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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] |
Theory
A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be scientific, belong to a non-scientific discipline, or no discipline at all. Depending on the context, a theory's assertions might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings. In modern science, the term "theory" refers to scientific theories, a well-confirmed type of explanation of nature, made in a way consistent with the scientific method, and fulfilling the criteria required by modern science. Such theories are described in such a way that scientific tests should be able to provide empirical support for it, or empirical contradiction ("falsify") of it. Scientific theories are the most reliable, rigorous, and compr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marquis De Condorcet
Marie Jean Antoine Nicolas de Caritat, Marquis of Condorcet (; 17 September 1743 – 29 March 1794), known as Nicolas de Condorcet, was a French philosopher and mathematician. His ideas, including support for a liberal economy, free and equal public instruction, constitutional government, and equal rights for women and people of all races, have been said to embody the ideals of the Age of Enlightenment, of which he has been called the "last witness," and Enlightenment rationalism. He died in prison after a period of hiding from the French Revolutionary authorities. Early years Condorcet was born in Ribemont (in present-day Aisne), descended from the ancient family of Caritat, who took their title from the town of Condorcet in Dauphiné, of which they were long-time residents. Fatherless at a young age, he was taken care of by his devoutly religious mother who dressed him as a girl till age eight. He was educated at the Jesuit College in Reims and at the ''Collège de Navarre'' i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Domain Of A Function
In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by \operatorname(f) or \operatornamef, where is the function. More precisely, given a function f\colon X\to Y, the domain of is . Note that in modern mathematical language, the domain is part of the definition of a function rather than a property of it. In the special case that and are both subsets of \R, the function can be graphed in the Cartesian coordinate system. In this case, the domain is represented on the -axis of the graph, as the projection of the graph of the function onto the -axis. For a function f\colon X\to Y, the set is called the codomain, and the set of values attained by the function (which is a subset of ) is called its range or image. Any function can be restricted to a subset of its domain. The restriction of f \colon X \to Y to A, where A\subseteq X, is written as \left. f \_A \colon A \to Y. Natural domain If a real function is giv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fair Division
Fair division is the problem in game theory of dividing a set of resources among several people who have an entitlement to them so that each person receives their due share. That problem arises in various real-world settings such as division of inheritance, partnership dissolutions, divorce settlements, electronic frequency allocation, airport traffic management, and exploitation of Earth observation satellites. It is an active research area in mathematics, economics (especially social choice theory), dispute resolution, etc. The central tenet of fair division is that such a division should be performed by the players themselves, maybe using a mediator but certainly not an arbiter as only the players really know how they value the goods. The archetypal fair division algorithm is divide and choose. It demonstrates that two agents with different tastes can divide a cake such that each of them believes that he got the best piece. The research in fair division can be seen as an exten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compensation Principle
In welfare economics, the compensation principle refers to a decision rule used to select between pairs of alternative feasible social states. One of these states is the hypothetical point of departure ("the original state"). According to the compensation principle, if the prospective gainers could compensate (any) prospective losers and leave no one worse off, the alternate state is to be selected (Chipman, 1987, p. 524). An example of a compensation principle is the Pareto criterion in which a change in states entails that such compensation is not merely feasible but required. Two variants are: * the Pareto principle, which requires any change such that ''all'' gain. * the (strong) Pareto criterion, which requires any change such that ''at least one'' gains and no one loses from the change. In non-hypothetical contexts such that the compensation occurs (say in the marketplace), invoking the compensation principle is unnecessary to effect the change. But its use is more ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interpersonal Utility Comparison
The concept of interpersonal relationship involves social associations, connections, or affiliations between two or more people. Interpersonal relationships vary in their degree of intimacy or self-disclosure, but also in their duration, in their reciprocity and in their power distribution, to name only a few dimensions. The context can vary from family or kinship relations, friendship, marriage, relations with associates, work, clubs, neighborhoods, and places of worship. Relationships may be regulated by law, custom, or mutual agreement, and form the basis of social groups and of society as a whole. Interpersonal relationships are created by people's interactions with one another in social situations. This association of interpersonal relations being based on social situation has inference since in some degree love, solidarity, support, regular business interactions, or some other type of social connection or commitment. Interpersonal relationships thrive through equitable a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Median Voter Theorem
The median voter theorem is a proposition relating to ranked preference voting put forward by Duncan Black in 1948.Duncan Black, "On the Rationale of Group Decision-making" (1948). It states that if voters and policies are distributed along a one-dimensional spectrum, with voters ranking alternatives in order of proximity, then any voting method which satisfies the Condorcet criterion will elect the candidate closest to the median voter. In particular, a majority vote between two options will do so. The theorem is associated with public choice economics and statistical political science. Partha Dasgupta and Eric Maskin have argued that it provides a powerful justification for voting methods based on the Condorcet criterion. Plott's majority rule equilibrium theorem extends this to two dimensions. A loosely related assertion had been made earlier (in 1929) by Harold Hotelling. It is not a true theorem and is more properly known as the median voter theory or median voter model. It ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Condorcet Jury Theorem
Condorcet's jury theorem is a political science theorem about the relative probability of a given group of individuals arriving at a correct decision. The theorem was first expressed by the Marquis de Condorcet in his 1785 work ''Essay on the Application of Analysis to the Probability of Majority Decisions''. The assumptions of the theorem are that a group wishes to reach a decision by majority rule, majority vote. One of the two outcomes of the vote is ''correct'', and each voter has an independent probability ''p'' of voting for the correct decision. The theorem asks how many voters we should include in the group. The result depends on whether ''p'' is greater than or less than 1/2: * If ''p'' is greater than 1/2 (each voter is more likely to vote correctly), then adding more voters increases the probability that the majority decision is correct. In the limit, the probability that the majority votes correctly approaches 1 as the number of voters increases. * On the other hand, if ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Arrow's Impossibility 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 syst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social Choice And Individual Values
Kenneth Arrow's monograph ''Social Choice and Individual Values'' (1951, 2nd ed., 1963, 3rd ed., 2012) and a theorem within it created modern social choice theory, a rigorous melding of social ethics and voting theory with an economic flavor. Somewhat formally, the "social choice" in the title refers to Arrow's representation of how ''social values'' from the ''set of individual orderings'' would be implemented under the ''constitution''. Less formally, each social choice corresponds to the feasible set of laws passed by a "vote" (the set of orderings) under the constitution even if not every individual voted in favor of all the laws. The work culminated in what Arrow called the "General Possibility Theorem," better known thereafter as Arrow's (impossibility) theorem. The theorem states that, absent restrictions on either individual preferences or neutrality of the constitution to feasible alternatives, there exists no social choice rule that satisfies a set of plausible requir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
