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Proportional-representation voting system
highest averages methods (also called divisor methods). By far the most common quota method are the largest remainders or quota-shift methods, which assign
Largest_remainder_method
Family of voting systems
Sainte-Laguë method (also known as the Webster method or the Schepers method) is used in Indonesia, New Zealand, Norway, and Sweden. The largest remainder (LR)
Party-list proportional representation
Party-list_proportional_representation
Method for allocating seats in parliaments
as the Bader–Ofer system. Jefferson's method uses a quota (called a divisor), as in the largest remainder method. The divisor is chosen as necessary so
D'Hondt_method
Proportional-representation electoral system
Sainte-Laguë method shows fewer apportionment paradoxes compared to largest remainder methods such as the Hare quota and other highest averages methods such as
Sainte-Laguë_method
Electoral system quota formula
apportionments under party-list proportional representation when using the largest remainder method. In such cases, the Hare quota gives unbiased apportionments that
Hare_quota
Method by which voters make a choice between options
Jefferson's method is equivalent to the D'Hondt method, Webster's method is the Sainte-Laguë method, and Hamilton's method is identical to the Hare largest remainder
Electoral_system
Number of votes a candidate needs to win
quota) is the most commonly used quota for apportionments using the largest remainder method of party-list representation. It was proposed by Thomas Hare in
Electoral_quota
Voting system that makes outcomes proportional to vote totals
widespread. Each uses one of a variety of methods of allocating seats – the D'Hondt method, the Sainte-Laguë method or a different one. Through the late 1800s
Proportional_representation
Votes required to win a seat in proportional systems
Eduard Hagenbach-Bischof in the context of STV and not for the largest remainder method. The Droop quota is used in almost all STV elections, including
Droop_quota
Lower house of the Algerian Parliament
counting the votes, the seats are distributed according to the largest remainder method, without an electoral threshold. Before the 2021 election (which
People's_National_Assembly
Way to distribute seats in a legislative body
These apportionment methods can be categorized into largest remainder methods and highest averages methods. Malapportionment is the creation of electoral districts
Apportionment_(politics)
Single-winner electoral system
method (/ˈʃʊltsə/), also known as the beatpath method, is a single winner ranked-choice voting rule developed by Markus Schulze. The Schulze method is
Schulze_method
Rule for proportional allocation
particular, divisor methods avoid the population paradox and spoiler effects, unlike the largest remainder methods. Divisor methods were first invented
Highest_averages_method
Legislature of Slovakia
suffrage under proportional representation with seats distributed via largest remainder method with Hagenbach-Bischoff quota every four years. Slovakia's parliament
National_Council_of_Slovakia
Federal Bundestag election regulation
paradoxes which occur with the largest remainder method are avoided by the recent introduction of the Sainte-Laguë method. The difficulty of "negative vote
Electoral_system_of_Germany
Pairwise-comparison electoral system
The Condorcet or majority-rule methods (English: /kɒndɔːrˈseɪ/; French: [kɔ̃dɔʁsɛ]) are a family of election systems that elect the majority-preferred
Condorcet_method
Election result affecting losing candidate
occur in some methods of proportional representation, such as the single transferable vote (STV or RCV-PR) and the largest remainders method of party-list
Spoiler_effect
Unicameral legislature of Denmark
by the D'Hondt method under a party-list system. The 40 levelling seats are allocated to the parties using the largest remainder method, and then distributed
Folketing
Plurality voting system
election result is an example of center squeeze. By contrast, Condorcet methods would elect Nashville (the actual capital) because it beats all others
First-past-the-post_voting
proportional representation via the additional member system and largest remainder method. The minimum voting age is set at 18. including Speaker of the
Next South Korean legislative election
Next_South_Korean_legislative_election
Selection of decision-makers by random sample
In ancient Athenian democracy, sortition was the traditional and primary method for appointing political officials, and its use was regarded as a principal
Sortition
House of the Federal Assembly of Switzerland
in the national census (including foreign residents), using the largest remainder method. A change in the division of the seats occurred in 2003, as a result
National Council (Switzerland)
National_Council_(Switzerland)
of valid votes in each region. Mandates are assigned using the largest remainder method, using the Imperiali quota in the first round and the Hagenbach-Bischoff
Next Czech parliamentary election
Next_Czech_parliamentary_election
Multi-winner electoral system
voter-determined lists of individual candidates in elections using the largest remainders method to elect the winning candidates, rather than list-based proportional
Single_transferable_vote
Method of allocating representative seats following elections
that have multi-member electoral districts. The system uses a Largest remainder method to determine some of the seats in each electoral district. However
National_remnant
Phenomenon in electoral systems
from the total number of seats and recalculating the quota (the largest remainder method was also recommended) to proportionally redistribute the list seats
Overhang_seat
Constituency of the National Assembly of Mauritania
Mauritanian wilaya of Nouakchott-Ouest. The electoral system uses the largest remainder method and a closed-list proportional representation, with no minimum
Nouakchott-Ouest (National Assembly district)
Nouakchott-Ouest_(National_Assembly_district)
Class of voting systems
method until a single candidate remains. The method used to determine the loser is called the base method. Common are the two-round system, instant-runoff
Sequential_elimination_method
Single-winner ranked-choice voting system
Dodgson's method is an electoral system based on a proposal by mathematician Charles Dodgson, better known as Lewis Carroll. The method searches for a
Dodgson's_method
Single-winner electoral system
instant-runoff procedure to create hybrid election methods that are called Nanson's method and Baldwin's method. Both methods are designed to satisfy the Condorcet
Nanson's_method
constituencies based on the departments, with seats allocated using the largest remainder method. Two members are elected by the Afro-Colombian community, one by
2026 Colombian parliamentary election
2026_Colombian_parliamentary_election
Single-winner ranked-voting electoral system
transferable voting (STV), instant-runoff voting (IRV), Coombs' method, and Baldwin's method – allow for many rounds of counting, often eliminating only one
Contingent_vote
Spoiler effect in RCV and two-round systems
candidate, which means they will be elected by any method compatible with majority-rule. However, in methods that strongly prioritize first preferences, these
Center_squeeze
Single-winner ranked vote system
The Copeland or Llull method is a ranked-choice voting system based on counting each candidate's pairwise wins and losses. In the system, voters rank candidates
Copeland's_method
Largest remainder method (voting systems) Level-set method Linear combination of atomic orbitals molecular orbital method (molecular orbitals) Method
List of mathematics-based methods
List_of_mathematics-based_methods
Single-winner ranked-choice electoral system
under the plurality-with-elimination family of voting methods, and is thus closely related to methods like the two-round system and party primary. Instant-runoff
Instant-runoff_voting
are allocated to the participating political parties using the largest remainder method. Parties normally need to receive at least 5% (7% for multi-party
2028 Lithuanian parliamentary election
2028_Lithuanian_parliamentary_election
proportional share of the remaining half of the seats based on the largest remainder method and Hare quota. "Cameroon: Assembly extends mandate of deputies
2026 Cameroonian parliamentary election
2026_Cameroonian_parliamentary_election
the way they allocated the proportional seats, both using the largest remainder method of allocating seats. The new electoral law was supported by the
Italian_electoral_law_of_2017
Hare quota Droop quota Largest remainder method (supplemental method to using quotas) Multi-round voting (common supplemental method to using absolute majority
List_of_electoral_systems
mandates is required. Seats are allocated using the Hare quota and largest remainder method, proportionally among all political forces that surpass the electoral
2026 Armenian parliamentary election
2026_Armenian_parliamentary_election
general councillors are elected from national lists using the largest remainder method of proportional representation. The parish lists and the national
2027 Andorran parliamentary election
2027_Andorran_parliamentary_election
Voting systems that use ranked ballots
ranks as weights. These systems are called positional voting. In the Borda method, the least-favored candidates on each ballot receive fewer points; the most-favored
Ranked_voting
Mixed electoral system
portion of a legislature is elected using one method, while another portion is elected using a different method, with all voters participating in both. Thus
Parallel_voting
Unicameral legislature
Final seats are assigned through the largest remainder method, and if the remainder is equal, the winner is determined by lottery among
National Assembly (South Korea)
National_Assembly_(South_Korea)
representation with closed lists. Seats are allocated using the largest remainder method with Hare quota. Voters have two votes: one for the parish seats
Elections_in_Andorra
unsuccessfully. National-at-large legislators are apportioned by largest remainder method. Political parties will gain seats upon reaching the 5% threshold
2024 Taiwanese legislative election
2024_Taiwanese_legislative_election
party-list proportional representation, distributed using the largest remainder method and the Hare quota. On election day itself ZANU–PF won 136 seats
2023 Zimbabwean general election
2023_Zimbabwean_general_election
the parties using the remaining votes using the Hare quota and largest remainder method. Dieter Nohlen, Florian Grotz & Christof Hartmann (2001) Elections
1965_Turkish_general_election
Property of electoral systems
(when one exists) include Ranked pairs, Schulze's method, and the Tideman alternative method. Methods that do not guarantee that the Cordorcet winner will
Condorcet_winner
two-seat districts, with larger districts using the proportional largest remainder method. Mauritania has a multi-party system with a dominant ruling party
Elections_in_Mauritania
Single-winner ranked voting rule
Coombs' method is a ranked voting system. Like instant-runoff (IRV-RCV), Coombs' method is a sequential-loser method, where the last-place finisher according
Coombs'_method
Point-based ranked voting system
The Borda method or order of merit is a positional voting rule that gives a candidate a number of points equal to the number of candidates ranked below
Borda_count
Lower house in the Parliament of Kazakhstan
electoral threshold to win seats (which are allocated according to the largest remainder method), and 29 seats via first-past-the-post in single-member constituencies
Mäjilis
Rule in math and political science
apportionment method satisfies the quota rule, it must fail to satisfy some apportionment paradox. For instance, although largest remainder method satisfies
Quota_rule
legislate the method of parliamentary apportionment for political parties in an election. In both cases, Greece uses the largest remainder method. Up to and
Apportionment in the Hellenic Parliament
Apportionment_in_the_Hellenic_Parliament
Unicameral national legislature of the Republic of China (Taiwan)
second ballot, based on nationwide votes, and calculated using the largest remainder method by the Hare quota. Any party which receives 5% or more of the party
Legislative_Yuan
Single-winner electoral system
finalists are preferred by an equal number of voters. As with any voting method, ties are more likely in elections with few voters. Under the rules published
STAR_voting
Decision rule that selects alternatives that have a majority
averages Largest remainders National remnant Biproportional List type Closed list Localized list Open list Free list No list Quota-remainder methods Single
Majority_rule
or electoral coalitions, with seats allocated according to the largest remainder method using a Hare quota. There were nine political party groups represented
2026 Bulgarian parliamentary election
2026_Bulgarian_parliamentary_election
Replacing a number with a simpler value
g. [1] for the apportionment of seats, implemented e.g. by the largest remainder method, see Mathematics of apportionment, and [2] for distributing the
Rounding
Measure of equal representation
Sainte-Laguë method. The D'Hondt method approximates proportionality by minimizing the largest seats-to-votes ratio among all parties. The largest seats-to-votes
Seats-to-votes_ratio
list voting system with proportional representation through the largest remainder method from seven multi-member constituencies which are based on the seven
2026 Costa Rican general election
2026_Costa_Rican_general_election
South African legal title
party-list proportional representation with a closed list, using the largest remainder method with the Droop quota to allocate any surplus. Members are elected
Member of the Provincial Legislature
Member_of_the_Provincial_Legislature
Assembly were elected by the D'Hondt method, which was changed in June 2023 from the hare quota largest remainders method used in previous elections. Mayors
2024 Salvadoran legislative election
2024_Salvadoran_legislative_election
geographical constituencies, proportional representation using the largest remainder method with Hare quota was adopted by the SAR government in replacement
Elections_in_Hong_Kong
Single-winner ranked-choice voting system
candidate with the largest (maximum) number of votes in their worst (minimum) matchup is declared the winner. The minimax Condorcet method selects the candidate
Minimax_Condorcet_method
Single-winner electoral system family
The Tideman Alternative method, also called[by whom?] Alternative-Smith voting, is a voting rule developed by Nicolaus Tideman which selects a single winner
Tideman_alternative_method
Single-winner electoral system
Black's method is an election method proposed by Duncan Black in 1958 as a compromise between the Condorcet method and the Borda count. This method selects
Black's_method
Lower house of the legislature of Mexico
majority, the position rotates annually among the coordinators of the three largest parliamentary groups. Article 27 of the Organic Law of the General Congress
Chamber_of_Deputies_(Mexico)
party-list proportional representation, distributed using the largest remainder method and the hare quota. The Senate has 80 members: 60 are elected for
Elections_in_Zimbabwe
Single-winner electoral system
Tideman method, is a ranked voting method that determines a single winner from ballots that rank candidates in order of preference. The method is like
Ranked_pairs
or electoral coalitions, with seats allocated according to the largest remainder method using a Hare quota. Below is the official list of parties and coalitions
October 2024 Bulgarian parliamentary election
October_2024_Bulgarian_parliamentary_election
Directly elected constituency in Hong Kong
party-list proportional representation with seats apportioned by the largest remainder method under the Hare Quota. Between 1998 and 2016, 5 geographical constituencies
Geographical_constituency
Multiple-winner electoral system
across multiple candidates. The candidates elected are those receiving the largest number of votes cast in the election, up to the number of representatives
Cumulative_voting
from one nationwide constituency. Seats are allocated using the largest remainder method. As president Geingob was ineligible for re-election after having
2024 Namibian general election
2024_Namibian_general_election
constituency level, seats were divided between open lists using the largest remainder method with the Imperiali quota. Remaining votes and seats were transferred
1946_Italian_general_election
proportional representation is used, with seats allocated using the largest remainder method. For three-seat constituencies, party lists must include a female
Next Mauritanian parliamentary election
Next_Mauritanian_parliamentary_election
nationally, also using the largest remainder method and Hare quota. Any seats still remaining were allocated to parties with the largest number of remaining
1955 Indonesian legislative election
1955_Indonesian_legislative_election
of valid votes in each region. Mandates are assigned using the largest remainder method, using the Imperiali quota in the first round and the Hagenbach-Bischoff
2025 Czech parliamentary election
2025_Czech_parliamentary_election
Unicameral legislature of East Germany
electoral threshold. Seats were calculated nationally using the largest remainder method, and distributed in multi-member constituencies corresponding to
Volkskammer
Lower house of the Italian Parliament
and 63% using proportional representation, allocated with the largest remainder method, with one round of voting. The 400 deputies are elected in: 147
Chamber_of_Deputies_(Italy)
Type of electoral system
majority-preferred winner, and as a result would be elected by any Condorcet method. Candidates are running in a 3-member district of 10 000 voters. Under non-transferable
Plurality_voting
About simultaneous modular congruences
In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then
Chinese_remainder_theorem
Non-proportional electoral system
non-transferable vote, and block plurality voting, is a type of block voting method for multi-winner elections. Each voter may cast as many votes as the number
Plurality_block_voting
Constituency of the National Assembly of Mauritania
Mauritanian wilaya of Nouakchott-Sud. The electoral system uses the largest remainder method and a closed-list proportional representation, with no minimum
Nouakchott-Sud (National Assembly district)
Nouakchott-Sud_(National_Assembly_district)
Type of mixed electoral system
party-list PR) and nationally-based compensatory top-up seats using the same method as MMP, however because the local MPs are also elected using PR, these systems
Mixed-member proportional representation
Mixed-member_proportional_representation
Variant of party-list voting system
transferable voting Allocation Highest averages method Webster/Sainte-Laguë D'Hondt Largest remainders method Quotas Droop quota/Hagenbach-Bischoff quota
Closed_list
Single-winner electoral system
The Kemeny method is an electoral system that uses ranked ballots and pairwise comparison counts to identify the most popular choices in an election. It
Kemeny_method
Grouping of candidates for election
averages Largest remainders National remnant Biproportional List type Closed list Localized list Open list Free list No list Quota-remainder methods Single
Electoral_list
allocation of seats won by the list is then carried out using the "largest remainder" method. At the beginning of December 2017, the government drafted a bill
Elections in the Democratic Republic of the Congo
Elections_in_the_Democratic_Republic_of_the_Congo
Proportional-representation voting system
Territory. With its use in 1909, it was one of the first uses of the Gregory method for transfers of winner's surplus votes. The name is derived from the names
Hare–Clark_electoral_system
Elections where only a part of the body is elected at a time
transferable voting Allocation Highest averages method Webster/Sainte-Laguë D'Hondt Largest remainders method Quotas Droop quota/Hagenbach-Bischoff quota
Staggered_elections
Class of electoral systems
organized 51%, or the largest minority in a contest with three or more slates, to win all three seats in the first round, so this method does not give proportional
Bucklin_voting
Political term about incumbents losing elections
transferable voting Allocation Highest averages method Webster/Sainte-Laguë D'Hondt Largest remainders method Quotas Droop quota/Hagenbach-Bischoff quota
Unseating
as the Webster/Sainte-Laguë method or largest remainder method. Regardless, the influence of the D'Hondt method in the bipolarization of the electoral
General_elections_in_Spain
Unicameral legislature of Hong Kong
party-list proportional representation, with seats allocated by the largest remainder method using the Hare quota as the quota for election. Under the 2021
Legislative Council of Hong Kong
Legislative_Council_of_Hong_Kong
departments, with seats allocated using the simple quotient and then the largest remainder method. The electoral threshold was revised in 2024, and any party that
2026 Beninese parliamentary election
2026_Beninese_parliamentary_election
Single-winner electoral system
summed, with support = +1 and opposition = −1. The candidate with the largest score is the winner. It is also possible to use ballots with two options
Combined_approval_voting
Voting system
from a single set of ordinal preferences. The two-round system is such a method, because the voters are not forced to vote according to a single ordinal
Two-round_system
LARGEST REMAINDER-METHOD
LARGEST REMAINDER-METHOD
Boy/Male
Sikh
Light of Moon, Victor over the enemy
Girl/Female
Sikh
Gods beloved
Boy/Male
Arabic, Muslim, Sindhi
Reminder
Boy/Male
Hindu, Indian, Sikh
Beloved God
Boy/Male
Muslim
Reminder
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
Remainder
Boy/Male
Indian, Punjabi, Sikh
God of Peace
Boy/Male
English
Retainer.
Male
English
Variant spelling of English Ernest, EARNEST means "battle (to the death), serious business."
Boy/Male
Tamil
Remainder
Boy/Male
English American German
Earnest.
Surname or Lastname
English
English : variant of Taggart.Possibly an altered spelling of French Target, a nickname for someone who carried a square buckler, Old French targe.
Boy/Male
Arabic, Muslim
Reminder
Surname or Lastname
English
English : from Old French argent ‘silver’, hence probably a nickname for someone with silver-gray hair, or possibly an occupational nickname for a silversmith or moneyer.
Boy/Male
Muslim/Islamic
Reminder
Male
Swedish
Variant spelling of Swedish Laris, LARES means "of Laurentum."
Surname or Lastname
English (Suffolk, of Norman origin)
English (Suffolk, of Norman origin) : nickname for someone with silvery hair, a variant of Argent, with the French definite article l(e).French : metonymic occupational name for a silversmith, from French argent ‘silver’.
Boy/Male
Indian, Punjabi, Sikh
Lord of Traditions
Boy/Male
Indian, Sanskrit
Remainder
Boy/Male
Indian, Punjabi, Sikh
Lord of Gold
LARGEST REMAINDER-METHOD
LARGEST REMAINDER-METHOD
LARGEST REMAINDER-METHOD
LARGEST REMAINDER-METHOD
LARGEST REMAINDER-METHOD
LARGEST REMAINDER-METHOD
LARGEST REMAINDER-METHOD
a.
Alt. of Largesse
v. t.
To stop; to check or hinder the motion or action of; as, to arrest the current of a river; to arrest the senses.
v. i.
To make a rejoinder.
superl.
Exceeding most other things of like kind in bulk, capacity, quantity, superficial dimensions, or number of constituent units; big; great; capacious; extensive; -- opposed to small; as, a large horse; a large house or room; a large lake or pool; a large jug or spoon; a large vineyard; a large army; a large city.
n.
The quantity or sum that is left after subtraction, or after any deduction.
v. t.
To coat with parget; to plaster, as walls, or the interior of flues; as, to parget the outside of their houses.
a.
Somewhat large.
a.
Remaining; left; left over; refuse.
n.
The remainder; others.
n.
A goblin, in the shape of a large dog, portending misfortune.
n.
One who has an estate after a particular estate is determined. See Remainder, n., 3.
adv.
Without limitation or remainder; quite; perfectly; wholly; entirely.
a.
Intent; fixed closely; as, earnest attention.
n.
The gathering and bringing home of the harvest; the time of harvest.
adv.
In a large manner.
a.
Longer; longest; -- obsolete compar. and superl. of long.
v. t.
To use in earnest.
n.
Anything that remains, or is left, after the separation and removal of a part; residue; remnant.
pl.
of Remainder-man
n.
An estate in expectancy, generally in land, which becomes an estate in possession upon the determination of a particular prior estate, created at the same time, and by the same instrument; for example, if land be conveyed to A for life, and on his death to B, A's life interest is a particuar estate, and B's interest is a remainder, or estate in remainder.