|
May's Theorem
In social choice theory, May's theorem states that simple majority voting is the only anonymous, neutral, and positively responsive social choice function between two alternatives. Further, this procedure is resolute when there are an odd number of voters and ties (indecision) are not allowed. Kenneth May first published this theorem in 1952. Various modifications have been suggested by others since the original publication. Mark Fey extended the proof to an infinite number of voters. Robert Goodin and Christian List showed that, among methods of aggregating first-preference votes over multiple alternatives, plurality rule uniquely satisfies May's conditions; under approval balloting, a similar statement can be made about approval voting. Arrow's theorem in particular does not apply to the case of two candidates, so this possibility result can be seen as a mirror analogue of that theorem. (Note that anonymity is a stronger form of non-dictatorship.) Another way of explaining the ... [...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] |
Simple Majority Voting
Majority rule is a principle that means the decision-making power belongs to the group that has the most members. In politics, majority rule requires the deciding vote to have majority, that is, more than half the votes. It is the binary decision rule used most often in influential decision-making bodies, including many legislatures of democratic nations. Distinction with plurality Decision-making in a legislature is different from election of representation, although the result of plurality (First Past the Post or FPTP) elections is often mistaken for majority rule. Plurality elections elect the option that has more votes than any other, regardless of whether the fifty percent threshold is passed. A plurality election produces representation of a majority when there are only two candidates in an election or, more generally, when there are only two options. However, when there are more than two alternatives, a candidate that has less than fifty percent of the votes cast in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anonymity (social Choice)
In social choice theory, Anonymity is a basic requirement of a social choice rule. It says that the rule does not discriminate apriori between different voters. In other words, the rule returns the same outcome (whatever this outcome may be) if the vector of votes is permuted arbitrarily.{{Cite book, last=Felix Brandt, chapter-url=https://books.google.com/books?id=0qY8DwAAQBAJ&dq=multiwinner++voting+a+new+challenge&pg=PA27, title=Trends in Computational Social Choice, date=2017-10-26, publisher=Lulu.com, isbn=978-1-326-91209-3, editor-last=Endriss, editor-first=Ulle, language=en, chapter=Roling the Dice: Recent Results in Probabilistic Social Choice Anonymous rules Most voting rules are anonymous by design. For example, plurality voting is anonymous, since only counts the number of votes received by each candidates, regardless of who cast these votes. Similarly, the utilitarian rule and egalitarian rule are both anonymous, since the only consider the set of utilities, regardless ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neutrality (social Choice)
In social choice theory, Neutrality is a basic requirement of a social choice rule. It says that the rule does not discriminate apriori between different candidates. In other words, if the vector of candidates is permuted arbitrarily, then the returned result is permuted in the same way.{{Cite book, last=Felix Brandt, chapter-url=https://books.google.com/books?id=0qY8DwAAQBAJ&q=multiwinner++voting+a+new+challenge&pg=PA27, title=Trends in Computational Social Choice, date=2017-10-26, publisher=Lulu.com, isbn=978-1-326-91209-3, editor-last=Endriss, editor-first=Ulle, language=en, chapter=Roling the Dice: Recent Results in Probabilistic Social Choice Neutral rules Most voting rules are neutral. For example, plurality voting is neutral, since only counts the number of votes received by each candidate, without giving an a-priori preference to any candidate. Similarly, the utilitarian rule and egalitarian rule are both neutral, since the only consider the utility given to each candidate, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kenneth May
Kenneth O. May (July 8, 1915, in Portland, Oregon – December 1977, in Toronto) was an American mathematician and historian of mathematics, who developed May's theorem. May was a prime mover behind the International Commission on the History of Mathematics, and was the first editor of its journal '' Historia Mathematica''. Every four years the ICHM awards the Kenneth O. May Prize for outstanding contributions to the history of mathematics. Biography Kenneth was born in 1915, the son of Samuel Chester "Sam" May (1887–1955) and Eleanor Ownsworth Perkin. His father, an alumnus of the University of Oregon and Yale Law School, practised law in Portland, Oregon beginning in 1913. After earning a Master of Arts degree from Columbia University, Sam in 1920 began teaching political science at Dartmouth College, and later at the University of California, Berkeley.C. V. Jones, Philip C. Enros, Henry S. Tropp (1984) "Kenneth O. May, 1915 — 1977, his early life to 1946", Historia Mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Goodin
Robert 'Bob' E. Goodin (born 30 November 1950) was Professor of Government at the University of Essex and is now Distinguished Professor of Philosophy and Social and Political theory at the Australian National University. Biography Goodin attended Oxford University, where he earned a DPhil in politics in 1975. He is a Fellow of the Academy of the Social Sciences in Australia and a Corresponding Fellow of the British Academy. In 2009 he won the Stein Rokkan Prize for Comparative Social Science Research, awarded by the International Social Science Council. He is the founding editor of ''The Journal of Political Philosophy'' and a co-editor of the ''British Journal of Political Science''. In 2022, Goodin was awarded the prestigious Johan Skytte Prize in Political Science ), location=Uppsala, Sweden, date= The Johan Skytte Prize in Political Science ( sv, Skytteanska priset) was established in 1995 by the Johan Skytte Foundation at Uppsala University. The foundation itself goes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christian List
Christian List (born 1973) is a German philosopher and political scientist who serves as professor of philosophy and decision theory at the Ludwig Maximilian University of Munich and co-director of the Munich Center for Mathematical Philosophy. He was previously professor of political science and philosophy at the London School of Economics. List's research interests relate to social choice theory, formal epistemology, political philosophy, and the philosophy of social science.Professor Christian List. London School of Economics. Retrieved 23 June 2015. Born in , Germany, on 7 November 1973, List earned his |
Arrow's Theorem
Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem in social choice theory that states that when voters have three or more distinct alternatives (options), no ranked voting electoral system can convert the ranked preferences of individuals into a community-wide (complete and transitive) ranking while also meeting the specified set of criteria: ''unrestricted domain'', ''non-dictatorship'', ''Pareto efficiency'', and ''independence of irrelevant alternatives''. The theorem is often cited in discussions of voting theory as it is further interpreted by the Gibbard–Satterthwaite theorem. The theorem is named after economist and Nobel laureate Kenneth Arrow, who demonstrated the theorem in his doctoral thesis and popularized it in his 1951 book ''Social Choice and Individual Values''. The original paper was titled "A Difficulty in the Concept of Social Welfare". In short, the theorem states that no rank-order electoral system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nakamura Number
In cooperative game theory and social choice theory, the Nakamura number measures the degree of rationality of preference aggregation rules (collective decision rules), such as voting rules. It is an indicator of the extent to which an aggregation rule can yield well-defined choices. *If the number of alternatives (candidates; options) to choose from is less than this number, then the rule in question will identify "best" alternatives without any problem. In contrast, *if the number of alternatives is greater than or equal to this number, the rule will fail to identify "best" alternatives for some pattern of voting (i.e., for some profile (tuple) of individual preferences), because a voting paradox will arise (a ''cycle'' generated such as alternative a socially preferred to alternative b, b to c, and c to a). The larger the Nakamura number a rule has, the greater the number of alternatives the rule can rationally deal with. For example, since (except in the case of four individuals ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
If And Only If
In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence), and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of either one of the connected statements requires the truth of the other (i.e. either both statements are true, or both are false), though it is controversial whether the connective thus defined is properly rendered by the English "if and only if"—with its pre-existing meaning. For example, ''P if and only if Q'' means that ''P'' is true whenever ''Q'' is true, and the only case in which ''P'' is true is if ''Q'' is also true, whereas in the case of ''P if Q'', there could be other scenarios where ''P'' is true and ''Q'' is ... [...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] |
1952 In Science
The year 1952 in science and technology involved some significant events, listed below. Biology * August 1 – Around 9 o'clock AM Pacific Time Zone, the San Benedicto rock wren goes extinct as its island home is smothered in a massive volcanic eruption. * August 14 – Alan Turing's paper "The Chemical Basis of Morphogenesis" is published, putting forward a reaction–diffusion hypothesis of pattern formation, considered a seminal piece of work in morphogenesis. * August 28 – Alan Hodgkin and Andrew Huxley publish the Hodgkin–Huxley model of action potentials in neurons of the squid giant axon. * September 20 – Publication of the paper on the Hershey–Chase experiment showing conclusively that DNA, not protein, is the genetic material of bacteriophages. * October – Danish virologist Preben von Magnus publishes his observation of the von Magnus phenomenon producing defective interfering particles. * Biochemists Jack Gross and Rosalind Pitt-Rivers discover the thyr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
