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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] |
Nicolaus Tideman
Thorwald Nicolaus Tideman (, not ; born August 11, 1943, in Chicago, Illinois) is a Georgist economist and professor at Virginia Tech. He received his Bachelor of Arts in economics and mathematics from Reed College in 1965 and his PhD in economics from the University of Chicago in 1969. Tideman was an assistant professor of economics at Harvard University from 1969 to 1973, during which time from 1970 to 1971 he was a Senior Staff Economist for the President's Council of Economic Advisors. Since 1973, he has been at Virginia Tech, with various visiting positions at Harvard Kennedy School (1979–1980), University of Buckingham (1985–1986), and the American Institute for Economic Research (1999–2000). Research Tideman's academic interests include taxation of land, voting theory, and political philosophy. Ranked Pairs In 1987, he devised the voting system called " ranked pairs" (or the "Tideman method" or simply "RP"), which is a type of Condorcet method. It selects a sin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Douglas R
Douglas may refer to: People * Douglas (given name) * Douglas (surname) Animals * Douglas (parrot), macaw that starred as the parrot ''Rosalinda'' in Pippi Longstocking * Douglas the camel, a camel in the Confederate Army in the American Civil War Businesses * Douglas Aircraft Company * Douglas (cosmetics), German cosmetics retail chain in Europe * Douglas Holding, former German company * Douglas (motorcycles), British motorcycle manufacturer Peerage and Baronetage * Duke of Douglas * Earl of Douglas, or any holder of the title * Marquess of Douglas, or any holder of the title * Douglas baronets Peoples * Clan Douglas, a Scottish kindred * Dougla people, West Indians of both African and East Indian heritage Places Australia * Douglas, Queensland, a suburb of Townsville * Douglas, Queensland (Toowoomba Region), a locality * Port Douglas, North Queensland, Australia * Shire of Douglas, in northern Queensland Canada * Douglas, New Brunswick * Douglas Parish, New ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Impartial Culture
Impartial culture (IC) or the culture of indifference is a probabilistic model used in social choice theory for analyzing ranked voting method rules. The model is understood to be unrealistic, and not a good representation of real-world voting behavior, however, it is useful for mathematical comparisons of voting methods under reproducible, worst-case scenarios. The model assumes that each voter provides a complete strict ranking of all the candidates (with no equal rankings or blanks), which is drawn from a set of all possible rankings. For m candidates, there are m! possible strict rankings (permutation In mathematics, a permutation of a set can mean one of two different things: * an arrangement of its members in a sequence or linear order, or * the act or process of changing the linear order of an ordered set. An example of the first mean ...s). There are three variations of the model that use different subsets of the full set of possible rankings, so that different ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Copeland's Method
The Copeland or Llull method is a ranked-choice voting system based on counting each candidate's pairwise wins and losses. In the system, voters rank candidates from best to worst on their ballot. Candidates then compete in a round-robin tournament, where the ballots are used to determine which candidate would be preferred by a majority of voters in each matchup. The candidate is the one who wins the most matchups (with ties winning half a point). Copeland's method falls in the class of Condorcet methods, as any candidate who wins every one-on-one election will clearly have the most victories overall. Copeland's method has the advantage of being likely the simplest Condorcet method to explain and of being easy to administer by hand. On the other hand, if there is no Condorcet winner, the procedure frequently results in ties. As a result, it is typically only used for low-stakes elections. History Copeland's method was devised by Ramon Llull in his 1299 treatise ''Ars Electio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smith Set
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] |
Landau Set
In the study of electoral systems, the uncovered set (also called the Landau set or the Fishburn set) is a set of candidates that generalizes the notion of a Condorcet winner whenever there is a Condorcet paradox. The Landau set can be thought of as the Pareto frontier for a set of candidates, when the frontier is determined by pairwise victories. The Landau set is a nonempty subset of the Smith set 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 C .... It was first discovered by Nicholas Miller. Definition The Landau set consists of all ''undominated'' or ''uncovered'' candidates''.'' One candidate (the ''Fishburn winner'') covers another (the ''Fishburn loser'') if they would win any matchup the Fishburn loser would win. Thus, the Fishburn winner has all the pairwise victories of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
