Approval voting is an electoral system in which voters can select many candidates instead of selecting only one candidate.
A Condorcet method is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, that is, a candidate preferred by more voters than any others, whenever there is such a candidate. A candidate with this property, the pairwise champion or beats-all winner, is formally called the Condorcet winner. The head-to-head elections need not be done separately; a voter's choice within any given pair can be determined from the ranking.
Copeland's method is a ranked voting method based on a scoring system of pairwise "wins", "losses", and "ties". The method has a long history:
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.
Bucklin voting is a class of voting methods that can be used for single-member and multi-member districts. As in highest median rules like the majority judgment, the Bucklin winner will be one of the candidates with the highest median ranking or rating. It is named after its original promoter, the Georgist politician James W. Bucklin of Grand Junction, Colorado, and is also known as the Grand Junction system.
Ranked pairs (RP) or the Tideman method is an electoral system developed in 1987 by Nicolaus Tideman that selects a single winner using votes that express preferences. RP can also be used to create a sorted list of winners.
An electoral system satisfies the Condorcet winner criterion if it always chooses the Condorcet winner when one exists. The candidate who wins a majority of the vote in every head-to-head election against each of the other candidates – that is, a candidate preferred by more voters than any others – is the Condorcet winner, although Condorcet winners do not exist in all cases. It is sometimes simply referred to as the "Condorcet criterion", though it is very different from the "Condorcet loser criterion". Any voting method conforming to the Condorcet winner criterion is known as a Condorcet method. The Condorcet winner is the person who would win a two-candidate election against each of the other candidates in a plurality vote. For a set of candidates, the Condorcet winner is always the same regardless of the voting system in question, and can be discovered by using pairwise counting on voters' ranked preferences.
The Smith criterion is a voting systems criterion defined such that it's satisfied when a voting system always elects a candidate that is in the Smith set, which is the smallest non-empty subset of the candidates such that every candidate in the subset is majority-preferred over every candidate not in the subset. The Smith set is named for mathematician John H Smith, whose version of the Condorcet criterion is actually stronger than that defined above for social welfare functions. Benjamin Ward was probably the first to write about this set, which he called the "majority set".
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:
The majority criterion is a single-winner voting system criterion, used to compare such systems. The criterion states that "if one candidate is ranked first by a majority of voters, then that candidate must win".
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.
The mutual majority criterion is a criterion used to compare voting systems. It is also known as the majority criterion for solid coalitions and the generalized majority criterion. The criterion states that if there is a subset S of the candidates, such that more than half of the voters strictly prefer every member of S to every candidate outside of S, this majority voting sincerely, the winner must come from S. This is similar to but stricter than the majority criterion, where the requirement applies only to the case that S contains a single candidate. This is also stricter than the majority loser criterion, where the requirement applies only to the case that S contains all but one candidate. The mutual majority criterion is the single-winner case of the Droop proportionality criterion.
In voting systems, the Minimax Condorcet method is one of several Condorcet methods used for tabulating votes and determining a winner when using ranked voting in a single-winner election. It is sometimes referred to as the Simpson–Kramer method, and the successive reversal method.
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 such as Minimax.
The later-no-harm criterion is a voting system criterion formulated by Douglas Woodall. Woodall defined the criterion as "[a]dding 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 their 1st preference being selected, fails later-no-harm.
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 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.
The term ranked voting refers to any voting system in which voters rank their candidates in a sequence of first or second on their respective ballots. The purpose of the ranking is to allow the voter to determine how the vote is to be transferred if the first preference is found to be un-electable or if is elected with surplus votes.
The later-no-help criterion 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.
Electoral systems are the rules for conducting elections, a main component of which is the algorithm for determining the winner from the ballots cast. This article discusses methods and results of comparing different electoral systems, both those which elect a unique candidate in a 'single-winner' election and those which elect a group of representatives in a multiwinner election.
STAR voting is an electoral system for single-seat elections. Variations also exist for multi-winner and proportional representation elections. The name stands for "Score then Automatic Runoff", referring to the fact that this system is a combination of score voting, to pick two finalists with the highest total scores, followed by a "virtual runoff" in which the finalist who is preferred on more ballots wins. It is a type of cardinal voting electoral system.
