There are a number of different criteria which can be used for voting systems in an election:
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:
In voting systems, the Smith set, named after John H. Smith, but also known as the top cycle, or as Generalized Top-Choice Assumption (GETCHA), is the smallest non-empty set of candidates in a particular election such that each member defeats every candidate outside the set in a pairwise election. The Smith set provides one standard of optimal choice for an election outcome. Voting systems that always elect a candidate from the Smith set pass the Smith criterion and are said to be 'Smith-efficient' or to satisfy the Smith criterion.
In voting systems, the Schwartz set is the union of all Schwartz set components. A Schwartz set component is any non-empty set S of candidates such that
Independence of Smith-dominated alternatives is a voting system criterion defined such that its satisfaction by a voting system occurs when the selection of the winner is independent of candidates who are not within the Smith set.
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 or the Tideman method is an electoral system developed in 1987 by Nicolaus Tideman that selects a single winner using votes that express preferences. The ranked-pairs procedure can also be used to create a sorted list of winners.
The Schulze method is an electoral system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. The method can also be used to create a sorted list of winners. The Schulze method is also known as Schwartz Sequential dropping (SSD), cloneproof Schwartz sequential dropping (CSSD), the beatpath method, beatpath winner, path voting, and path winner. The Schulze method is a Condorcet method, which means that if there is a candidate who is preferred by a majority over every other candidate in pairwise comparisons, then this candidate will be the winner when the Schulze method is applied.
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 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.
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. Both methods are designed to satisfy the Condorcet criterion, and allow for incomplete ballots and equal rankings.
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.
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.
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 majority loser criterion is a criterion to evaluate single-winner voting systems. The criterion states that if a majority of voters prefers every other candidate over a given candidate, then that candidate must not win.
Majority judgment (MJ) is a single-winner voting system proposed in 2010 by Michel Balinski and Rida Laraki. It uses a highest median rule, i.e., a cardinal voting system that elects the candidate with the highest median rating.
Comparison of electoral systems is the result of comparative politics for electoral systems. 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 that elect a unique candidate in a 'single-winner' election and those that elect a group of representatives in a multiwinner election.
Tideman's Alternative Methods, including Alternative Smith and Alternative Schwartz, are two electoral systems developed by Nicolaus Tideman which select a single winner using votes that express preferences. These methods can also create a sorted list of winners.
Black's method is an election method proposed by Duncan Black in 1958 as a compromise between the Condorcet method and the Borda count. This method selects a Condorcet winner. If a Condorcet winner does not exist, then the candidate with the highest Borda score is selected.