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Mathematical Theory Of Democracy
The mathematical theory of democracy is an interdisciplinary branch of the public choice and social choice theories conceptualized by Andranik Tangian. It operationalizes the fundamental idea to modern democracies – that of political representation, in particular focusing on policy representation, i.e. how well the electorate's policy preferences are represented by the party system and the government. The representative capability is measured by means of dedicated indices that are used both for analytical purposes and practical applications. History The mathematical approach to politics goes back to Aristotle, who explained the difference between democracy, oligarchy and mixed constitution in terms of vote weighting. The historical mathematization of social choice principles is reviewed by Iain McLean and Arnold Urken. Modern mathematical studies in democracy are due to the game, public choice and social choice theories, which emerged after the World War II; for reviews see. I ...
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Public Choice
Public choice, or public choice theory, is "the use of economic tools to deal with traditional problems of political science".Gordon Tullock, The New Palgrave: A Dictionary of Economics, [1987] 2008, "public choice," ''The New Palgrave Dictionary of Economics''. . Its content includes the study of political behavior. In political science, it is the subset of positive political theory that studies self-interested Agent (economics), agents (voters, politicians, bureaucrats) and their interactions, which can be represented in a number of ways – using (for example) standard constrained utility maximization, game theory, or decision theory. It is the origin and intellectual foundation of contemporary work in political economy.Alberto Alesina, Torsten Persson, Guido Tabellini, 2006. “Reply to Blankart and Koester's Political Economics versus Public Choice Two Views of Political Economy in Competition,” Kyklos, 59(2), pp. 201–208 In popular use, "public choice" is often used as ...
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Nikolai Nikolayevich Vorobyov (mathematician)
Nikolai Nikolayevich Vorobyov (also Vorobiev) (russian: Николай Николаевич Воробьёв, 18 September 1925, Leningrad — July 14, 1995) was a Soviet and Russian mathematician, an expert in the field of abstract algebra, mathematical logic and probability theory, the founder of the Soviet school of game theory. He is an author of two textbooks, three monographs, a large number of mathematical articles and a number of popular science books. He supervised over 30 kandidat and D.Sc (habilitation) dissertations.Николай Николаевич Воробьев
a biography at the

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Share Price
A share price is the price of a single share of a number of saleable equity shares of a company. In layman's terms, the stock price is the highest amount someone is willing to pay for the stock, or the lowest amount that it can be bought for. Behaviour of share prices In economics and financial theory, analysts use random walk techniques to model behavior of asset prices, in particular share prices on stock markets. This practice has its basis in the presumption that investors act rationally and without biases, and that at any moment they estimate the value of an asset based on future expectations. Under these conditions, all existing information affects the price, which changes only when new information comes out. By definition, new information appears randomly and influences the asset price randomly. Empirical studies have demonstrated that prices do not completely follow random walks. Low serial correlations (around 0.05) exist in the short term, and slightly stronger correl ...
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Political Spectrum
A political spectrum is a system to characterize and classify different political positions in relation to one another. These positions sit upon one or more geometric axes that represent independent political dimensions. The expressions political compass and political map are used to refer to the political spectrum as well, especially to popular two-dimensional models of it. Most long-standing spectra include the left–right dimension as a measure of social, political and economic hierarchy which originally referred to seating arrangements in the French parliament after the Revolution (1789–1799), with radicals on the left and aristocrats on the right. While communism and socialism are usually regarded internationally as being on the left, conservatism and reactionism are generally regarded as being on the right. Liberalism can mean different things in different contexts, being sometimes on the left (social liberalism) and other times on the right (conservative liberalis ...
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Athenian Democracy
Athenian democracy developed around the 6th century BC in the Greek city-state (known as a polis) of Athens, comprising the city of Athens and the surrounding territory of Attica. Although Athens is the most famous ancient Greek democratic city-state, it was not the only one, nor was it the first; multiple other city-states adopted similar democratic constitutions before Athens. By the late 4th century BC as many as half of the over one thousand existing Greek city-states might have been democracies. Athens practiced a political system of legislation and executive bills. Participation was open to adult, male citizens (i.e., not a foreign resident, regardless of how many generations of the family had lived in the city, nor a slave, nor a woman), who "were probably no more than 30 percent of the total adult population". Solon (in 594 BC), Cleisthenes (in 508–07 BC), and Ephialtes (in 462 BC) contributed to the development of Athenian democracy. Cleisthenes broke up the unlimite ...
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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 ...
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Council Of Europe
The Council of Europe (CoE; french: Conseil de l'Europe, ) is an international organisation founded in the wake of World War II to uphold European Convention on Human Rights, human rights, democracy and the Law in Europe, rule of law in Europe. Founded in 1949, it has 46 member states, with a population of approximately 675 million; it operates with an annual budget of approximately 500 million euros. The organisation is distinct from the European Union (EU), although it is sometimes confused with it, partly because the EU has adopted the original Flag of Europe, European flag, created for the Council of Europe in 1955, as well as the Anthem of Europe, European anthem. No country has ever joined the EU without first belonging to the Council of Europe. The Council of Europe is an official United Nations General Assembly observers, United Nations Observer. Being an international organization, the Council of Europe cannot make laws, but it does have the ability to push for the enf ...
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World Forum For Democracy
The World Forum for Democracy is a gathering each November in Strasbourg, France to debate the complex challenges facing democracies today and foster democratic innovation. The Forum is hosted by the Council of Europe and brings together members of civil society, political leaders and representatives of business, academia, media and professional groups. Past editions have revolved around themes such as "Bridging the gap: democracy between old models and new realities", "Re-wiring Democracy: connecting institutions and citizens in the digital age" and "From participation to influence: can youth revitalise democracy?". The Forum's concept is that the challenges of 21st century democracy need to be addressed with 21st century means, using the power of networked communication, and harnessing social and political innovation from the grassroots. The exchanges that take place during the World Forum meetings focus on real-life initiatives by public authorities or grassroots actors, which are ...
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Electoral System Of Germany
The German federal election system regulates the election of the members of the national parliament, called the Bundestag. According to the principles governing the elections laws, set down in Art. 38 of the German Basic Law, elections are to be universal, direct, free, equal, and secret. Furthermore, the German Basic Law stipulates that Bundestag elections are to take place every four years and that one can vote, and be elected, upon reaching the age of 18. All other stipulations for the federal elections are regulated by the Federal Electoral Act. Elections always take place on a Sunday. Mail votes are possible upon application. Germans elect their members of parliament with two votes. The first vote is for a ''direct candidate'', who is required to receive a plurality vote in their electoral district. The second vote is used to elect a party list in each state as established by its respective party caucus. The Bundestag comprises seats representing each electoral district, with ...
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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 ...
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Kenneth Arrow
Kenneth Joseph Arrow (23 August 1921 – 21 February 2017) was an American economist, mathematician, writer, and political theorist. He was the joint winner of the Nobel Memorial Prize in Economic Sciences with John Hicks in 1972. In economics, he was a major figure in post-World War II neo-classical economic theory. Many of his former graduate students have gone on to win the Nobel Memorial Prize themselves. His most significant works are his contributions to social choice theory, notably "Arrow's impossibility theorem", and his work on general equilibrium analysis. He has also provided foundational work in many other areas of economics, including endogenous growth theory and the economics of information. Education and early career Arrow was born on 23 August 1921, in New York City. Arrow's mother, Lilian (Greenberg), was from Iași, Romania, and his father, Harry Arrow, was from nearby Podu Iloaiei. The Arrow family were Romanian Jews. His family was very supportive of his ...
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Discursive Dilemma
Discursive dilemma or doctrinal paradox is a paradox in social choice theory. The paradox is that aggregating judgments with majority voting can result in self-contradictory judgments. Consider a community voting on road repairs asked three questions; the repairs go ahead if all three answers are 'Yes'. The questions are: "Are the roads important?", "Is the weather right for road repair?" and "Are there available funds for repairs?" Imagine that three (non-overlapping) groups of 20% of people vote 'No' for each question, and everyone else votes 'Yes'. Then each question has an 80% agreement of 'Yes', so the repairs go ahead. However, now consider the situation where the community are asked one question: "Are all three conditions (importance, weather and funds) met?" Now 60% of people disagree with one of these conditions, so only 40% agree on a 'Yes' vote. In this case, the repairs do not go ahead. Thus the road repair team gets different feedback depending on how they poll their c ...
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