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Black Electoral System
Black's method is an election method proposed by Duncan Black in 1958 as a compromise between the Condorcet method and the Borda count. This method selects a Condorcet winner. If a Condorcet winner does not exist, then the candidate with the highest Borda score is selected. Properties Among methods satisfying the majority criterion, Black's method gives the minimum power to the majority and hence the method is best at protecting minorities. Satisfied criteria Black's method satisfies the following criteria: * Unrestricted domain * Non-imposition ( a.k.a. citizen sovereignty) * Non-dictatorship * Homogeneity * Condorcet criterion * Majority criterion * Pareto criterion ( a.k.a. unanimity) * Monotonicity criterion * Majority loser criterion * Condorcet loser criterion * Reversal symmetry * Resolvability criterion * Polynomial time Failed criteria Black's method does not satisfy the following criteria: * Mutual majority criterion * Smith criterion * Participation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Election Method
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] |
Resolvability Criterion
A voting system is called decisive, resolvable, or resolute if it ensures a low probability of tied elections. There are two different criterion that formalize this. * In Nicolaus Tideman's version of the criterion, adding one extra vote (with no tied ranks) should make the winner unique. * Douglas R. Woodall's version requires that the probability of a tied vote under an impartial culture model gives a tie approaches zero as the number of voters increases toward infinity. A non-resolvable social choice function is often only considered to be a ''partial'' electoral method, sometimes called a voting correspondence or set-valued voting rule. Such methods frequently require tiebreakers that can substantially affect the result. However, non-resolute methods can be used as a first stage to eliminate candidates before ties are broken with some other method. Methods that have been used this way include the Copeland set, the Smith set, and the Landau set. References {{voting syst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonic Condorcet Methods
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), so it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Single-winner Electoral Systems
A single-member district or constituency is an electoral district represented by a single officeholder. It contrasts with a multi-member district, which is represented by multiple officeholders. In some countries, such as Australia and India, members of the lower house of parliament are elected from single-member districts, while members of the upper house are elected from multi-member districts. In some other countries, such as Singapore, members of parliament can be elected from either single-member or multi-member districts. History in the United States The United States Constitution, ratified in 1789, states: "The House of Representatives shall be composed of Members chosen every second Year by the People of the several States...Representatives...shall be apportioned among the several States which may be included within this Union, according to their respective Numbers." In other words, the Constitution specifies that each state will be apportioned a number of representat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sincere Favorite Criterion
The sincere favorite or no favorite-betrayal criterion is a voting system criterion, property of some voting systems that says voters should have no incentive to vote for someone else over their favorite.Alex Small, “Geometric construction of voting methods that protect voters’ first choices,” arXiv:1008.4331 (August 22, 2010), http://arxiv.org/abs/1008.4331. It protects voters from having to engage in lesser-evil voting or a strategy called "decapitation" (removing the "head" off a ballot). Most rated voting systems, including score voting, satisfy the criterion. Duverger's law says that systems vulnerable to this strategy will typically (though not always) develop Two-party system, two-party systems, as voters will abandon minor-party candidates to support stronger major-party candidates. US Presidential elections The "sincere favorite criterion" suggests that a voter should always rank their sincere favorite candidate as their top choice, without strategizing based ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Local Independence Of Irrelevant Alternatives
In social choice theory and politics, a spoiler effect happens when a losing candidate affects the results of an election simply by participating. Voting rules that are not affected by spoilers are said to be spoilerproof. The frequency and severity of spoiler effects depends substantially on the voting method. Instant-runoff voting (IRV), the two-round system (TRS), and especially first-past-the-post (FPP) without winnowing or primary elections are highly sensitive to spoilers (though IRV and TRS less so in some circumstances), and all three rules are affected by center-squeeze and vote splitting. Majority-rule (or Condorcet) methods are only rarely affected by spoilers, which are limited to rare situations called cyclic ties.. "This is a kind of stability property of Condorcet winners: you cannot dislodge a Condorcet winner ''A'' by adding a new candidate ''B'' to the election if A beats B in a head-to-head majority vote. For example, although the 2000 U.S. Presidential Ele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence Of Irrelevant Alternatives
Independence of irrelevant alternatives (IIA) is an axiom of decision theory which codifies the intuition that a choice between A and B (which are both related) should not depend on the quality of a third, unrelated outcome C. There are several different variations of this axiom, which are generally equivalent under mild conditions. As a result of its importance, the axiom has been independently rediscovered in various forms across a wide variety of fields, including economics, cognitive science, social choice, fair division, rational choice, artificial intelligence, probability, and game theory. It is closely tied to many of the most important theorems in these fields, including Arrow's impossibility theorem, the Balinski–Young theorem, and the money pump arguments. In behavioral economics, failures of IIA (caused by irrationality) are called menu effects or menu dependence. Motivation This is sometimes explained with a short story by philosopher Sidney Morgenbesser:Mor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence Of Clones Criterion
In social choice theory, the independence of (irrelevant) clones criterion says that adding a ''clone'', i.e. a new candidate very similar to an already-existing candidate, should not spoil the results. It can be considered a weak form of the independence of irrelevant alternatives (IIA) criterion that nevertheless is failed by a number of voting rules. A method that passes the criterion is said to be clone independent. A group of candidates are called clones if they are always ranked together, placed side-by-side, by every voter; no voter ranks any of the non-clone candidates between or equal to the clones. In other words, the process of ''cloning'' a candidate involves taking an existing candidate ''C'', then replacing them with several candidates ''C1'', ''C2..''. who are slotted into the original ballots in the spot where ''C'' previously was, with the clones being arranged in any order. If a set of clones contains at least two candidates, the criterion requires that deleti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence Of Smith-dominated Alternatives
Independence of Smith-dominated alternatives (ISDA, also known as Smith- IIA) is a voting system criterion which says that the winner of an election should not be affected by candidates who are not in the Smith set. Another way of defining ISDA is to say that adding a new candidate should not change the winner of an election, ''unless'' that new candidate would beat the original winner, either directly or indirectly. Complying methods Schulze and Ranked Pairs are independent of Smith-dominated alternatives. Any voting system can be forced to satisfy ISDA by first eliminating all candidates outside the Smith set, then running the full algorithm. Ambiguity Smith- IIA can sometimes be taken to mean independence of non-Smith ''irrelevant'' alternatives, i.e. that no ''losing'' candidate outside the Smith set can affect the result. This differs slightly from the above definition, in that methods passing independence of irrelevant alternatives (but not the Smith criterion) also sa ... [...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] |
Participation Criterion
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 random ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smith Criterion
The Smith set, sometimes called the top-cycle or Condorcet winning set, generalizes the idea of a Condorcet winner to cases where no such winner exists. It does so by allowing cycles of candidates to be treated jointly, as if they were a single Condorcet winner. Voting systems that always elect a candidate from the Smith set pass the Smith criterion. The Smith set and Smith criterion are both named for mathematician John H. Smith. The Smith set provides one standard of optimal choice for an election outcome. An alternative, stricter criterion is given by the Landau set. Definition The Smith set is formally defined as the smallest set such that every candidate inside the set ''S'' pairwise defeats every candidate outside ''S''. Alternatively, it can be defined as the set of all candidates with a (non-strict) beatpath to any candidate who defeats them. A set of candidates each of whose members pairwise defeats every candidate outside the set is known as a ''dominating set' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
