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Encyclopedia > D'Hondt method
Electoral methods

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Politics and the Election series A voting system is a means of choosing between a number of options, based on the input of a number of voters. ... For other uses, see Politics (disambiguation). ... This article is about the political process. ...

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The D'Hondt method (mathematically but not operationally equivalent to Jefferson's method, and Budder-Ofer method) is a highest averages method for allocating seats in party-list proportional representation. The method is named after Belgian mathematician Victor D'Hondt. This system is less proportional than the other popular divisor method, Sainte-Laguë, because D'Hondt slightly favors large parties and coalitions over scattered small parties, whereas Sainte-Laguë is neutral. Single-winner voting systems are voting systems in which a predetermined constituency elects a single person to some office; they contrast generally with proportional representation, in which constituencies are combined to elect several representatives at once. ... An example of a plurality ballot. ... An example of runoff voting. ... The exhaustive ballot is a voting system used to elect a single winner. ... Preferential voting (or preference voting) is a type of ballot structure used in several electoral systems in which voters rank a list or group of candidates in order of preference. ... The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. ... A Condorcet method is a single winner election method in which voters rank candidates in order of preference. ... Copelands method is a Condorcet method in which the winner is determined by finding the candidate with the most pairwise victories. ... The Kemeny-Young method is a voting system that uses preferential ballots, a tally table, and sequence scores to identify the most popular choice, and also identify the second-most popular choice, the third-most popular choice, and so on down to the least-popular choice. ... Minimax is often considered to be the simplest of the Condorcet methods. ... The Borda count can be combined with an Instant Runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method. ... It has been suggested that Maximize Affirmed Majorities be merged into this article or section. ... The Schulze method is a voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. ... Bucklin is a voting system that can be used for single-member districts and also multi-member districts. ... The Coombs method, created by Clyde Coombs, is a voting system used for single-winner elections in which each voter rank-orders the candidates. ... Example Instant-runoff voting ballot Instant-runoff voting (IRV) is a voting system most commonly used for single member elections in which voters have one vote, but can rank candidates in order of preference. ... On an approval ballot, the voter can vote for any number of candidates. ... Range voting (also called ratings summation, average voting, cardinal ratings, 0â€“99 voting, or the score system or point system) is a voting system for one-seat elections under which voters score each candidate, the scores are added up, and the candidate with the highest score wins. ... Voters at the voting booths in the US in 1945 Voting systems are methods (algorithms) for groups of people to select one or more options from many, taking into account the individual preferences of the group members. ... Proportional representation (sometimes referred to as full representation, or PR), is a category of electoral formula aiming at a close match between the percentage of votes that groups of candidates (grouped by a certain measure) obtain in elections and the percentage of seats they receive (usually in legislative assemblies). ... A points method ballot design like this one is the most common for governmental elections using cumulative voting. ... Mixed member proportional representation, also termed mixed-member proportional voting and commonly abbreviated to MMP, is a voting system used to elect representatives to numerous legislatures around the world. ... Party-list proportional representation systems are a family of voting systems used in multiple-winner elections (e. ... Open list describes any variant of party-list proportional representation where voters have at least some influence on the (by the political party itself supplied) order in which party candidates are elected. ... Closed list describes the variant of party_list proportional representation where voters can (effectively) only vote for political parties as a whole and thus have no influence on the (party-supplied) order in which party candidates are elected. ... The highest averages method is one way of allocating seats proportionally for representative assemblies with party list voting systems. ... The largest remainder method is one way of allocating seats proportionally for representative assemblies with party list voting systems. ... The Sainte-LaguÃ« method of the highest average (equivalent to Websters method or divisor method with standard rounding) is one way of allocating seats proportionally for representative assemblies with party list voting systems. ... This STV ballot for the Australian Senate illustrates group voting tickets. ... The Additional Member System (AMS) is a voting system in which some representatives are elected from geographic constituencies and others are elected under proportional representation from party lists. ... Parallel voting describes a mixed voting system where voters in effect participate in two separate elections using different systems, and where the results in one election have little or no impact on the results of the other. ... A points method ballot design like this one is the most common for governmental elections using cumulative voting. ... The Single Non-Transferable Vote or SNTV is an electoral system used in multi-member constituency elections. ... Bloc voting (or block voting) refers to a class of voting systems which can be used to elect several representatives from a single multimember constituency. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Sortition, also known as allotment, is a fair method of selection by some form of lottery such as drawing coloured pebbles from a bag. ... The highest averages method is one way of allocating seats proportionally for representative assemblies with party list voting systems. ... Party-list proportional representation systems are a family of voting systems used in multiple-winner elections (e. ... Victor Dâ€™Hondt[1] (20 November 1841 - 30 May 1901) was a Belgian lawyer, professor of civil law at Ghent University, and mathematician. ... The Sainte-LaguÃ« method of the highest average (equivalent to Websters method or divisor method with standard rounding) is one way of allocating seats proportionally for representative assemblies with party list voting systems. ...

The system has also been used in Northern Ireland to allocate the ministerial positions in the Northern Ireland Executive, for the 'top-up' seats in the London Assembly, in some countries during elections to the European Parliament, and during the 1997 Constitution-era for allocating party-list parliamentary seats in Thailand.[1]. A modified form was used for elections in the Australian Capital Territory Legislative Assembly but abandoned in favour of the Hare-Clarke system. Northern Ireland (Irish: , Ulster Scots: Norlin Airlann) is a constituent country of the United Kingdom lying in the northeast of the island of Ireland, covering 5,459 square miles (14,139 kmÂ², about a sixth of the islands total area). ... The Northern Ireland Executive as established by the Northern Ireland Act 1998 is the (currently suspended) executive body for Northern Ireland, answerable to the Northern Ireland Assembly. ... The London Assembly is an elected body that supervises the Greater London Authority and the Mayor of London. ... Elections to the European Parliament were held from June 10, 2004 to June 13, 2004 in the 25 member states of the European Union, using varying election days according to local custom. ... The ACT Legislative Assembly building, as seen from the front The Australian Capital Territory Legislative Assembly (or, more formally and fully, the Legislative Assembly for the Australian Capital Territory) is the unicameral legislature of the Australian Capital Territory. ...

## Contents

After all the votes have been tallied, successive quotients or 'averages' are calculated for each list. The formula for the quotient is $frac{V}{s+1}$, where:

• V is the total number of votes that list received; and
• s is the number of seats that party has been allocated so far (initially 0 for all parties in a list only ballot, but includes the number of seats already won where combined with a separate ballot, as happens in Wales and Scotland).

Whichever list has the highest quotient or average gets the next seat allocated, and their quotient is recalculated given their new seat total. The process is repeated until all seats have been allocated.

The order in which seats allocated to a list are then allocated to individuals on the list is irrelevant to the allocation procedure. It may be internal to the party (a closed list system) or the voters may have influence over it through various methods (an open list system). Closed list describes the variant of party_list proportional representation where voters can (effectively) only vote for political parties as a whole and thus have no influence on the (party-supplied) order in which party candidates are elected. ... Open list describes any variant of party-list proportional representation where voters have at least some influence on the (by the political party itself supplied) order in which party candidates are elected. ...

The rationale behind this procedure (and the Sainte-Laguë procedure) is to allocate seats in proportion to the number of votes a list received, by maintaining the ratio of votes received to seats allocated as close as possible. This makes it possible for parties having relatively few votes to be represented.

An important result of the method is that a single popular candidate can "draw with him" a lot of less-known party colleagues with few personal votes. Also, if the party colleagues with less support fail to pass the threshold, then the elected candidate also represents the failed candidates. For example, candidate B promises to eliminate the dog tax, but is not elected. Then, the votes gained by B benefit party colleague A, who proposes the elimination of dog tax, which was originally B's promise.

## Example

 Party A Party B Party C Party D Party E Votes 340,000 280,000 160,000 60,000 15,000 Seat 1 340,000 280,000 160,000 60,000 15,000 Seat 2 170,000 280,000 160,000 60,000 15,000 Seat 3 170,000 140,000 160,000 60,000 15,000 Seat 4 113,333 140,000 160,000 60,000 15,000 Seat 5 113,333 140,000 80,000 60,000 15,000 Seat 6 113,333 93,333 80,000 60,000 15,000 Seat 7 85,000 93,333 80,000 60,000 15,000 Total Seats 3 3 1 0 0

## D'Hondt and Jefferson

The D'Hondt method is equivalent to the Jefferson method (named after the U.S. statesman Thomas Jefferson) in that they always give the same results, but the method of calculating the apportionment is different. The Jefferson method, invented in 1792 for U.S. congressional apportionment rather than elections, uses a quota as in the Largest remainder method but the quota (called a divisor) is adjusted as necessary so that the resulting quotients, disregarding any fractional remainders, sum to the required total (so the two methods share the additional property of not using all numbers, whether of state populations or of party votes, in the apportioning of seats). One of a range of quotas will accomplish this, and applied to the above example of party lists this extends as integers from 85,001 to 93,333, the highest number always being the same as the last average to which the D'Hondt method awards a seat if it is used rather than the Jefferson method. Thomas Jefferson (13 April 1743 N.S.â€“4 July 1826) was the third President of the United States (1801â€“09), the principal author of the Declaration of Independence (1776), and one of the most influential Founding Fathers for his promotion of the ideals of Republicanism in the United States. ... 1792 was a leap year starting on Sunday (see link for calendar). ... The largest remainder method is one way of allocating seats proportionally for representative assemblies with party list voting systems. ...

## Variations

In some cases, a threshold or barrage is set, and any list which does not receive that threshold will not have any seats allocated to it, even if it received enough votes to otherwise have been rewarded with a seat. Examples of countries using this threshold are Israel (2%), Turkey (10%), Poland (5%, or 8% for coalitions), Romania (5%) and Belgium (5%, on regional basis). In the Netherlands, a party must win enough votes for one full seat (note that this is not necessary in plain D'Hondt), which with 150 seats in the lower chamber gives an effective threshold of 0.67%. In Estonia, candidates receiving the simple quota in their electoral districts are considered elected, but in the second (district level) and third round of counting (nationwide, modified D'Hondt method) mandates are awarded only to candidate lists receiving more than the threshold of 5% of the votes nationally. In party-list proportional representation systems, an election threshold is a clause that stipulates that a party must receive a minimum percentage of votes, either nationally or within a particular district, to get any seats in the parliament. ...

The method can cause a hidden threshold. In Finland's parliamentary elections, there is no official threshold, but the effective threshold is gaining one seat. The country is divided into districts with different numbers of representatives, so there is a hidden threshold, different in each district. The largest district, Uusimaa with 33 representatives, has a hidden threshold of 3%, while the smallest district, South Savo with 6 representatives, has a hidden threshold of 14%. [2] This favors large parties in the small districts.

Some systems allow parties to associate their lists together into a single cartel in order to overcome the threshold, while some systems set a separate threshold for cartels. Smaller parties often form pre-election coalitions to make sure they get past the election threshold. In the Netherlands, cartels (lijstverbindingen) cannot be used to overcome the threshold, but they do influence the distribution of remainder seats; thus, smaller parties can use them to get a chance which is more like that of the big parties. A coalition is an alliance among entities, during which they cooperate in joint action, each in their own self-interest. ...

The D'Hondt method can also be used in conjunction with a quota formula to allocate most seats, applying the D'Hondt method to allocate any remaining seats to get a result identical to that achieved by the standard D'Hondt formula. This variation is known as the Hagenbach-Bischoff System, and is the formula frequently used when a country's electoral system is referred to simply as 'D'Hondt'. The Hagenbach-Bischoff system is a variant of the DHondt method, used for allocating seats in party-list proportional representation. ...

Results from FactBites:

 NationMaster - Encyclopedia: Largest remainder method (1238 words) The largest remainder method requires the number of votes for each party to be divided by a quota representing the number of votes required for a seat, and this gives a notional number of seats to each, usually including an integer and either a fraction or alternatively a remainder. The largest remainder method requires the number of votes for each party to be divided by a quota representing the number of votes required for a seat, and this gives a notional number of seats to each, usually including an integer and either a vulgar fraction or alternatively a remainder. The dHondt method is a method for allocating seats in party-list proportional representation.
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