Approval voting is an electoral system in which voters can select any number of candidates instead of selecting only one.
Score voting or range voting is an electoral system for single-seat elections, in which voters give each candidate a score, the scores are added, and the candidate with the highest total is elected. It has been described by various other names including evaluative voting, utilitarian voting, interval measure voting, point-sum voting, ratings summation, 0-99 voting, and average voting. It is a type of cardinal voting electoral system that aims to approximate the utilitarian social choice rule.
Strategic voting, also called tactical voting, sophisticated voting or insincere voting, occurs in voting systems when a voter votes for a candidate or party other than their sincere preference to prevent an undesirable outcome. For example, in a simple plurality election, a voter might gain a better outcome by voting for a less preferred but more generally popular candidate.
The Condorcet paradox in social choice theory is a situation noted by the Marquis de Condorcet in the late 18th century, in which collective preferences can be cyclic, even if the preferences of individual voters are not cyclic. This is paradoxical, because it means that majority wishes can be in conflict with each other: Suppose majorities prefer, for example, candidate A over B, B over C, and yet C over A. When this occurs, it is because the conflicting majorities are each made up of different groups of individuals.
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.
Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem in social choice theory that states that when voters have three or more distinct alternatives (options), no ranked voting electoral system can convert the ranked preferences of individuals into a community-wide ranking while also meeting the specified set of criteria: unrestricted domain, non-dictatorship, Pareto efficiency, and independence of irrelevant alternatives. The theorem is often cited in discussions of voting theory as it is further interpreted by the Gibbard–Satterthwaite theorem. The theorem is named after economist and Nobel laureate Kenneth Arrow, who demonstrated the theorem in his doctoral thesis and popularized it in his 1951 book Social Choice and Individual Values. The original paper was titled "A Difficulty in the Concept of Social Welfare".
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
- Every candidate inside the set S is pairwise unbeaten by every candidate outside S; and
- No non-empty proper subset of S fulfills the first property.
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 participation criterion, sometimes called join consistency, is a voting system criterion that says that a candidate should never lose an election because they had "too much support." In other words, adding a ballot that ranks A higher than B should not cause A to lose to B.
The majority criterion is a voting system criterion. The criterion states that "if only one candidate is ranked first by a majority of voters, then that candidate must win."
Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a collective decision or social welfare in some sense. Whereas choice theory is concerned with individuals making choices based on their preferences, social choice theory is concerned with how to translate the preferences of individuals into the preferences of a group. A non-theoretical example of a collective decision is enacting a law or set of laws under a constitution. Another example is voting, where individual preferences over candidates are collected to elect a person that best represents the group's preferences.
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 says if there is a subset S of candidates, with more than half of voters strictly preferring any member of S to every candidate outside of S, 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.
The Kemeny–Young method is an electoral system that uses ranked ballots and pairwise comparison counts to identify the most popular choices in an election. It is a Condorcet method because if there is a Condorcet winner, it will always be ranked as the most popular choice.
The term ranked voting, also known as preferential voting or ranked choice voting, pertains to any voting system where voters use 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. An electoral system that utilizes ranked voting employs one of numerous counting methods to determine the winning candidate or candidates. Additionally, in some ranked voting systems, officials mandate voters to rank a specific number of candidates, sometimes all; while in others, voters may rank as many candidates as they desire.
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.
Impartial culture (IC) or the culture of indifference is a probabilistic model used in social choice theory for analyzing ranked voting method rules.
Social utility efficiency (SUE) is a measurement of the utilitarian performance of voting methods—how likely they are to elect the candidate who best represents the voters' preferences.
Multiwinner voting, also called multiple-winner elections or committee voting or committee elections, is an electoral system in which multiple candidates are elected. The number of elected candidates is usually fixed in advance. For example, it can be the number of seats in a country's parliament, or the required number of members in a committee.
Fractional social choice is a branch of social choice theory in which the collective decision is not a single alternative, but rather a weighted sum of two or more alternatives. For example, if society has to choose between three candidates: A B or C, then in standard social choice, exactly one of these candidates is chosen, while in fractional social choice, it is possible to choose "2/3 of A and 1/3 of B". A common interpretation of the weighted sum is as a lottery, in which candidate A is chosen with probability 2/3 and candidate B is chosen with probability 1/3. Due to this interpretation, fractional social choice is also called random social choice, probabilistic social choice, or stochastic social choice. But it can also be interpreted as a recipe for sharing, for example:
