Borda system of proportional voting, based on the Borda count. In mathematical logic, he developed an intermediate logic, already studied by Kurt Gödel: the Gödel–Dummett logic. Education and army service Born 27 June 1925, Dummett was the son of George Herbert Dummett (1880–1970), a silk merchant, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
