Approval voting is a single-winner electoral system in which voters mark all the candidates they support, instead of just choosing one. The candidate with the highest approval rating is elected.
The two-round system, also called ballotage, top-two runoff, or two-round plurality, is a voting method used to elect a single winner. In the United States, it is often called a jungle or nonpartisan primary. It is sometimes called plurality runoff, although this term can also be used for other systems.
In social choice theory, Condorcet's voting paradox is a fundamental discovery by the Marquis de Condorcet that majority rule is inherently self-contradictory. The result states that it is logically impossible for any voting system to guarantee the winner has a majority of the vote, because it is possible no such winner exists: in some situations, a majority of voters will prefer A to B, B to C, and also C to A, even if every voter's individual preferences are rational and avoid self-contradiction. Examples of Condorcet's paradox are called Condorcet cycles or cyclic ties.
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.
Arrow's impossibility theorem is a key result in social choice showing that no rank-order method for collective decision-making can satisfy the requirements of rational choice. Specifically, any such rule violates independence of irrelevant alternatives, the principle that a choice between and should not depend on the quality of a third, unrelated option .
Voting is a method by which a group, such as a meeting or an electorate, convenes together for the purpose of making a collective decision or expressing an opinion usually following discussions, debates or election campaigns. Democracies elect holders of high office by voting. Residents of a jurisdiction represented by an elected official are called "constituents", and the constituents who choose to cast a ballot for their chosen candidate are called "voters." There are different systems for collecting votes, but while many of the systems used in decision-making can also be used as electoral systems, any which cater to proportional representation can only be used in elections.
The Copeland or Llull method is a ranked-choice voting system based on counting each candidate's pairwise wins and losses.
Majoritarianism is a political philosophy or ideology with an agenda asserting that a majority, whether based on a religion, language, social class, or other category of the population, is entitled to a certain degree of primacy in society, and has the right to make decisions that affect the society. This traditional view has come under growing criticism, and liberal democracies have increasingly included constraints on what the parliamentary majority can do, in order to protect citizens' fundamental rights. Majoritarianism should not be confused with electoral systems that give seats to candidates with only a plurality of votes. Although such systems are sometimes called majoritarian systems, they use plurality, not majority, to set winners. Some electoral systems, such as instant-runoff voting, are most often majoritarian – winners are most often determined by having majority of the votes that are being counted – but not always. A parliament that gives lawmaking power to any group that holds a majority of seats may be called a majoritarian parliament. Such is the case in the Parliament of the United Kingdom and the Parliament of Saudi Arabia and many other chambers of power.
In social choice theory, May's theorem, also called the general possibility theorem, says that majority vote is the unique ranked social choice function between two candidates that satisfies the following criteria:
The participation criterion, sometimes called votermonotonicity, is a voting system criterion that says candidates should never lose an election as a result of receiving too many votes in support. More formally, it says that adding more voters who prefer Alice to Bob should not cause Alice to lose the election to Bob.
In political science and social choice theory, Black'smedian 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 majority favorite criterion is a voting system criterion that says that, if a candidate would win more than half the vote in a first-preference plurality election, that candidate should win. Equivalently, if only one candidate is ranked first by a over 50% of voters, that candidate must win. It is occasionally referred to simply as the "majority criterion", but this term is more often used to refer to Condorcet's majority-rule principle.
Social choice theory is a branch of welfare economics that analyzes methods of combining individual opinions, beliefs, or preferences to reach a collective decision or create measures of social well-being. It contrasts with political science in that it is a normative field that studies how societies should make decisions, whereas political science is descriptive. Social choice incorporates insights from economics, mathematics, philosophy, political science, and game theory to find the best ways to combine individual preferences into a coherent whole, called a social welfare function.
Bullet, single-shot, or plump voting is when a voter supports only a single candidate, typically to show strong support for a single favorite.
The Borda method or order of merit is a positional voting rule which gives each candidate a number of points equal to the number of candidates ranked below them: the lowest-ranked candidate gets 0 points, the second-lowest gets 1 point, and so on. Once all votes have been counted, the option or candidate with the most points is the winner.
Instant-runoff voting (IRV), also known as ranked-choice voting or the alternative vote (AV), combines ranked voting together with a system for choosing winners from these rankings by repeatedly eliminating the candidate with the fewest first-place votes and reassigning their votes until only one candidate is left. It can be seen as a modified form of a runoff election or exhaustive ballot in which, after eliminating some candidates, the choice among the rest is made from already-given voter rankings rather than from a separate election. Many sources conflate this system of choosing winners with ranked-choice voting more generally, for which several other systems of choosing winners have also been used.
Rated, evaluative, graded, or cardinalvotingsystems are a class of voting methods which allow voters to state how strongly they support a candidate, which involves giving each one a grade on a separate scale. Cardinal methods and ordinal methods are the two categories of modern voting systems.
Ranked voting is any voting system that uses voters' orderings (rankings) of candidates to choose a single winner or multiple winners. Many ranked voting systems apply lower preferences just as contingency choices when higher preferences are found to be ineffective or the vote or part thereof needs to be transferred on in cases where higher preference was elected.
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.
A jury theorem is a mathematical theorem proving that, under certain assumptions, a decision attained using majority voting in a large group is more likely to be correct than a decision attained by a single expert. It serves as a formal argument for the idea of wisdom of the crowd, for decision of questions of fact by jury trial, and for democracy in general.
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