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Median Mechanism
A median mechanism is a voting rule that allows people to decide on a value in a one-dimensional domain. Each person votes by writing down his/her ideal value, and the rule selects a single value which is (in the basic mechanism) the ''median'' of all votes. The median mechanism can be used, for example, to decide on the size of the country's budget: each person says what the ideal budget size should be, and the chosen size is the median of the declared values. Another possible application is deciding how long the annual school vacation should be: each person says the ideal length in days, and the median is selected. A third example is: deciding what temperature the air-conditioner in an office should be set to. A fourth example is a facility location problem in one dimension. An important feature of the median mechanism is that it is ''truthful'': if the utility of each voter is higher whenever the chosen value is closer to his ideal value, then an optimal strategy for each voter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electoral System
An electoral system or voting system is a set of rules that determine how elections and Referendum, referendums are conducted and how their results are determined. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, Nonprofit organization, non-profit organisations and informal organisations. These rules govern all aspects of the voting process: when elections occur, suffrage, who is allowed to vote, who can stand as a candidate, voting method, how ballots are marked and cast, how the ballots are counted, how votes translate into the election outcome, limits on campaign finance, campaign spending, and other factors that can affect the result. Political electoral systems are defined by constitutions and electoral laws, are typically conducted by election commissions, and can use multiple types of elections for different offices. Some electoral systems elect a single winner to a unique position, such as prime ministe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Median
In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic feature of the median in describing data compared to the mean (often simply described as the "average") is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of a "typical" value. Median income, for example, may be a better way to suggest what a "typical" income is, because income distribution can be very skewed. The median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data are contaminated, the median is not an arbitrarily large or small result. Finite data set of numbers The median of a finite list of numbers is the "middle" number, when those numbers are list ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Facility Location Problem
The study of facility location problems (FLP), also known as location analysis, is a branch of operations research and computational geometry concerned with the optimal placement of facilities to minimize transportation costs while considering factors like avoiding placing hazardous materials near housing, and competitors' facilities. The techniques also apply to cluster analysis. Minimum facility location A simple facility location problem is the Weber problem, in which a single facility is to be placed, with the only optimization criterion being the minimization of the weighted sum of distances from a given set of point sites. More complex problems considered in this discipline include the placement of multiple facilities, constraints on the locations of facilities, and more complex optimization criteria. In a basic formulation, the facility location problem consists of a set of potential facility sites ''L'' where a facility can be opened, and a set of demand points ''D'' that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strategyproofness
In game theory, an asymmetric game where players have private information is said to be strategy-proof or strategyproof (SP) if it is a weakly-dominant strategy for every player to reveal his/her private information, i.e. given no information about what the others do, you fare best or at least not worse by being truthful. SP is also called truthful or dominant-strategy-incentive-compatible (DSIC), to distinguish it from other kinds of incentive compatibility. An SP game is not always immune to collusion, but its robust variants are; with group strategyproofness no group of people can collude to misreport their preferences in a way that makes every member better off, and with strong group strategyproofness no group of people can collude to misreport their preferences in a way that makes at least one member of the group better off without making any of the remaining members worse off. Examples Typical examples of SP mechanisms are majority voting between two alternatives, second- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Average
In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7, and 9 (summing to 25) is 5. Depending on the context, an average might be another statistic such as the median, or mode. For example, the average personal income is often given as the median—the number below which are 50% of personal incomes and above which are 50% of personal incomes—because the mean would be higher by including personal incomes from a few billionaires. For this reason, it is recommended to avoid using the word "average" when discussing measures of central tendency. General properties If all numbers in a list are the same number, then their average is also equal to this number. This property is shared by each of the many types of average. Another universal property is monotonicity: if two lists of numbers ''A'' and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Line
In elementary mathematics, a number line is a picture of a graduated straight line (geometry), line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point. The integers are often shown as specially-marked points evenly spaced on the line. Although the image only shows the integers from –3 to 3, the line includes all real numbers, continuing forever in each direction, and also numbers that are between the integers. It is often used as an aid in teaching simple addition and subtraction, especially involving negative numbers. In advanced mathematics, the number line can be called as a real line or real number line, formally defined as the set (mathematics), set of all real numbers, viewed as a geometry, geometric space (mathematics), space, namely the Euclidean space of dimension one. It can be thought of as a vector space (or affine space), a metric space, a topological ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Single Peaked Preferences
Single-peaked preferences are a class of preference relations. A group of agents is said to have single-peaked preferences over a set of possible outcomes if the outcomes can be ordered along a line such that: # Each agent has a "best outcome" in the set, and - # For each agent, outcomes that are further from his or her best outcome are preferred less. Single-peaked preferences are typical of one-dimensional domains. A typical example is when several consumers have to decide on the amount of public good to purchase. The amount is a one-dimensional variable. Usually, each consumer decides on a certain quantity which is best for him or her, and if the actual quantity is more/less than that ideal quantity, the agent is then less satisfied. With single-peaked preferences, there is a simple truthful mechanism for selecting an outcome: it is to select the median quantity. See the median voter theorem. It is truthful because the median function satisfies the strong monotonicity proper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anonymity (social Choice)
In social choice theory, Anonymity is a basic requirement of a social choice rule. It says that the rule does not discriminate apriori between different voters. In other words, the rule returns the same outcome (whatever this outcome may be) if the vector of votes is permuted arbitrarily.{{Cite book, last=Felix Brandt, chapter-url=https://books.google.com/books?id=0qY8DwAAQBAJ&dq=multiwinner++voting+a+new+challenge&pg=PA27, title=Trends in Computational Social Choice, date=2017-10-26, publisher=Lulu.com, isbn=978-1-326-91209-3, editor-last=Endriss, editor-first=Ulle, language=en, chapter=Roling the Dice: Recent Results in Probabilistic Social Choice Anonymous rules Most voting rules are anonymous by design. For example, plurality voting is anonymous, since only counts the number of votes received by each candidates, regardless of who cast these votes. Similarly, the utilitarian rule and egalitarian rule are both anonymous, since the only consider the set of utilities, regardless ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Strategyproof
In game theory, an asymmetric game where players have private information is said to be strategy-proof or strategyproof (SP) if it is a weakly-dominant strategy for every player to reveal his/her private information, i.e. given no information about what the others do, you fare best or at least not worse by being truthful. SP is also called truthful or dominant-strategy-incentive-compatible (DSIC), to distinguish it from other kinds of incentive compatibility. An SP game is not always immune to collusion, but its robust variants are; with group strategyproofness no group of people can collude to misreport their preferences in a way that makes every member better off, and with strong group strategyproofness no group of people can collude to misreport their preferences in a way that makes at least one member of the group better off without making any of the remaining members worse off. Examples Typical examples of SP mechanisms are majority voting between two alternatives, second ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pareto-efficient
Pareto efficiency or Pareto optimality is a situation where no action or allocation is available that makes one individual better off without making another worse off. The concept is named after Vilfredo Pareto (1848–1923), Italian civil engineer and economist, who used the concept in his studies of economic efficiency and income distribution. The following three concepts are closely related: * Given an initial situation, a Pareto improvement is a new situation where some agents will gain, and no agents will lose. * A situation is called Pareto-dominated if there exists a possible Pareto improvement. * A situation is called Pareto-optimal or Pareto-efficient if no change could lead to improved satisfaction for some agent without some other agent losing or, equivalently, if there is no scope for further Pareto improvement. The Pareto front (also called Pareto frontier or Pareto set) is the set of all Pareto-efficient situations. Pareto originally used the word "optimal" for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unanimity
Unanimity is agreement by all people in a given situation. Groups may consider unanimous decisions as a sign of social, political or procedural agreement, solidarity, and unity. Unanimity may be assumed explicitly after a unanimous vote or implicitly by a lack of objections. It does not necessarily mean uniformity and can sometimes be the opposite of majority in terms of outcomes. Voting Practice varies as to whether a vote can be considered unanimous if some voter abstains. In ''Robert's Rules of Order'', a "unanimous vote" is not specifically defined, although an abstention is not counted as a vote regardless of the voting threshold. Also in this book, action could be taken by "unanimous consent", or "general consent", if there are no objections raised. However, unanimous consent may not necessarily be the same as a unanimous vote (see Not the same as unanimous vote). In either case, it does not take into account the members who were not present. In contrast, a United Natio ... [...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] |
