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Cyclic Tie
In social choice theory, Condorcet's voting paradox is a fundamental discovery by the Marquis de Condorcet that majority rule is inherently self-contradictory. The result implies that it is logically impossible for any voting system to guarantee that a winner will have support from a majority of voters; for example, there can be rock-paper-scissors scenarios where a majority of voters will prefer A to B, B to C, and also C to A, even if every voter's individual preferences are rational and avoid self-contradiction. Examples of Condorcet's paradox are called Condorcet cycles or cyclic ties. In such a cycle, every possible choice is rejected by the electorate in favor of another alternative, who is preferred by more than half of all voters. Thus, any attempt to ground social decision-making in majoritarianism must accept such self-contradictions (commonly called spoiler effects). Systems that attempt to do so, while minimizing the rate of such self-contradictions, are called Condo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social Choice Theory
Social choice theory is a branch of welfare economics that extends the Decision theory, theory of rational choice to collective decision-making. Social choice studies the behavior of different mathematical procedures (social welfare function, social welfare functions) used to combine individual preferences into a coherent whole.Amartya Sen (2008). "Social Choice". ''The New Palgrave Dictionary of Economics'', 2nd EditionAbstract & TOC./ref> It contrasts with political science in that it is a Normative economics, normative field that studies how a society can make good decisions, whereas political science is a Positive economics, descriptive field that observes how societies actually do make decisions. While social choice began as a branch of economics and decision theory, it has since received substantial contributions from mathematics, philosophy, political science, and game theory. Real-world examples of social choice rules include constitution, constitutions and Parliamentary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voting Paradox Example
Voting is the process of choosing officials or policies by casting a ballot, a document used by people to formally express their preferences. Republics and representative democracies are governments where the population chooses representatives by voting. The procedure for identifying the winners based on votes varies depending on both the country and the political office. Political scientists call these procedures electoral systems, while mathematicians and economists call them social choice rules. The study of these rules and what makes them good or bad is the subject of a branch of welfare economics known as social choice theory. In smaller organizations, voting can occur in many different ways: formally via ballot to elect others for example within a workplace, to elect members of political associations, or to choose roles for others; or informally with a spoken agreement or a gesture like a raised hand. In larger organizations, like countries, voting is generally confin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Online Poll
An open-access poll is a type of opinion poll in which a nonprobability sample of participants self-select into participation. The term includes call-in, mail-in, and some online polls. The most common examples of open-access polls ask people to phone a number, click a voting option on a website, or return a coupon cut from a newspaper. By contrast, professional polling companies use a variety of techniques to attempt to ensure that the polls they conduct are representative, reliable and scientific. The most glaring difference between an open-access poll and a scientific poll is that scientific polls typically randomly select their samples and sometimes use statistical weights to make them representative of the target population. Advantages and disadvantages Since participants in an open-access poll are volunteers rather than a random sample, such polls represent the most interested individuals, just as in voting. In the case of political polls, such participants might be mor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermometer Scale
A feeling thermometer, also known as a thermometer scale, is a type of visual analog scale that allows respondents to rank their views of a given subject on a scale from "cold" (indicating disapproval) to "hot" (indicating approval), analogous to the temperature scale of a real thermometer. It is often used in survey and political science research to measure how positively individuals feel about a given group, individual, issue, or organisation, as well as in quality of life research to measure individuals' subjective health status. It typically uses a rating scale with options ranging from a minimum of 0 to a maximum of 100. Questions using the feeling thermometer have been included in every year of the American National Election Studies since 1968. Since its inclusion in a national forum, the tool has developed and become popular in both the political sphere and for medical and psychological research purposes. As it is a relatively new method of research and is still being studi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American National Election Studies
The American National Election Studies (ANES) are academically-run national surveys of voters in the United States, conducted before and after every presidential election. Although it was formally established by a National Science Foundation grant in 1977, the data are a continuation of studies going back to 1948. The study has been based at the University of Michigan since its origin and, since 2005, has been run in partnership with Stanford University. Its principal investigators for the first four years of the partnership were Arthur Lupia and Jon Krosnick. As of 2025, the principal investigators are Nicholas Valentino of the University of Michigan and Shanto Iyengar of Stanford University. With more than 9,800 citations in published work, data spanning over 75 years, and more than 70 datasets, the American National Election Studies has acted as a cornerstone for public opinion research for the past 75 years, asking a representative sample of the American population survey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electoral Reform Society
The Electoral Reform Society (ERS) is an Advocacy group, independent advocacy organisation in the United Kingdom which promotes electoral reform. It seeks to replace first-past-the-post voting with proportional representation, advocating the single transferable vote, and Reform of the House of Lords, an elected upper house of Parliament. It is the world's oldest still-extant electoral reform campaign. Overview The Electoral Reform Society seeks a "representative democracy fit for the 21st century." The society advocates the replacement of the first-past-the-post voting, first-past-the-post and Plurality block voting, plurality-at-large voting systems with a proportional voting system, the single transferable vote. First-past-the-post is currently used for Elections in the United Kingdom#General elections, elections to the House of Commons and for most local elections in England and Wales, while plurality-at-large is used in multi-member council wards in England and Wales, and w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ranked Voting
Ranked voting is any voting system that uses voters' Ordinal utility, rankings of candidates to choose a single winner or multiple winners. More formally, a ranked vote system depends only on voters' total order, order of preference of the candidates. Ranked voting systems vary dramatically in how preferences are tabulated and counted, which gives them Comparison of voting rules, very different properties. In instant-runoff voting (IRV) and the single transferable vote system (STV), lower preferences are used as contingencies (back-up preferences) and are only applied when all higher-ranked preferences on a ballot have been eliminated or when the vote has been cast for a candidate who has been elected and surplus votes need to be transferred. Ranked votes of this type do not suffer the problem that a marked lower preference may be used against a voter's higher marked preference. Some ranked vote systems use ranks as weights; these systems are called positional voting. In the B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spatial Model Of Voting
In political science and social choice theory, the spatial (sometimes ideological or ideal-point) model of voting, also known as the Hotelling–Downs model, is a mathematical model of voting behavior. It describes voters and candidates as varying along one or more axes (or dimensions), where each axis represents an attribute of the candidate that voters care about. Voters are modeled as having an ideal point in this space and preferring candidates closer to this point over those who are further away; these kinds of preferences are called single-peaked. The most common example of a spatial model is a political spectrum or compass, such as the traditional left-right axis, but issue spaces can be more complex. For example, a study of German voters found at least four dimensions were required to adequately represent all political parties. Besides ideology, a dimension can represent any attribute of the candidates, such as their views on one particular issue. It can also represen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Impartial Culture
Impartial culture (IC) or the culture of indifference is a probabilistic model used in social choice theory for analyzing ranked voting method rules. The model is understood to be unrealistic, and not a good representation of real-world voting behavior, however, it is useful for mathematical comparisons of voting methods under reproducible, worst-case scenarios. The model assumes that each voter provides a complete strict ranking of all the candidates (with no equal rankings or blanks), which is drawn from a set of all possible rankings. For m candidates, there are m! possible strict rankings (permutation In mathematics, a permutation of a set can mean one of two different things: * an arrangement of its members in a sequence or linear order, or * the act or process of changing the linear order of an ordered set. An example of the first mean ...s). There are three variations of the model that use different subsets of the full set of possible rankings, so that different ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A289505
A, or a, is the first letter and the first vowel letter of the Latin alphabet, used in the modern English alphabet, and others worldwide. Its name in English is '' a'' (pronounced ), plural ''aes''. It is similar in shape to the Ancient Greek letter alpha, from which it derives. The uppercase version consists of the two slanting sides of a triangle, crossed in the middle by a horizontal bar. The lowercase version is often written in one of two forms: the double-storey and single-storey . The latter is commonly used in handwriting and fonts based on it, especially fonts intended to be read by children, and is also found in italic type. In English, '' a'' is the indefinite article, with the alternative form ''an''. Name In English, the name of the letter is the ''long A'' sound, pronounced . Its name in most other languages matches the letter's pronunciation in open syllables. History The earliest known ancestor of A is ''aleph''—the first letter of the Phoenician ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cauchy Distribution
The Cauchy distribution, named after Augustin-Louis Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution f(x; x_0,\gamma) is the distribution of the -intercept of a ray issuing from (x_0,\gamma) with a uniformly distributed angle. It is also the distribution of the Ratio distribution, ratio of two independent Normal distribution, normally distributed random variables with mean zero. The Cauchy distribution is often used in statistics as the canonical example of a "pathological (mathematics), pathological" distribution since both its expected value and its variance are undefined (but see below). The Cauchy distribution does not have finite moment (mathematics), moments of order greater than or equal to one; only fractional absolute moments exist., Chapter 16. The Cauchy dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Central Limit Theorem
In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the Probability distribution, distribution of a normalized version of the sample mean converges to a Normal distribution#Standard normal distribution, standard normal distribution. This holds even if the original variables themselves are not Normal distribution, normally distributed. There are several versions of the CLT, each applying in the context of different conditions. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions. This theorem has seen many changes during the formal development of probability theory. Previous versions of the theorem date back to 1811, but in its modern form it was only precisely stated as late as 1920. In statistics, the CLT can be stated as: let X_1, X_2, \dots, X_n denote a Sampling ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
