Approval voting is an electoral system in which voters can select any number of candidates instead of selecting only one.
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, but also lets voters give partial (in-between) approval ratings to candidates.
In social choice theory and politics, the spoiler effect refers to a situation where the entry of a losing candidate affects the results of an election. A voting system that is not affected by spoilers satisfies independence of irrelevant alternatives or independence of spoilers.
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, 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.
The Copeland or Llull method is a ranked-choice voting system based on counting each candidate's pairwise wins and losses.
In an election, a candidate is called a Condorcet, beats-all, or majority winner if a majority of voters would support them in a race against any other candidate. Such a candidate is also called an undefeated or tournament champion. Voting systems in which a majority-rule winner will always win the election are said to satisfy the majority-rule principle, also called the Condorcet criterion. Methods that satisfy this criterion extend majority rule to elections with more than one candidate.
The Smith criterion is a voting system criterion that formalizes the concept of a majority rule. A voting system satisfies the Smith criterion if it always elects a candidate from the Smith set, which generalizes the idea of a "Condorcet winner" to cases where there may be cycles or ties, by allowing for several who together can be thought of as being "Condorcet winners." A Smith method will always elect a candidate from the Smith set.
The participation criterion, also called vote or population monotonicity, is a voting system criterion that says that a candidate should never lose an election as a result of receiving too many votes in support. It says that adding a voter who prefers Alice to Bob should not cause Alice to lose the election to Bob.
In political science and social choice theory, the median voter theorem states that if voters and candidates are distributed along a one-dimensional spectrum and voters have single peaked preferences, any voting method satisfying the Condorcet criterion will elect the candidate preferred by the median voter.
The mutual majority criterion is a criterion for evaluating electoral system. It requires that whenever a majority of voters prefer a group of candidates above all others, someone from that group must win. It is the single-winner case of Droop-Proportionality for Solid Coalitions.
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.
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.
Later-no-harm is a property of some 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 this higher-ranked candidate to lose.
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. It is a relative criterion: it states how changing an election should or shouldn't affect the outcome.
The Borda count is a family of positional voting rules which gives each candidate, for each ballot, a number of points corresponding to the number of candidates ranked lower. In the original variant, the lowest-ranked candidate gets 0 points, the next-lowest gets 1 point, etc., and the highest-ranked candidate gets n − 1 points, where n is the number of candidates. Once all votes have been counted, the option or candidate with the most points is the winner. The Borda count is intended to elect broadly acceptable options or candidates, rather than those preferred by a majority, and so is often described as a consensus-based voting system rather than a majoritarian one.
The term ranked voting, also known as preferential voting or ranked-choice voting, pertains to any voting system where voters indicate a rank to order candidates or options—in a sequence from first, second, third, and onwards—on their ballots. Ranked voting systems vary based on the ballot marking process, how preferences are tabulated and counted, the number of seats available for election, and whether voters are allowed to rank candidates equally.
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.
A major branch of social choice theory is devoted to the comparison of electoral systems, otherwise known as social choice functions. Viewed from the perspective of political science, electoral systems are rules for conducting elections and determining winners from the ballots cast. From the perspective of economics, mathematics, and philosophy, a social choice function is a mathematical function that determines how a society should make choices, given a collection of individual preferences.
Multiwinner, at-large, or committeevoting refers to electoral systems that elect several candidates at once. Such methods can be used to elect parliaments or committees.
