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Kemeny–Young Method
The Kemeny–Young method is an electoral system that uses preferential ballots and pairwise comparison counts to identify the most popular choices in an election. It is a Condorcet method because if there is a Condorcet winner, it will always be ranked as the most popular choice. This method assigns a score for each possible sequence, where each sequence considers which choice might be most popular, which choice might be second-most popular, which choice might be third-most popular, and so on down to which choice might be least-popular. The sequence that has the highest score is the winning sequence, and the first choice in the winning sequence is the most popular choice. (As explained below, ties can occur at any ranking level.) The Kemeny–Young method is also known as the Kemeny rule, VoteFair popularity ranking, the maximum likelihood method, and the median relation. Description The Kemeny–Young method uses preferential ballots on which voters rank choices according t ... [...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] |
Monotonicity Criterion
The monotonicity criterion is a voting system criterion used to evaluate both single and multiple winner ranked voting systems. A ranked voting system is monotonic if it is neither possible to prevent the election of a candidate by ranking them higher on some of the ballots, nor possible to elect an otherwise unelected candidate by ranking them lower on some of the ballots (while nothing else is altered on any ballot).D R Woodall"Monotonicity and Single-Seat Election Rules" ''Voting matters'', Issue 6, 1996 That is to say, in single winner elections no winner is harmed by up-ranking and no loser is helped by down-ranking. Douglas Woodall called the criterion mono-raise. Raising a candidate on some ballots ''while changing'' the orders of other candidates does ''not'' constitute a failure of monotonicity. E.g., harming candidate by changing some ballots from to would violate the monotonicity criterion, while harming candidate by changing some ballots from to would not. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial Time
In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor. Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is generally expresse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schwartz Set
In voting systems, the Schwartz set is the union of all Schwartz set components. A Schwartz set component is any non-empty set ''S'' of candidates such that # Every candidate inside the set ''S'' is pairwise unbeaten by every candidate outside ''S''; and # No non-empty proper subset of ''S'' fulfills the first property. A set of candidates that meets the first requirement is also known as an undominated set. The Schwartz set provides one standard of optimal choice for an election outcome. Voting systems that always elect a candidate from the Schwartz set pass the Schwartz criterion. The Schwartz set is named for political scientist Thomas Schwartz. Properties *The Schwartz set is always non-empty—there is always at least one Schwartz set component. *Any two distinct Schwartz set components are disjoint. *If there is a Condorcet winner, it is the only member of the Schwartz set. If there is only one member in the Schwartz set, it is at least a weak Condorcet winner. *If a Schw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tactical Voting
Strategic voting, also called tactical voting, sophisticated voting or insincere voting, occurs in voting systems when a voter votes for another candidate or party than their ''sincere preference'' to prevent an undesirable outcome. For example, in a simple plurality election, a voter might gain a better outcome by voting for a less preferred but more generally popular candidate. Gibbard's theorem shows that ''all'' single-winner voting methods are susceptible to strategic voting, unless there are only two options or ''dictatorial'' (i.e., a distinguished agent exists who can impose the outcome). For multi-winner elections no general theorem for strategic voting exists. Strategic voting is observed due to non-proportionality, electoral thresholds and quotas. Types of strategic voting ; (sometimes "useful vote"): A voter insincerely ranks an alternative higher in the hope of getting that candidate elected. For example, in the first-past-the-post election, voters may vote for ... [...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] |
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] |
Later-no-harm Criterion
The later-no-harm criterion is a voting system criterion formulated by Douglas Woodall. Woodall defined the criterion as " ding a later preference to a ballot should not harm any candidate already listed." For example, a ranked voting method in which a voter adding a 3rd preference could reduce the likelihood of their 1st preference being selected, fails later-no-harm. Voting systems that fail the later-no-harm criterion are vulnerable to the tactical voting strategies called bullet voting and burying, which can deny victory to a sincere Condorcet winner. However, the fact that all cardinal voting methods fail the later-no-harm criterion is essential to their favoring consensus options (broad, moderate support) over majoritarian options (narrow, strong support). Complying methods Two-round system, Single transferable vote, Instant Runoff Voting, Contingent vote, Minimax Condorcet (a pairwise opposition variant which does not satisfy the Condorcet Criterion), and Descending S ... [...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] |
Tactical Voting
Strategic voting, also called tactical voting, sophisticated voting or insincere voting, occurs in voting systems when a voter votes for another candidate or party than their ''sincere preference'' to prevent an undesirable outcome. For example, in a simple plurality election, a voter might gain a better outcome by voting for a less preferred but more generally popular candidate. Gibbard's theorem shows that ''all'' single-winner voting methods are susceptible to strategic voting, unless there are only two options or ''dictatorial'' (i.e., a distinguished agent exists who can impose the outcome). For multi-winner elections no general theorem for strategic voting exists. Strategic voting is observed due to non-proportionality, electoral thresholds and quotas. Types of strategic voting ; (sometimes "useful vote"): A voter insincerely ranks an alternative higher in the hope of getting that candidate elected. For example, in the first-past-the-post election, voters may vote for ... [...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] |
Reversal Symmetry
Reversal symmetry is a voting system criterion which requires that if candidate A is the unique winner, and each voter's individual preferences are inverted, then A must not be elected. Methods that satisfy reversal symmetry include Borda count, ranked pairs, Kemeny-Young method, and Schulze method. Methods that fail include Bucklin voting, instant-runoff voting and Condorcet methods that fail the Condorcet loser criterion In single-winner voting system theory, the Condorcet loser criterion (CLC) is a measure for differentiating voting systems. It implies the majority loser criterion but does not imply the Condorcet winner criterion. A voting system complying wi ... such as Minimax. For cardinal voting systems which can be meaningfully reversed, approval voting and range voting satisfy the criterion. Examples Instant-runoff voting Consider a preferential system where 11 voters express their preferences as: *5 voters prefer A then B then C *4 voters prefer B then C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
