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Sequential Elimination Method
The sequential elimination methods are a class of voting systems that repeatedly eliminate the last-place finisher of another voting method until a single candidate remains. The method used to determine the loser is called the ''base method''. Common are the two-round system, instant-runoff voting, and some primary systems. Instant-runoff voting is a sequential loser method based on plurality voting, while Baldwin's method is a sequential loser method based on the Borda count. Properties Proofs of criterion compliance for loser-elimination methods often use mathematical induction, and so can be easier than proving such compliance for other method types. For instance, if the base method passes the majority criterion, a sequential loser-elimination method based on it will pass mutual majority. Loser-elimination methods are also not much harder to explain than their base methods. However, loser-elimination methods often fail monotonicity due to chaotic effects (sensitivity to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequential Loser Method
The sequential elimination methods are a class of Voting system, voting systems that repeatedly eliminate the last-place finisher of another voting method until a single candidate remains. The method used to determine the loser is called the ''base method''. Common are the two-round system, instant-runoff voting, and some Primary election, primary systems. Instant-runoff voting is a sequential loser method based on plurality voting, while Baldwin method, Baldwin's method is a sequential loser method based on the Borda count. Properties Proofs of criterion compliance for loser-elimination methods often use mathematical induction, and so can be easier than proving such compliance for other method types. For instance, if the base method passes the majority criterion, a sequential loser-elimination method based on it will pass mutual majority. Loser-elimination methods are also not much harder to explain than their base methods. However, loser-elimination methods often fail monot ... [...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] |
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] |
Condorcet Criterion
A Condorcet winner (, ) is a candidate who would receive the support of more than half of the electorate in a one-on-one race against any one of their opponents. Voting systems where a majority winner will always win are said to satisfy the Condorcet winner criterion. The Condorcet winner criterion extends the principle of majority rule to elections with multiple candidates. Named after Nicolas de Condorcet, it is also called a majority winner, a majority-preferred candidate, a beats-all winner, or tournament winner (by analogy with round-robin tournaments). A Condorcet winner may not necessarily always exist in a given electorate: it is possible to have a rock, paper, scissors-style cycle, when multiple candidates defeat each other (Rock < Paper < Scissors < Rock). This is called , and is analogous to the counterintuitive [...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] |
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] |
Chaos Theory
Chaos theory is an interdisciplinary area of Scientific method, scientific study and branch of mathematics. It focuses on underlying patterns and Deterministic system, deterministic Scientific law, laws of dynamical systems that are highly sensitive to initial conditions. These were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause or prevent a tornado in Texas. Text was copied from this source, which is avai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Induction
Mathematical induction is a method for mathematical proof, proving that a statement P(n) is true for every natural number n, that is, that the infinitely many cases P(0), P(1), P(2), P(3), \dots all hold. This is done by first proving a simple case, then also showing that if we assume the claim is true for a given case, then the next case is also true. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder: A proof by induction consists of two cases. The first, the base case, proves the statement for n = 0 without assuming any knowledge of other cases. The second case, the induction step, proves that ''if'' the statement holds for any given case n = k, ''then'' it must also hold for the next case n = k + 1. These two steps establish that the statement holds for every natural number n. The base case does not necessarily begin with n = 0, but often with n = 1, and possibly with any fixed natural number n = N, establishing the trut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Sequential Loser Elimination Method
The sequential elimination methods are a class of voting systems that repeatedly eliminate the last-place finisher of another voting method until a single candidate remains. The method used to determine the loser is called the ''base method''. Common are the two-round system, instant-runoff voting, and some primary systems. Instant-runoff voting is a sequential loser method based on plurality voting, while Baldwin's method is a sequential loser method based on the Borda count. Properties Proofs of criterion compliance for loser-elimination methods often use mathematical induction, and so can be easier than proving such compliance for other method types. For instance, if the base method passes the majority criterion, a sequential loser-elimination method based on it will pass mutual majority. Loser-elimination methods are also not much harder to explain than their base methods. However, loser-elimination methods often fail monotonicity due to chaotic effects (sensitivity to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plurality Voting
Plurality voting refers to electoral systems in which the candidates in an electoral district who poll more than any other (that is, receive a plurality) are elected. Under single-winner plurality voting, and in systems based on single-member districts, plurality voting is called single member istrictplurality (SMP), which is widely known as " first-past-the-post". In SMP/FPTP the leading candidate, whether or not they have a majority of votes, is elected. There are several versions of plurality voting for multi-member district. The system that elects multiple winners at once with the plurality rule and where each voter casts as many X votes as the number of seats in a multi-seat district is referred to as plurality block voting. A semi-proportional system that elects multiple winners elected at once with the plurality rule and where each voter casts more than one vote but fewer than the number of seats to fill in a multi-seat district is known as limited voting. A semi-prop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Instant-runoff Voting
Instant-runoff voting (IRV; ranked-choice voting (RCV), preferential voting, alternative vote) is a single-winner ranked voting election system where Sequential loser method, one or more eliminations are used to simulate Runoff (election), runoff elections. When no candidate has a majority of the votes in the first round of counting, each following round eliminates the candidate with the fewest First-preference votes, first-preferences (among the remaining candidates) and transfers their votes if possible. This continues until one candidate accumulates a majority of the votes still in play. Instant-runoff voting falls under the plurality-based voting-rule family, in that under certain conditions the candidate with the least votes is eliminated, making use of secondary rankings as contingency votes. Thus it is related to the Runoff election, two-round runoff system and the exhaustive ballot. IRV could also be seen as a single-winner equivalent of Single transferable vote, sin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
