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Baldwin Method
The Borda count electoral system can be combined with an instant-runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method (also called Total Vote Runoff or TVR). Both methods are designed to satisfy the Condorcet criterion, and allow for incomplete ballots and equal rankings. Nanson method The Nanson method is based on the original work of the mathematician Edward J. Nanson in 1882. Nanson's method eliminates those choices from a Borda count tally that are at or below the average Borda count score, then the ballots are retallied as if the remaining candidates were exclusively on the ballot. This process is repeated if necessary until a single winner remains. If a Condorcet winner exists, they will be elected. If not, (there is a Condorcet cycle) then the preference with the smallest majority will be eliminated. Nanson's method can be adapted to handle incomplete ballots (including " plumping") and equal rankings ("bracketing"), th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Borda Count
The Borda method or order of merit is a positional voting rule that gives each candidate a number of points equal to the number of candidates ranked below them: the lowest-ranked candidate gets 0 points, the second-lowest gets 1 point, and so on. The candidate with the most points wins. The Borda count has been independently reinvented several times, with the first recorded proposal in 1435 being by Nicholas of Cusa (see History below), but is named after the 18th-century French mathematician and naval engineer Jean-Charles de Borda, who re-devised the system in 1770. The Borda count is well-known in social choice theory both for its pleasant theoretical properties and its ease of manipulation. In the absence of strategic voting and strategic nomination, the Borda count tends to elect broadly-acceptable options or candidates (rather than consistently following the preferences of a majority); when both voting and nomination patterns are completely random, the Borda count gener ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonicity Criterion
Electoral system criteria In social choice, the negative response, perversity, or additional support paradox is a pathological behavior of some voting rules where a candidate loses as a result of having too much support (or wins because of increased opposition). In other words, increasing (decreasing) a candidate's ranking or rating causes that candidate to lose (win), respectively. Electoral systems that do not exhibit perversity are sometimes said to satisfy the monotonicity criterion.D R Woodall"Monotonicity and Single-Seat Election Rules" '' Voting matters'', Issue 6, 1996 Perversity is often described by social choice theorists as an exceptionally severe kind of electoral pathology, as such rules can have "backwards" responses to voters' opinions, where popularity causes defeat while unpopularity leads to a win. Similar rules treat the well-being of some voters as "less than worthless". These issues have led to constitutional prohibitions on such systems as violating ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anglican
Anglicanism, also known as Episcopalianism in some countries, is a Western Christianity, Western Christian tradition which developed from the practices, liturgy, and identity of the Church of England following the English Reformation, in the context of the Protestant Reformation in Europe. It is one of the largest branches of Christianity, with around 110 million adherents worldwide . Most are members of national or regional Ecclesiastical province#Anglican Communion, ecclesiastical provinces of the international Anglican Communion, one of the largest Christian bodies in the world, and the world's third-largest Christian communion. When united and uniting churches, united churches in the Anglican Communion and the breakaway Continuing Anglican movement were not counted, there were an estimated 97.4 million Anglicans worldwide in 2020. Adherents of Anglicanism are called ''Anglicans''; they are also called ''Episcopalians'' in some countries. The provinces within the Anglican ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marquette, Michigan
Marquette ( ) is the county seat of Marquette County, Michigan, Marquette County and the largest city in the Upper Peninsula of Michigan, United States. Located on the shores of Lake Superior, Marquette is a major port known primarily for shipping iron ore from the Marquette Iron Range. The city is partially surrounded by Marquette Township, Marquette County, Michigan, Marquette Township, but the two are administered autonomously. Marquette is named after Jacques Marquette, a French Jesuit missionary who had explored the Great Lakes region. Marquette had a population of 20,629 at the 2020 United States census, 2020 census, making it the largest city in Michigan north of the Tri-Cities (Michigan), Tri-Cities. Marquette is also the third-largest American city on Lake Superior, behind Duluth, Minnesota and Superior, Wisconsin. Marquette's urban area extends south toward the community of Harvey, Michigan, Harvey and west toward Negaunee, Michigan, Negaunee and Ishpeming, Michigan, Ish ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States
The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 contiguous states border Canada to the north and Mexico to the south, with the semi-exclave of Alaska in the northwest and the archipelago of Hawaii in the Pacific Ocean. The United States asserts sovereignty over five Territories of the United States, major island territories and United States Minor Outlying Islands, various uninhabited islands in Oceania and the Caribbean. It is a megadiverse country, with the world's List of countries and dependencies by area, third-largest land area and List of countries and dependencies by population, third-largest population, exceeding 340 million. Its three Metropolitan statistical areas by population, largest metropolitan areas are New York metropolitan area, New York, Greater Los Angeles, Los Angel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NP-completeness
In computational complexity theory, NP-complete problems are the hardest of the problems to which ''solutions'' can be verified ''quickly''. Somewhat more precisely, a problem is NP-complete when: # It is a decision problem, meaning that for any input to the problem, the output is either "yes" or "no". # When the answer is "yes", this can be demonstrated through the existence of a short (polynomial length) ''solution''. # The correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions. # The problem can be used to simulate every other problem for which we can verify quickly that a solution is correct. Hence, if we could find solutions of some NP-complete problem quickly, we could quickly find the solutions of every other problem to which a given solution can be easily verified. The name "NP-complete" is short for "nondeterministic polynomial-time complete". In this name, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Complexity
In theoretical 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 gene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reversal Symmetry
The reversal symmetry criterion is a voting system criterion which says that if every voter's opinions on each of the candidates is perfectly reversed (i.e. they rank candidates in order from worst to best), the outcome of the election should be reversed as well, i.e. the first- and last-place finishers should switch places. In other words, the results of the election should not depend arbitrarily on whether voters rank candidates from best to worst (and then select the best candidate), or whether we ask them to rank candidates from worst to best (and then select the least-bad candidate). Another, equivalent way to motivate the criterion is to say that a voting system should never elect the worst candidate, according to the method itself (as doing so suggests the method is, in some sense, self-contradictory). The worst candidate can be identified by reversing all ballots (to rank candidates from worst-to-best) and then running the algorithm to find a single worst candidate. Sit ... [...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] |
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 with the Condorcet loser criterion will never allow a ''Condorcet loser'' to win. A Condorcet loser is a candidate who can be defeated in a head-to-head competition against each other candidate.https://arxiv.org/pdf/1801.05911 "We say that an alternative is a Condorcet loser if it would be defeated by every other alternative in a kind of one-on-one contest that takes place in a sequential pairwise voting with a fixed agenda4.– Condorcet loser criterion (CLC), ..we say that a social choice procedure satisfies the Condorcet loser criterion (CLC) provided that a Condorcet loser is never among the social choices." (Not all elections will have a Condorcet loser since it is possible for three or more candidates to be mutually defeatable in di ... [...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] |
