Plurality voting refers to electoral systems in which the candidates in an electoral district who poll more than any other are elected.
Proportional representation (PR) refers to any type of electoral system under which subgroups of an electorate are reflected proportionately in the elected body. The concept applies mainly to political divisions among voters. The essence of such systems is that all votes cast – or almost all votes cast – contribute to the result and are effectively used to help elect someone. Under other election systems, a bare plurality or a scant majority are all that are used to elect candidates. PR systems provide balanced representation to different factions, reflecting how votes are cast.
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.
The two-round system, also called ballotage, top-two runoff, or two-round plurality, is a single winner voting method. It is sometimes called plurality-runoff, although this term can also be used for other, closely-related systems such as ranked-choice voting or the exhaustive ballot. It falls under the class of plurality-based voting rules, together with instant-runoff and first-past-the-post (FPP). In a two-round system, both rounds are held under choose-one voting, where the voter marks a single favorite candidate. The two candidates with the most votes in the first round proceed to a second round, where all other candidates are excluded.
The single transferable vote (STV), a type of proportional ranked choice voting, is a multi-winner electoral system in which each voter casts a single vote in the form of a ranked-choice ballot. Voters have the option to rank candidates, and their vote may be transferred according to alternative preferences if their preferred candidate is eliminated or elected with surplus votes, so that their vote is used to elect someone they prefer over others in the running. STV aims to approach proportional representation based on votes cast in the district where it is used, so that each vote is worth about the same as another.
In social choice, a no-show paradox is a pathology in some voting rules, where a candidate loses an election as a result of having too many supporters. More formally, a no-show paradox occurs when adding voters who prefer Alice to Bob causes Alice to lose the election to Bob. Voting systems without the no-show paradox are said to satisfy the participation criterion.
The single transferable vote (STV) is a proportional representation system that elects multiple winners. It is one of several ways of choosing winners from ballots that rank candidates by preference. Under STV, an elector's vote is initially allocated to their first-ranked candidate. Candidates are elected (winners) if their vote tally reaches quota. After the winners in the first count are determined, if seats are still open, surplus votes — those in excess of an electoral quota— are transferred from winners to the remaining candidates (hopefuls) according to the surplus ballots' next usable back-up preference.
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.
Instant-runoff voting (IRV), also known as ranked-choice voting (RCV), preferential voting (PV), or the alternative vote (AV), is a multi-round elimination method where the loser of each round is determined by the first-past-the-post method. In academic contexts, the term instant-runoff voting is generally preferred as it does not run the risk of conflating the method with methods of ranked voting in general.
An electoral or voting system is a set of rules used to determine the results of an election. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, non-profit organisations and informal organisations. These rules govern all aspects of the voting process: when elections occur, who is allowed to vote, who can stand as a candidate, how ballots are marked and cast, how the ballots are counted, how votes translate into the election outcome, limits on campaign spending, and other factors that can affect the result. Political electoral systems are defined by constitutions and electoral laws, are typically conducted by election commissions, and can use multiple types of elections for different offices.
Proportional approval voting (PAV) is a proportional electoral system for multiwinner elections. It is a multiwinner approval method that extends the highest averages method of apportionment commonly used to calculate apportionments for party-list proportional representation. However, PAV allows voters to support only the candidates they approve of, rather than being forced to approve or reject all candidates on a given party list.
Combinatorial participatory budgeting, also called indivisible participatory budgeting or budgeted social choice, is a problem in social choice. There are several candidate projects, each of which has a fixed costs. There is a fixed budget, that cannot cover all these projects. Each voter has different preferences regarding these projects. The goal is to find a budget-allocation - a subset of the projects, with total cost at most the budget, that will be funded. Combinatorial participatory budgeting is the most common form of participatory budgeting.
Justified representation (JR) is a criterion of fairness in multiwinner approval voting. It can be seen as an adaptation of the proportional representation criterion to approval voting.
Multiwinner approval voting, sometimes also called approval-based committee (ABC) voting, refers to a family of multi-winner electoral systems that use approval ballots. Each voter may select ("approve") any number of candidates, and multiple candidates are elected.
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.
Phragmén's voting rules are rules for multiwinner voting. They allow voters to vote for individual candidates rather than parties, but still guarantee proportional representation. They were published by Lars Edvard Phragmén in French and Swedish between 1893 and 1899, and translated to English by Svante Janson in 2016.
The method of equal shares is a proportional method of counting ballots that applies to participatory budgeting, to committee elections, and to simultaneous public decisions. It can be used when the voters vote via approval ballots, ranked ballots or cardinal ballots. It works by dividing the available budget into equal parts that are assigned to each voter. The method is only allowed to use the budget share of a voter to implement projects that the voter voted for. It then repeatedly finds projects that can be afforded using the budget shares of the supporting voters. In contexts other than participatory budgeting, the method works by equally dividing an abstract budget of "voting power".
Multi-issue voting is a setting in which several issues have to be decided by voting. Multi-issue voting raises several considerations, that are not relevant in single-issue voting.
Fully proportional representation(FPR) is a property of multiwinner voting systems. It extends the property of proportional representation (PR) by requiring that the representation be based on the entire preferences of the voters, rather than on their first choice. Moreover, the requirement combines PR with the requirement of accountability - each voter knows exactly which elected candidate represents him, and each candidate knows exactly which voters he represents.
Thiele's voting rules are rules for multiwinner voting. They allow voters to vote for individual candidates rather than parties, but still guarantee proportional representation. They were published by Thorvald Thiele in Danish in 1895, and translated to English by Svante Janson in 2016. They were used in Swedish parliamentary elections to distribute seats within parties, and are still used in city council elections.
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