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Multi-issue Voting
Multi-issue voting is a setting in which several issues have to be decided by voting. Multi-issue voting raises several considerations, that are not relevant in single-issue voting. The first consideration is attaining ''fairness'' both for the majority and for minorities. To illustrate, consider a group of friends who decide each evening whether to go to a movie or a restaurant. Suppose that 60% of the friends prefer movies and 40% prefer restaurants. In a one-time vote, the group will probably accept the majority preference and go to a movie. However, making the same decision again and again each day is unfair, since it satisfies 60% of the friends 100% of the time, while the other 40% are never satisfied. Considering this problem as multi-issue voting allows attain a fair sequence of decisions by going 60% of the evenings to a movie and 40% of the evenings to a restaurant. The study of fair multi-issue voting mechanisms is sometimes called fair public decision making. The speci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voting
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 confi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Method Of Equal Shares
The method of equal shares is a proportional method of counting ballots that applies to participatory budgeting, to committee elections, and to simultaneous public decisions. It can be used when the voters vote via approval ballots, ranked ballots or cardinal ballots. It works by dividing the available budget into equal parts that are assigned to each voter. The method is only allowed to use the budget share of a voter to implement projects that the voter voted for. It then repeatedly finds projects that can be afforded using the budget shares of the supporting voters. In contexts other than participatory budgeting, the method works by equally dividing an abstract budget of "voting power". In 2023, the method of equal shares was being used in a participatory budgeting program in the Polish city of Wieliczka. The program, known as Green Million (''Zielony Milion''), was set to distribute 1 million złoty to ecological projects proposed by residents of the city. It was also used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
House Monotonicity
House monotonicity (also called house-size monotonicity) is a property of apportionment methods. These are methods for allocating seats in a parliament among federal states (or among political parties). The property says that, if the number of seats in the "house" (the parliament) increases, and the method is re-activated, then no state (or party) should have fewer seats than it previously had. A method that fails to satisfy house-monotonicity is said to have the Alabama paradox. In the context of committee elections, house monotonicity is often called committee monotonicity. It says that, if the size of the committee increases, then all the candidate that were previously elected, are still elected. House monotonicity is the special case of ''resource monotonicity'' for the setting in which the resource consists of identical discrete items (the seats). Methods violating house-monotonicity An example of a method violating house-monotonicity is the largest remainder method (= H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Local Optimum
In mathematical analysis, the maximum and minimum of a function are, respectively, the greatest and least value taken by the function. Known generically as extremum, they may be defined either within a given range (the ''local'' or ''relative'' extrema) or on the entire domain (the ''global'' or ''absolute'' extrema) of a function. Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum. In statistics, the corresponding concept is the sample maximum and minimum. Definition A real-valued function ''f'' defined on a domain ''X'' has a global (or absolute) maximum point at ''x''∗, if for all ''x'' in ''X''. Similarly, the function has a global (or absolute) minimum point at ''x''∗, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Local Search (constraint Satisfaction)
In constraint satisfaction, local search is an incomplete method for finding a solution to a problem. It is based on iteratively improving an assignment of the variables until all constraints are satisfied. In particular, local search algorithms typically modify the value of a variable in an assignment at each step. The new assignment is close to the previous one in the space of assignment, hence the name ''local search''. All local search algorithms use a function that evaluates the quality of assignment, for example the number of constraints violated by the assignment. This amount is called the ''cost'' of the assignment. The aim of local search is that of finding an assignment of minimal cost, which is a solution if any exists. Two classes of local search algorithms exist. The first one is that of greedy or non-randomized algorithms. These algorithms proceed by changing the current assignment by always trying to decrease (or at least, non-increase) its cost. The main problem o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Number
In mathematics, the -th harmonic number is the sum of the reciprocals of the first natural numbers: H_n= 1+\frac+\frac+\cdots+\frac =\sum_^n \frac. Starting from , the sequence of harmonic numbers begins: 1, \frac, \frac, \frac, \frac, \dots Harmonic numbers are related to the harmonic mean in that the -th harmonic number is also times the reciprocal of the harmonic mean of the first positive integers. Harmonic numbers have been studied since antiquity and are important in various branches of number theory. They are sometimes loosely termed harmonic series, are closely related to the Riemann zeta function, and appear in the expressions of various special functions. The harmonic numbers roughly approximate the natural logarithm function and thus the associated harmonic series grows without limit, albeit slowly. In 1737, Leonhard Euler used the divergence of the harmonic series to provide a new proof of the infinity of prime numbers. His work was extended into the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phragmen's Voting Rules
Phragmén's voting rules are rules for multiwinner voting. They allow voters to vote for individual candidates rather than parties, but still guarantee proportional representation. They were published by Lars Edvard Phragmén in French and Swedish between 1893 and 1899, and translated to English by Svante Janson in 2016. Background In multiwinner approval voting, each voter can vote for one or more candidates, and the goal is to select a fixed number ''k'' of winners (where ''k'' may be, for example, the number of parliament members). The question is how to determine the set of winners? * The simplest method is ''multiple non-transferable vote'', in which the ''k'' candidates with the largest number of approvals are elected. But this method tends to select ''k'' candidates of the largest party, leaving the smaller parties with no representation at all. * In the 19th century, there was much discussion regarding election systems that could guarantee proportional representatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gottlob Frege
Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, philosophy of logic, logic, and Philosophy of mathematics, mathematics. Though he was largely ignored during his lifetime, Giuseppe Peano (1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers. Frege is widely considered to be the greatest logician since Aristotle, and one of the most profound philosophers of mathematics ever. His contributions include the History of logic#Rise of modern logic, development of modern logic in the ''Begriffsschrift'' and work in the foundations of mathematics. His book the ''Foundations of Arithmetic'' is the seminal text of the logicist project, and is ci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apportionment Method
Apportionment is the process by which seats in a legislative body are distributed among administrative divisions, such as states or parties, entitled to representation. This page presents the general principles and issues related to apportionment. The apportionment by country page describes the specific practices used around the world. The Mathematics of apportionment page describes mathematical formulations and properties of apportionment rules. The simplest and most universal principle is that elections should give each vote an equal weight. This is both intuitive and stated in laws such as the Fourteenth Amendment to the United States Constitution (the Equal Protection Clause). One example of deliberate malapportionment is seen in bicameral legislatures: while one house, often called a house of commons or representatives, is based on proportional representation, the other is based on regional representation. This is modeled after the Connecticut Compromise, which formed the ba ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
