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Majority Judgment
Majority judgment (MJ) is a single-winner voting system proposed in 2010 by Michel Balinski and Rida Laraki. It is a kind of highest median rule, a cardinal voting system that elects the candidate with the highest median rating. Voting process Voters grade as many of the candidates as they wish with regard to their suitability for office according to a series of grades. Balinski and Laraki suggest the options "Excellent, Very Good, Good, Acceptable, Poor, or Reject," but any scale can be used (e.g. the common letter grade scale). Voters can assign the same grade to multiple candidates. As with all highest median voting rules, the candidate with the highest median grade is declared winner. If more than one candidate has the same median grade, majority judgment breaks the tie by removing (one-by-one) any grades equal to the shared median grade from each tied candidate's column. This procedure is repeated until only one of the tied candidates is found to have the highest median ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voting System
An electoral or voting system is a set of rules used to determine the results of an election. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, nonprofit organizations and informal organisations. These rules govern all aspects of the voting process: when elections occur, who is allowed to vote, who can stand as a candidate, how ballots are marked and cast, how the ballots are counted, how votes translate into the election outcome, limits on 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 minister, president or governor, while others elect multiple winners, such as members of parliament or boards of directors. When electing a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Later-no-harm
Later-no-harm is a property of some ranked-choice voting systems, first described by Douglas Woodall. In later-no-harm systems, increasing the rating or rank of a candidate ranked below the winner of an election cannot cause a higher-ranked candidate to lose. It is a common property in the plurality-rule family of voting systems. For example, say a group of voters ranks Alice 2nd and Bob 6th, and Alice wins the election. In the next election, Bob focuses on expanding his appeal with this group of voters, but does not manage to defeat Alice—Bob's rating increases from 6th-place to 3rd. Later-no-harm says that this increased support from Alice's voters should not allow Bob to win. Later-no-harm may be confused as implying center squeeze, since later-no-harm is a defining characteristic of first-preference plurality (FPP) and instant-runoff voting (IRV), and descending solid coalitions (DSC), systems that have similar mechanics that are based on first preference counting. These ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Neumann–Morgenstern Utility Theorem
In decision theory, the von Neumann–Morgenstern (VNM) utility theorem demonstrates that rational choice under uncertainty involves making decisions that take the form of maximizing the expected value of some cardinal utility function. The theorem forms the foundation of expected utility theory. In 1947, John von Neumann and Oskar Morgenstern proved that any individual whose preferences satisfied four axioms has a utility function, where such an individual's preferences can be represented on an interval scale and the individual will always prefer actions that maximize expected utility. Neumann, John von and Morgenstern, Oskar, '' Theory of Games and Economic Behavior''. Princeton, NJ. Princeton University Press, 1953. That is, they proved that an agent is (VNM-)rational ''if and only if'' there exists a real-valued function ''u'' defined by possible outcomes such that every preference of the agent is characterized by maximizing the expected value of ''u'', which can then be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedean Property
In abstract algebra and mathematical analysis, analysis, the Archimedean property, named after the ancient Greek mathematician Archimedes of Syracuse, Italy, Syracuse, is a property held by some algebraic structures, such as ordered or normed group (algebra), groups, and field (mathematics), fields. The property, as typically construed, states that given two positive numbers x and y, there is an integer n such that nx > y. It also means that the set of natural numbers is not bounded above. Roughly speaking, it is the property of having no ''infinitely large'' or ''infinitely small'' elements. It was Otto Stolz who gave the axiom of Archimedes its name because it appears as Axiom V of Archimedes’ ''On the Sphere and Cylinder''. The notion arose from the theory of magnitude (mathematics), magnitudes of ancient Greece; it still plays an important role in modern mathematics such as David Hilbert's Hilbert's axioms, axioms for geometry, and the theories of linearly ordered group, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous Function
In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function. This implies there are no abrupt changes in value, known as '' discontinuities''. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to sufficiently small changes of its argument. A discontinuous function is a function that is . Until the 19th century, mathematicians largely relied on intuitive notions of continuity and considered only continuous functions. The epsilon–delta definition of a limit was introduced to formalize the definition of continuity. Continuity is one of the core concepts of calculus and mathematical analysis, where arguments and values of functions are real and complex numbers. The concept has been generalized to functions between metric spaces and between topological spaces. The latter are the most general continuous functions, and their d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonic Function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysis In calculus, a function f defined on a subset of the real numbers with real values is called ''monotonic'' if it is either entirely non-decreasing, or entirely non-increasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is termed ''monotonically increasing'' (also ''increasing'' or ''non-decreasing'') if for all x and y such that x \leq y one has f\!\left(x\right) \leq f\!\left(y\right), so f preserves the order (see Figure 1). Likewise, a function is called ''monotonically decreasing'' (also ''decreasing'' or ''non-increasing'') if, whenever x \leq y, then f\!\left(x\right) \geq f\!\left(y\right), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Consistency Criterion
A voting system satisfies join-consistency (also called the reinforcement criterion) if combining two sets of votes, both electing ''A'' over ''B'', always results in a combined electorate that ranks ''A'' over ''B''. It is a stronger form of the participation criterion. Systems that fail the consistency criterion (such as instant-runoff voting or Condorcet method, Condorcet methods) are susceptible to the multiple-district paradox, a Pathological (mathematics), pathological behavior where a candidate can win an election without carrying even a single precinct. Conversely, it can be seen as allowing for a particularly egregious kind of gerrymander: it is possible to draw boundaries in such a way that a candidate who wins the overall election fails to carry even a single electoral district. Rules susceptible to the multiple-districts paradox include all Condorcet methods and Instant-runoff voting, instant-runoff (or ranked-choice) voting. Rules that are not susceptible to it includ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Positional Voting
Positional voting is a ranked voting electoral system in which the options or candidates receive points based on their rank position on each ballot and the one with the most points overall wins. The lower-ranked preference in any adjacent pair is generally of less value than the higher-ranked one. Although it may sometimes be weighted the same, it is never worth more. A valid progression of points or weightings may be chosen at will (Voting at the Eurovision Song Contest, Eurovision Song Contest) or it may form a mathematical sequence such as an arithmetic progression (Borda count), a geometric one (Positional notation, positional number system) or a harmonic one (Borda count#Dowdall system (Nauru), Nauru/Dowdall method). The set of weightings employed in an election heavily influences the rank ordering of the candidates. The steeper the initial decline in preference values with descending rank, the more polarised and less consensual the positional voting system becomes. Position ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
No Show Paradox
The participation criterion is a voting system criterion that says candidates should never lose an election as a result of receiving too many votes in support. More formally, it says that adding more voters who prefer ''Alice'' to ''Bob'' should not cause ''Alice'' to lose the election to ''Bob''. Voting systems that fail the participation criterion exhibit the no-show paradox, where a voter is effectively disenfranchised by the electoral system because turning out to vote could make the result worse for them; such voters are sometimes referred to as having negative vote weights, particularly in the context of German constitutional law, where courts have ruled such a possibility violates the principle of one man, one vote. Positional methods and score voting satisfy the participation criterion. All deterministic voting rules that satisfy pairwise majority-rule can fail in situations involving four-way cyclic ties, though such scenarios are empirically rare, and the randomized C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mutual Majority Criterion
The mutual majority criterion is a criterion for evaluating electoral systems. It is also known as the majority criterion for solid coalitions and the generalized majority criterion. This criterion requires that whenever a majority of voters prefer a group of candidates above all others, then the winner must be a candidate from that group. The mutual majority criterion may also be thought of as the single-winner case of Droop- Proportionality for Solid Coalitions. Formal definition Let L be a subset of candidates. A solid coalition in support of L is a group of voters who strictly prefer all members of L to all candidates outside of L. In other words, each member of the solid coalition ranks their least-favorite member of L higher than their favorite member outside L. Note that the members of the solid coalition may rank the members of L differently. The mutual majority criterion says that if there is a solid coalition of voters in support of L, and this solid coalition consist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Majority Favorite Criterion
The majority criterion is a voting system criterion applicable to voting rules over ordinal preferences required that if only one candidate is ranked first by over 50% of voters, that candidate must win. Some methods that comply with this criterion include any Condorcet method, instant-runoff voting, Bucklin voting, plurality voting, and approval voting. The mutual majority criterion is a generalized form of the criterion meant to account for when the majority prefers multiple candidates above all others; voting methods which pass majority but fail mutual majority can encourage all but one of the majority's preferred candidates to drop out in order to ensure one of the majority-preferred candidates wins, creating a spoiler effect. Difference from the Condorcet criterion By the majority criterion, a candidate ''C'' should win if a majority of voters answers affirmatively to the question "Do you (strictly) prefer ''C'' to every other candidate?" The Condorcet criterion gives a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
