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Black's Method
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 * Arrow's impossibility theorem, Non-imposition (Aka (initialism), a.k.a. Arrow's impossibility theorem, citizen sovereignty) * Non-dictatorship * Homogeneity criterion, Homogeneity * Condorcet criterion * Majority criterion * Arrow's impossibility theorem, Pareto criterion (Aka (initialism), a.k.a. Arrow's impossibility theorem, unanimity) * Monotonicity criterion * Majority loser criterion * Condorcet loser criterion * Reversal symmetry * Resolv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Election Method
An electoral system or voting system is a set of rules that determine how elections and 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, non-profit organisations 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 membe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resolvability Criterion
Resolvability criterion can refer to any voting system criterion that ensures a low possibility of tie votes. * In Nicolaus Tideman's version of the criterion, for every (possibly tied) winner in a result, there must exist a way for one added vote to make that winner unique. * Douglas R. Woodall's version requires that the proportion of profiles giving a tie approaches zero as the number of voters increases toward infinity. Methods that satisfy both versions include approval voting, range voting, Borda count, instant-runoff voting, minimax Condorcet, plurality, Tideman's ranked pairs, and Schulze. Methods that violate both versions include Copeland's method Copeland's method is a ranked voting method based on a scoring system of pairwise "wins", "losses", and "ties". The method has a long history: * Ramon Llull described the system in 1299, so it is sometimes referred to as "Llull's method" * The ... and the Slater rule. References {{voting systems Electoral system c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonic Condorcet Methods
In mathematics, a monotonic function (or monotone function) is a function (mathematics), function between List of order structures in mathematics, ordered sets that preserves or reverses the given order relation, 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 and only if it is either entirely non-increasing, or entirely non-decreasing. 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 called ''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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Single-winner Electoral Systems
A single-member district is an electoral district represented by a single officeholder. It contrasts with a multi-member district, which is represented by multiple officeholders. Single-member districts are also sometimes called single-winner voting, winner-takes-all, or single-member constituencies. A number of electoral systems use single-member districts, including plurality voting (first-past-the-post), two-round systems, instant-runoff voting (IRV), approval voting, range voting, Borda count, and Condorcet methods (such as the Minimax Condorcet, Schulze method, and Ranked Pairs). Of these, plurality and runoff voting are the most common. In some countries, such as Australia and India, members of the lower house of parliament are elected from single-member districts; and members of the upper house are elected from multi-member districts. In some other countries like Singapore, members of parliament can be elected from both single-member districts as well as multi-member dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Local Independence Of Irrelevant Alternatives
The independence of irrelevant alternatives (IIA), also known as binary independence or the independence axiom, is an axiom of decision theory and various social sciences. The term is used in different connotation in several contexts. Although it always attempts to provide an account of rational individual behavior or aggregation of individual preferences, the exact formulation differs widely in both language and exact content. Perhaps the easiest way to understand the axiom is how it pertains to casting a ballot. There the axiom says that if Charlie (the irrelevant alternative) enters a race between Alice and Bob, with Alice (leader) liked better than Bob (runner-up), then the individual voter who likes Charlie less than Alice will not switch his vote from Alice to Bob. Because of this, a violation of IIA is commonly referred to as the "spoiler effect": support for Charlie "spoils" the election for Alice, while it "logically" should not have. After all, Alice ''was'' liked better t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peyton Young
Hobart Peyton Young (born March 9, 1945) is an American game theorist and economist known for his contributions to evolutionary game theory and its application to the study of institutional and technological change, as well as the theory of learning in games. He is currently centennial professor at the London School of Economics, James Meade Professor of Economics Emeritus at the University of Oxford, professorial fellow at Nuffield College Oxford, and research principal at the Office of Financial Research at the U.S. Department of the Treasury. Peyton Young was named a fellow of the Econometric Society in 1995, a fellow of the British Academy in 2007, and a fellow of the American Academy of Arts and Sciences in 2018. He served as president of the Game Theory Society from 2006–08. He has published widely on learning in games, the evolution of social norms and institutions, cooperative game theory, bargaining and negotiation, taxation and cost allocation, political representati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence Of Irrelevant Alternatives
The independence of irrelevant alternatives (IIA), also known as binary independence or the independence axiom, is an axiom of decision theory and various social sciences. The term is used in different connotation in several contexts. Although it always attempts to provide an account of rational individual behavior or aggregation of individual preferences, the exact formulation differs widely in both language and exact content. Perhaps the easiest way to understand the axiom is how it pertains to casting a ballot. There the axiom says that if Charlie (the irrelevant alternative) enters a race between Alice and Bob, with Alice (leader) liked better than Bob (runner-up), then the individual voter who likes Charlie less than Alice will not switch his vote from Alice to Bob. Because of this, a violation of IIA is commonly referred to as the "spoiler effect": support for Charlie "spoils" the election for Alice, while it "logically" should not have. After all, Alice ''was'' liked better t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence Of Clones Criterion
In voting systems theory, the independence of clones criterion measures an election method's robustness to strategic nomination. Nicolaus Tideman was the first to formulate this criterion, which states that the winner must not change due to the addition of a non-winning candidate who is similar to a candidate already present. To be more precise, a subset of the candidates, called a set of clones, exists if no voter ranks any candidate outside the set between (or equal to) any candidates that are in the set. If a set of clones contains at least two candidates, the criterion requires that deleting one of the clones must not increase or decrease the winning chance of any candidate not in the set of clones. In some systems (such as the plurality vote), the addition of a similar candidate divides support between similar candidates, which can cause them both to lose. In some other systems (such as the Borda count), the addition of a similar alternative increases the apparent support fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence Of Smith-dominated Alternatives
Independence of Smith-dominated alternatives (ISDA, also known as Smith-IIA or Weak independence of irrelevant alternatives) is a voting system criterion defined such that its satisfaction by a voting system occurs when the selection of the winner is independent of candidates who are not within the Smith set. A simple way to describe it is that if a voting system is ISDA, then whenever you can partition the candidates into group ''A'' and group ''B'' such that each candidate in group ''A'' is preferred over each candidate in group ''B'', you can eliminate all candidates of group ''B'' without changing the outcome of the election. Any election method that is independent of Smith-dominated alternatives automatically satisfies the Smith criterion (because all candidates not in the Smith set can be eliminated without changing the result, implying that the winner was someone in the Smith set), and all criteria implied by it, notably the Condorcet criterion and the mutual majority crit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Consistency Criterion
A voting system is consistent if, whenever the electorate is divided (arbitrarily) into several parts and elections in those parts garner the same result, then an election of the entire electorate also garners that result. Smith calls this property separability and Woodall calls it convexity. It has been proven a ranked voting system is "consistent if and only if it is a scoring function", i.e. a positional voting system. Borda count is an example of this. The failure of the consistency criterion can be seen as an example of Simpson's paradox Simpson's paradox is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combined. This result is often encountered in social-science and medical-science st .... As shown below under Kemeny-Young, passing or failing the consistency criterion can depend on whether the election selects a single winner or a full ranking of the candidates (sometimes refe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Participation Criterion
The participation criterion is a voting system criterion. Voting systems that fail the participation criterion are said to exhibit the no show paradox and allow a particularly unusual strategy of tactical voting: abstaining from an election can help a voter's preferred choice win. The criterion has been defined as follows: * In a deterministic framework, the participation criterion says that the addition of a ballot, where candidate A is strictly preferred to candidate B, to an existing tally of votes should not change the winner from candidate A to candidate B. * In a probabilistic framework, the participation criterion says that the addition of a ballot, where each candidate of the set X is strictly preferred to each other candidate, to an existing tally of votes should not reduce the probability that the winner is chosen from the set X. Plurality voting, approval voting, range voting, and the Borda count all satisfy the participation criterion. All Condorcet methods, Bucklin vo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smith Criterion
The Smith criterion (sometimes generalized Condorcet criterion, but this can have other meanings) is a voting systems criterion defined such that it's satisfied when a voting system always elects a candidate that is in the Smith set, which is the smallest non-empty subset of the candidates such that every candidate in the subset is majority-preferred over every candidate not in the subset. (A candidate X is said to be majority-preferred over another candidate Y if, in a one-on-one competition between X & Y, the number of voters who prefer X over Y exceeds the number of voters who prefer Y over X.) The Smith set is named for mathematician John H Smith, whose version of the Condorcet criterion is actually stronger than that defined above for social welfare functions. Benjamin Ward was probably the first to write about this set, which he called the "majority set". The Smith set is also called the ''top cycle''. The term ''top cycle'' may be somewhat misleading, however, since th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
