Party-list proportional representation (list-PR) is a subset of proportional representation electoral systems in which multiple candidates are elected through their position on an electoral list. They can also be used as part of mixed-member electoral systems.
The single transferable vote (STV), sometimes mistakenly conflated with proportional ranked choice voting (P-RCV), 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 alternate 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 the study of electoral systems, the Droop quota is the minimum number of votes needed for a party or candidate to guarantee they will win at least one seat in a legislature.
The D'Hondt method, also called the Jefferson method or the greatest divisors method, is an apportionment method for allocating seats in parliaments among federal states, or in proportional representation among political parties. It belongs to the class of highest-averages methods. Compared to ideal proportional representation, the D'Hondt method reduces somewhat the political fragmentation for smaller electoral district sizes, where it favors larger political parties over small parties.
The Webster method, also called the Sainte-Laguë method, is a highest averages apportionment method for allocating seats in a parliament among federal states, or among parties in a party-list proportional representation system. The Sainte-Laguë method shows a more equal seats-to-votes ratio for different sized parties among apportionment methods.
In mathematics, economics, and social choice theory, the highest averages methods, also called the divisor methods, are a family of apportionment methods. These methods seek to fairly divide a legislature between several groups, such as political parties or states. The two names for these methods—highest averages and divisors—reflect two different ways to ways of thinking about them, and their two independent inventions. However, both procedures are equivalent and give the same answer.
The largest remainder methods or quota methods are methods of allocating seats proportionally that are based on calculating a quota, i.e. a certain number of votes needed to be guaranteed a seat in parliament. Then, any leftover seats are handed over to "plurality" winners. They are typically contrasted with the more popular highest averages methods.
In the study of apportionment, the Harequota is the number of voters represented by each legislator under an idealized system of proportional representation, where every legislator represents an equal number of voters. The Hare quota is the total number of votes divided by the number of seats to be filled. The Hare quota was used in the original proposal for a single transferable vote system, and is still occasionally used, although it has since been largely supplanted by the Droop quota.
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another.
The single transferable vote (STV) is a semi-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 Huntington–Hill method is a highest averages method for assigning seats in a legislature to political parties or states. Since 1941, this method has been used to apportion the 435 seats in the United States House of Representatives following the completion of each decennial census.
Leveling seats, commonly known also as adjustment seats, are an election mechanism employed for many years by all Nordic countries in elections for their national legislatures. In 2013, Germany also introduced national leveling seats for their national parliament, the Bundestag. The electoral reform in Germany in 2023 removed the leveling seats, and replaced them with Zweitstimmendeckung. Leveling seats are seats of additional members elected to supplement the members directly elected by each constituency. The purpose of these additional seats is to ensure that each party's share of the total seats is roughly proportional to the party's overall shares of votes at the national level.
In proportional representation systems, an electoral quota is the number of votes a candidate needs to be guaranteed election.
Proportionality for solid coalitions (PSC) is a fairness criterion for ranked voting systems. It is an adaptation of the proportional representation criterion to voting systems in which there are no parties, the voters can vote directly for candidates, and can rank candidates in any way they want. This criterion was proposed by the British philosopher and logician Michael Dummett.
An electoral system or voting system is a set of rules that determine how elections and referendums are conducted and how their results are determined. 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.
The Parliament of Malta is the constitutional legislative body in Malta, located in Valletta. The parliament is unicameral, with a democratically elected House of Representatives and the president of Malta. By constitutional law, all government ministers, including the prime minister, must be members of the House of Representatives.
National remnant is an apportionment scheme used in some party-list proportional representation systems that have multi-member electoral districts. The system uses a Largest remainder method to determine some of the seats in each electoral district. However, after the integer part of the seats in each district is allocated to the parties, the seats left unallocated will then be allocated not in each electoral district in isolation, but in a larger division, such as nationwide or in large separate regions that each encompass multiple electoral districts.
The Loosemore–Hanby index measures disproportionality of electoral systems, how much the principle of one person, one vote is violated. It computes the absolute difference between votes cast and seats obtained using the formula:
Apportionment in the Hellenic Parliament refers to those provisions of the Greek electoral law relating to the distribution of Greece's 300 parliamentary seats to the parliamentary constituencies, as well as to the method of seat allocation in Greek legislative elections for the various political parties. The electoral law was codified for the first time through a 2012 Presidential Decree. Articles 1, 2, and 3 deal with how the parliamentary seats are allocated to the various constituencies, while articles 99 and 100 legislate the method of parliamentary apportionment for political parties in an election. In both cases, Greece uses the largest remainder method.
Mathematics of apportionment describes mathematical principles and algorithms for fair allocation of identical items among parties with different entitlements. Such principles are used to apportion seats in parliaments among federal states or political parties. See apportionment (politics) for the more concrete principles and issues related to apportionment, and apportionment by country for practical methods used around the world.
