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Average Satisfaction
Justified representation (JR) is a criterion of fairness in multiwinner approval voting. It can be seen as an adaptation of the proportional representation criterion to approval voting. Background Proportional representation (PR) is an important consideration in designing electoral systems. It means that the various groups and sectors in the population should be represented in the parliament in proportion to their size. The most common system for ensuring proportional representation is the party-list system. In this system, the candidates are partitioned into parties, and each citizen votes for a single party. Each party receives a number of seats proportional to the number of citizens who voted for it. For example, for a parliament with 10 seats, if exactly 50% of the citizens vote for party A, exactly 30% vote for party B, and exactly 20% vote for party C, then proportional representation requires that the parliament contains exactly 5 candidates from party A, exactly 3 can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiwinner Approval Voting
Multiwinner approval voting, sometimes also called approval-based committee (ABC) voting, refers to a family of multi-winner Electoral system, electoral systems that use Approval ballot, approval ballots. Each voter may select ("approve") any number of candidates, and multiple candidates are elected. Multiwinner approval voting is an adaptation of approval voting to Multiwinner voting, multiwinner elections. In a single-winner approval voting system, it is easy to determine the winner: it is the candidate approved by the largest number of voters. In multiwinner approval voting, there are many different ways to decide which candidates will be elected. Approval block voting In approval block voting (also called unlimited voting), each voter either approves or disapproves of each candidate, and the ''k'' candidates with the most approval votes win (where ''k'' is the predetermined committee size). It does not provide proportional representation. Proportional approval voting P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Piotr Skowron
Piotr Skowron is an assistant professor at the University of Warsaw. He is known for his research in artificial intelligence (AI) and theoretical computer science, especially for his work on social choice, and committee elections. Biography Piotr Skowron received his Ph.D. in computer science from the University of Warsaw in 2015. His doctoral dissertation won the runner-up for IFAAMAS Victor Lesser Distinguished Dissertation Award for the best dissertation in the area of autonomous agents and multi-agent systems. Subsequently, he was a postdoctoral researcher at the University of Oxford (2016), and at Technische Universität Berlin (2017), where he was supported by the Alexander von Humboldt Foundation. In 2018, he joined the Faculty of Mathematics, Informatics and Mechanics at University of Warsaw as a faculty member. Research and awards In 2022, Piotr Skowron won the IJCAI Computers and Thought Award The IJCAI Computers and Thought Award is presented every two years by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degressive Proportionality
Degressive or progressive proportionality is an approach to the allocation of seats in a legislative body among administrative divisions of varying population sizes. It aims for fair representation of each division while also taking into account the number of voters in each one. Under systems using degressive proportionality, smaller divisions therefore have a higher seats-to-votes ratio. It is used in the European Parliament and the Bundesrat of Germany, among others. Degressive proportionality is an alternative to, for instance, each subdivision electing the same number of members, or electing a number of members strictly proportional to its population. Degressive proportionality is intermediate between those two approaches. Degressive proportionality can be achieved through various methods, and the term does not describe any one particular formula. Any system that reserves a minimum number of seats for a sub-body is to some extent degressively proportional. Uses Germany ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Dummett
Sir Michael Anthony Eardley Dummett (; 27 June 1925 – 27 December 2011) was an English academic described as "among the most significant British philosophers of the last century and a leading campaigner for racial tolerance and equality." He was, until 1992, Wykeham Professor of Logic at the University of Oxford. He wrote on the history of analytic philosophy, notably as an interpreter of Frege, and made original contributions particularly in the philosophies of mathematics, logic, language and metaphysics. He was known for his work on truth and meaning and their implications to debates between realism and anti-realism, a term he helped to popularize. In mathematical logic, he developed an intermediate logic, a logical system intermediate between classical logic and intuitionistic logic that had already been studied by Kurt Gödel: the Gödel–Dummett logic. In voting theory, he devised the Quota Borda system of proportional voting, based on the Borda count, and conj ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Party-approval Voting
Multiwinner approval voting, sometimes also called approval-based committee (ABC) voting, refers to a family of multi-winner electoral systems that use approval ballots. Each voter may select ("approve") any number of candidates, and multiple candidates are elected. Multiwinner approval voting is an adaptation of approval voting to multiwinner elections. In a single-winner approval voting system, it is easy to determine the winner: it is the candidate approved by the largest number of voters. In multiwinner approval voting, there are many different ways to decide which candidates will be elected. Approval block voting In approval block voting (also called unlimited voting), each voter either approves or disapproves of each candidate, and the ''k'' candidates with the most approval votes win (where ''k'' is the predetermined committee size). It does not provide proportional representation. Proportional approval voting Proportional approval voting refers to voting methods w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Price Of Fairness
In the theory of fair division, the price of fairness (POF) is the ratio of the largest economic welfare attainable by a division to the economic welfare attained by a ''fair'' division. The POF is a quantitative measure of the loss of welfare that society has to take in order to guarantee fairness. In general, the POF is defined by the following formula:POF=\frac The exact price varies greatly based on the kind of division, the kind of fairness and the kind of social welfare we are interested in. The most well-studied type of social welfare is '' utilitarian social welfare'', defined as the sum of the (normalized) utilities of all agents. Another type is '' egalitarian social welfare'', defined as the minimum (normalized) utility per agent. Numeric example In this example we focus on the ''utilitarian price of proportionality'', or UPOP. Consider a heterogeneous land-estate that has to be divided among 100 partners, all of whom value it as 100 (or the value is normalized to 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Fully Proportional Representation
Fully proportional representation (FPR) is a property of multiwinner voting systems. It extends the property of proportional representation (PR) by requiring that the representation be based on the entire preferences of the voters, rather than on their first choice. Moreover, the requirement combines PR with the requirement of ''accountability'' - each voter knows exactly which elected candidate represents him, and each candidate knows exactly which voters he represents. The term was coined in 1995 by Burt L. Monroe, but a similar idea appeared already in 1983 in a paper by John R. Chamberlin and Paul N. Courant. The two voting rules known to satisfy this property are known - respectively - as Monroe's voting rule and the Chamberlin-Courant (CC) voting rule. Background Most existing electoral systems for proportional representation (PR) are based only on the voters' first preferences, for example: if 40% vote for party A as their first choice, then 40% of the parliament members ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Committee 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] |
Submodular Optimization
In mathematics, a submodular set function (also known as a submodular function) is a set function that, informally, describes the relationship between a set of inputs and an output, where adding more of one input has a decreasing additional benefit (diminishing returns). The natural diminishing returns property which makes them suitable for many applications, including approximation algorithms, game theory (as functions modeling user preferences) and electrical networks. Recently, submodular functions have also found utility in several real world problems in machine learning and artificial intelligence, including automatic summarization, multi-document summarization, feature selection, active learning, sensor placement, image collection summarization and many other domains. Definition If \Omega is a finite set, a submodular function is a set function f:2^\rightarrow \mathbb, where 2^\Omega denotes the power set of \Omega, which satisfies one of the following equivalent conditions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greedy Algorithm For Egyptian Fractions
In mathematics, the greedy algorithm for Egyptian fractions is a greedy algorithm, first described by Fibonacci, for transforming rational numbers into Egyptian fractions. An Egyptian fraction is a representation of an irreducible fraction as a sum of distinct unit fractions, such as . As the name indicates, these representations have been used as long ago as ancient Egypt, but the first published systematic method for constructing such expansions was described in 1202 in the '' Liber Abaci'' of Leonardo of Pisa (Fibonacci). It is called a greedy algorithm because at each step the algorithm chooses greedily the largest possible unit fraction that can be used in any representation of the remaining fraction. Fibonacci actually lists several different methods for constructing Egyptian fraction representations. He includes the greedy method as a last resort for situations when several simpler methods fail; see Egyptian fraction for a more detailed listing of these methods. The gre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
