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Later-no-help Criterion
The later-no-help criterion (or LNHe, not to be confused with LNH) is a voting system criterion formulated by Douglas Woodall. The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less-preferred candidate can not cause a more-preferred candidate to win. Voting systems that fail the later-no-help criterion are vulnerable to the tactical voting strategy called mischief voting, which can deny victory to a sincere Condorcet winner. Complying methods Approval, instant-runoff, highest medians, and score all satisfy the later-no-help criterion. Plurality voting satisfies it trivially (as plurality only applies to the top-ranked candidate). Descending Solid Coalitions also satisfies later-no-help. Noncomplying methods All Minimax Condorcet methods, Ranked Pairs, Schulze method, Kemeny-Young method, Copeland's method, and Nanson's method do not satisfy later-no-help. The Condorcet criterion is incompatible with later-n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Later-no-harm Criterion
Later-no-harm is a property of some Ranked voting, ranked-choice voting systems, first described by Douglas Woodall. In later-no-harm systems, increasing the rating or rank of a candidate ranked below the winner of an election cannot cause a higher-ranked candidate to lose. It is a common property in the plurality-rule family of voting systems. For example, say a group of voters ranks Alice 2nd and Bob 6th, and Alice wins the election. In the next election, Bob focuses on expanding his appeal with this group of voters, but does not manage to defeat Alice—Bob's rating increases from 6th-place to 3rd. Later-no-harm says that this increased support from Alice's voters should not allow Bob to win. Later-no-harm may be confused as implying center squeeze, since later-no-harm is a defining characteristic of Plurality voting, first-preference plurality (FPP) and Instant-runoff voting, instant-runoff voting (IRV), and descending solid coalitions (DSC), systems that have similar mechani ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triviality (mathematics)
In mathematics, the adjective trivial is often used to refer to a claim or a case which can be readily obtained from context, or a particularly simple object possessing a given structure (e.g., group (mathematics), group, topological space). The noun triviality usually refers to a simple technical aspect of some proof or definition. The origin of the term in mathematical language comes from the medieval Trivium (education), trivium curriculum, which distinguishes from the more difficult quadrivium curriculum. The opposite of trivial is nontrivial, which is commonly used to indicate that an example or a solution is not simple, or that a statement or a theorem is not easy to prove. Triviality does not have a rigorous definition in mathematics. It is Subjectivity and objectivity (philosophy), subjective, and often determined in a given situation by the knowledge and experience of those considering the case. Trivial and nontrivial solutions In mathematics, the term "trivial" is ofte ... [...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] |
Nanson's 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") ... [...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] |
Schulze Method
Articles with example pseudocode Debian Electoral systems Monotonic Condorcet methods Single-winner electoral systems The Schulze method (), also known as the beatpath method, is a single winner ranked-choice voting rule developed by Markus Schulze. The Schulze method is a Condorcet completion method, which means it will elect a majority-preferred candidate if one exists. In other words, if most people rank ''A'' above ''B'', ''A'' will defeat ''B'' (whenever this is possible). Schulze's method breaks cyclic ties by using indirect victories. The idea is that if Alice beats Bob, and Bob beats Charlie, then Alice (indirectly) beats Charlie; this kind of indirect win is called a "beatpath". For proportional representation, a single transferable vote (STV) variant known as Schulze STV also exists. The Schulze method is used by several organizations including Debian, Ubuntu, Gentoo, Pirate Party political parties and many others. It was also used by Wikimedia prior to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimax Condorcet
In voting systems, the Minimax Condorcet method is a single-winner ranked-choice voting method that always elects the majority (Condorcet) winner. Minimax compares all candidates against each other in a round-robin tournament, then ranks candidates by their worst election result (the result where they would receive the fewest votes). The candidate with the ''largest'' (maximum) number of votes in their ''worst'' (minimum) matchup is declared the winner. Description of the method The Minimax Condorcet method selects the candidate for whom the greatest pairwise score for another candidate against him or her is the least such score among all candidates. Football analogy Imagine politicians compete like football teams in a round-robin tournament, where every team plays against every other team once. In each matchup, a candidate's score is equal to the number of voters who support them over their opponent. Minimax finds each team's (or candidate's) worst game – the one wher ... [...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] |
Voting System
An electoral or voting system is a set of rules used to determine the results of an election. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, nonprofit organizations 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 members of parliament or boards of directors. When electing a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Range Voting
Score voting, sometimes called range voting, is an electoral system for single-seat elections. Voters give each candidate a numerical score, and the candidate with the highest average score is elected. Score voting includes the well-known approval voting (used to calculate approval ratings), but also lets voters give partial (in-between) approval ratings to candidates. Usage Political use Historical A crude form of score voting was used in some elections in ancient Sparta, by measuring how loudly the crowd shouted for different candidates. This has a modern-day analog of using clapometers in some television shows and the judging processes of some athletic competitions. Beginning in the 13th century, the Republic of Venice elected the Doge of Venice using a multi-stage process with multiple rounds of score voting. This may have contributed to the Republic's longevity, being partly responsible for its status as the longest-lived democracy in world history. Score voting w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
