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In the study of apportionment, the Hare quota (sometimes called the simple, ideal, or Hamilton quota) 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 and where every vote is used to elect someone. 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.

The quota continues to be used in setting electoral thresholds, as well as for calculating apportionments by the largest remainder method (LR-Hare) or other quota-based methods of proportional representation. In such cases, the Hare quota gives unbiased apportionments that favor neither large nor small parties.^[1] However in certain circumstances when the Hare quota is used, a party with a majority of votes in the district would not win a majority of the seats.^[2]

In 1792, a U.S. national figure, Alexander Hamilton, proposed to use the Hare quota to establish representation by population, by fairly allocating seats in the House of Representatives to each state, with the largest remainder method used to allocate seats to states with remaining leftover partial quota units of population.[1][2]

Formula

The Hare quota may be given as:

{\frac {{\mbox{total}}\;{\mbox{votes}}}{{\mbox{total}}\;{\mbox{seats}}}}

where

Total votes = the total valid poll; that is, the number of valid (unspoilt) votes cast in an election.
Total seats = the total number of seats to be filled in the election.

Use in STV

In an STV election a candidate who reaches the quota is elected while any votes a candidate receives above the quota in many cases have the opportunity to be transferred to another candidate in accordance to the voter's next usable marked preference. Thus the quota is used both to determine who is elected and to determine the number of surplus votes when a person is elected with quota. When the Droop quota is used, often about a quota of votes are not used to elect anyone (a much lower proportion that under the first-past-the-post voting system) so the quota is a cue to the number of votes that are used to actually elect someone.^[3]

The Hare quota was devised by Thomas Hare, one of the first to work out a complete STV system. In 1868, Henry Richmond Droop (1831–1884) invented the Droop quota as an alternative to the Hare quota. The Hare quota today is rarely used with STV due to fact that Droop is considered more fair to both large parties and small parties.

The number of votes in the quota is determined by the district magnitude of the district in conjunction with the number of valid votes cast.^[4]

Example

To see how the Hare quota works in an STV election, imagine an election in which there are two seats to be filled and three candidates: Andrea, Brad, and Carter. One hundred voters voted, each casting one vote and marking a back-up preference, to be used only in case the first preference candidate is un-electable or elected with surplus. There are 100 ballots showing preferences as follows:

Number of voters	60 voters	26 voters	14 voters
1st preference	Andrea	Brad	Carter
2nd preference	Carter	Andrea	Andrea

Because there are 100 voters and 2 seats, the Hare quota is:

{\frac {100}{2}}=50

To begin the count the first preferences cast for each candidate are tallied and are as follows:

Andrea: 60
Brad: 26
Carter: 14

Andrea has reached the quota and is declared elected. She has 10 votes more than the quota so these votes are transferred to Carter, as specified on the ballots. The tallies of the remaining candidates therefore now become:

Brad: 26
Carter: 24

At this stage, there are only two candidates remaining and one seat open. The most-popular candidate is declared elected; the other is declared defeated.

Although Brad has not reached the quota, he is declared elected since he has more votes than Carter.

The winners are therefore Andrea and Brad.

Use in party-list PR

Hong Kong and Brazil use the Hare quota in largest-remainder systems.

In Brazil's largest remainder system the Hare quota is used to set the basic number of seats allocated to each party or coalition. Any remaining seats are allocated according to the D'Hondt method.^[5] This procedure is used for the Federal Chamber of Deputies, State Assemblies, Municipal and Federal District Chambers.

In Hong Kong

For geographical constituencies, the SAR government adopted weakly-proportional representation using the largest remainder method with Hare quota in 1997^{[citation needed]}. Typically, largest remainders paired with the Hare quota produces unbiased results that are difficult to manipulate.^[1] However, the combination of extremely small districts, no electoral thresholds, and low led to a system that parties could manipulate using careful vote management.

By running candidates on separate tickets, Hong Kong parties aimed to ensure they received no seats in the first step of apportionment, but still received enough votes to take several of the remainder seats when running against a divided opposition.^[6] The Democratic Party, for example, filled three separate tickets in the 8-seat New Territories West constituency in the 2008 Legislative Council elections. In the 2012 election, no candidate list won more than one seat in any of the six PR constituencies (a total of 40 seats). In Hong Kong, the Hare quota has effectively created a multi-member single-vote system in the territory.^[7]^[8]^[9]

Mathematical properties

In situations where parties' total share of the vote varies randomly, the Hare quota is the unique unbiased quota for an electoral system based on vote-transfers or quotas.^[1] However, if the quota is used in small constituencies with no electoral threshold, it is possible to manipulate the system by running several candidates on separate lists, allowing each to win a remainder seat with less than a full quota. This can make the method behave like the single non-transferable vote in practice, as has happened in Hong Kong.^[9] By contrast, Droop quota cannot be manipulated in the same way, as it is never possible for a party to gain seats by splitting.^[1]

References

^ ^a ^b ^c ^d Pukelsheim, Friedrich (2017). "17". Proportional Representation. SpringerLink. pp. 108–109. doi:10.1007/978-3-319-64707-4. ISBN 978-3-319-64707-4.
^ Humphreys, Proportional Representation (1911), p. 138
^ Baily, PR in large constituencies (1872) (hathitrust online)
^ Baily, PR in large constituencies (1872) (hathitrust online)
^ (in Portuguese) Brazilian Electoral Code, (Law 4737/1965), Articles 106 to 109.
^ Tsang, Jasper Yok Sing (11 March 2008). "Divide then conquer". South China Morning Post. Hong Kong. p. A17.
^ Ma Ngok (25 July 2008). 港式比例代表制議會四分五裂 [Hong Kong-style proportional representation is divided]. Ming Pao (in Chinese (Hong Kong)). Hong Kong. p. A31.
^ Choy, Ivan Chi Keung (31 July 2008). 港式選舉淪為變相多議席單票制 [Hong Kong-style elections become a multi-seat multi-seat single-vote system]. Ming Pao (in Chinese (Hong Kong)). Hong Kong. p. A29.
^ ^a ^b Carey, John M. "Electoral Formula and Fragmentation in Hong Kong" (PDF). {{cite journal}}: Cite journal requires |journal= (help)

[:0-1] Pukelsheim, Friedrich (2017). "17". Proportional Representation. SpringerLink. pp. 108–109. doi:10.1007/978-3-319-64707-4. ISBN 978-3-319-64707-4.

[2] Humphreys, Proportional Representation (1911), p. 138

[3] Baily, PR in large constituencies (1872) (hathitrust online)

[4] Baily, PR in large constituencies (1872) (hathitrust online)

[5] (in Portuguese) Brazilian Electoral Code, (Law 4737/1965), Articles 106 to 109.

[6] Tsang, Jasper Yok Sing (11 March 2008). "Divide then conquer". South China Morning Post. Hong Kong. p. A17.

[7] Ma Ngok (25 July 2008). 港式比例代表制議會四分五裂 [Hong Kong-style proportional representation is divided]. Ming Pao (in Chinese (Hong Kong)). Hong Kong. p. A31.

[8] Choy, Ivan Chi Keung (31 July 2008). 港式選舉淪為變相多議席單票制 [Hong Kong-style elections become a multi-seat multi-seat single-vote system]. Ming Pao (in Chinese (Hong Kong)). Hong Kong. p. A29.

[Carey-9] Carey, John M. "Electoral Formula and Fragmentation in Hong Kong" (PDF). {{cite journal}}: Cite journal requires |journal= (help)

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[2]

[3]

[4]

[5]

[6]

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@@ Line 2: / Line 2: @@
 {{Use dmy dates|date=August 2020}}
 {{Electoral systems}}
-The '''Hare quota''' (also known as the '''simple quota''') is a formula used under some forms of [[proportional representation]]. In these [[voting system]]s the quota is the number of votes that guarantees a candidate, or a party in some cases, captures a seat. The Hare quota is the total number of votes divided by the number of seats to be filled. This is the simplest quota, but the [[Droop quota]] is mostly used currently.
+In the study of [[Apportionment (politics)|apportionment]], the [[Thomas Hare (political scientist)|'''Hare''']] '''quota''' (sometimes called the '''simple''', '''ideal''', or [[Alexander Hamilton|'''Hamilton''']] '''quota''') is the number of voters represented by each legislator under an idealized system of [[proportional representation]], where every legislator [[One man, one vote|represents an equal number of voters]] and where every vote is used to elect someone. 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]].
-The Hare quota can be used in the [[single transferable vote]] (STV-Hare) system and the [[largest remainder method]] (LR-Hare) and other [[quota rule]] compatible methods of [[party-list proportional representation]]. Both versions are named after the political scientist [[Thomas Hare (political scientist)|Thomas Hare]], but the largest remainder method in which it is used is also sometimes called the '''Hare–Niemeyer method''' (after [[Horst Niemeyer]]) or the '''Hamilton method''' (after [[Alexander Hamilton]]).
+The quota continues to be used in setting [[Electoral threshold|electoral thresholds]], as well as for calculating [[Apportionment (politics)|apportionments]] by the [[largest remainder method]] (LR-Hare) or other [[quota rule|quota-based]] methods of [[proportional representation]]. In such cases, the Hare quota gives unbiased apportionments that favor neither large nor small parties.<ref name=":0">{{Cite book |last=Pukelsheim |first=Friedrich |title=Proportional Representation |date=2017 |publisher=SpringerLink |isbn=978-3-319-64707-4 |pages=108-109 |chapter=17 |doi=10.1007/978-3-319-64707-4}}</ref> However in certain circumstances when the Hare quota is used, a party with a majority of votes in the district would not win a majority of the seats.<ref>Humphreys, Proportional Representation (1911), p. 138</ref>
+In 1792, a U.S. national figure, [[Alexander Hamilton]], proposed to use the Hare quota to establish representation by population, by fairly allocating seats in the House of Representatives to each state, with the largest remainder method used to allocate seats to states with remaining leftover partial quota units of population.[https://study.com/academy/lesson/hamiltons-method-of-apportionment-in-politics.html#:~:text=Within%20Hamilton's%20Method%20of%20Apportionment,value%20is%20usually%20a%20decimal.][https://people.math.osu.edu/maharry.1/1116Sp2013/Math1116Chapter4ApportionmentDay2Done.pdf]
 ==Formula==
@@ Line 15: / Line 17: @@
 == Use in STV ==
+In an STV election a candidate who reaches the quota is elected while any votes a candidate receives above the quota in many cases have the opportunity to be transferred to another candidate in accordance to the voter's next usable marked preference. Thus the quota is used both to determine who is elected and to determine the number of surplus votes when a person is elected with quota. When the Droop quota is used, often about a quota of votes are not used to elect anyone (a much lower proportion that under the [[first-past-the-post voting]] system) so the quota is a cue to the number of votes that are used to actually elect someone.<ref>Baily, PR in large constituencies (1872) (hathitrust online)</ref>
-The Hare quota is the simplest quota that can be used in elections held under the STV system. In an STV election a candidate who reaches the quota is elected while any votes a candidate receives above the quota are transferred to another candidate.
-The Hare quota was devised by [[Thomas Hare (political scientist)|Thomas Hare]], one of the earliest supporters of STV. In 1868, [[Henry Richmond Droop]] (1831–1884) invented the [[Droop quota]] as an alternative to the Hare quota, and Droop is now widely used, the Hare quota today being rarely used with STV.
+The Hare quota was devised by [[Thomas Hare (political scientist)|Thomas Hare]], one of the first to work out a complete STV system. In 1868, [[Henry Richmond Droop]] (1831–1884) invented the [[Droop quota]] as an alternative to the Hare quota. The Hare quota today is rarely used with STV due to fact that Droop is considered more fair to both large parties and small parties.
+The number of votes in the quota is determined by the [[district magnitude]] of the district in conjunction with the number of valid votes cast.<ref>Baily, PR in large constituencies (1872) (hathitrust online)</ref>
 === Example ===
-To see how the Hare quota works in an STV election, imagine an election in which there are 2 seats to be filled and 3 candidates: Andrea, Brad, and Carter. One hundred voters voted, each casting one vote and marking a back-up preference to be used only in case the first preference candidate is un-electable or elected with surplus. There are 100 ballots showing preferences as follows:
+To see how the Hare quota works in an STV election, imagine an election in which there are two seats to be filled and three candidates: Andrea, Brad, and Carter. One hundred voters voted, each casting one vote and marking a back-up preference, to be used only in case the first preference candidate is un-electable or elected with surplus. There are 100 ballots showing preferences as follows:
 {| class="wikitable" border="1"
 |'''Number of voters'''
 | valign="top" |
-'''60 voters'''
+voters
 |valign=top|
-'''26 voters'''
+voters
 | valign="top" |
-'''14 voters'''
+voters
 |-
 |'''1st preference'''
@@ Line 49: / Line 53: @@
 *Andrea: '''60'''
+*Brad: 26
 *Carter: 14
-*Brad: 26
-Andrea has more than 50 votes. She therefore has reached the quota and is declared elected. She has 10 votes more than the quota so these votes are [[Single transferable vote|transferred]] to Carter, as specified on the ballots. The tallies therefore now become:
+Andrea has reached the quota and is declared elected. She has 10 votes more than the quota so these votes are [[Single transferable voting|transferred]] to Carter, as specified on the ballots. The tallies of the remaining candidates therefore now become:
+*Brad: '''26'''
 *Carter: 24
-*Brad: '''26'''
-At this stage, there are only two candidates remaining and one seat open. The most popular candidate is declared elected and the other is declared defeated.
+At this stage, there are only two candidates remaining and one seat open. The most-popular candidate is declared elected; the other is declared defeated.
 Although Brad has not reached the quota, he is declared elected since he has more votes than Carter.
@@ Line 66: / Line 70: @@
 Hong Kong and Brazil use the Hare quota in largest-remainder systems.
-In [[Brazil]]'s largest remainder system the Hare quota is used to set the minimum number of seats allocated to each party or coalition. Remaining seats are allocated according to the [[D'Hondt method]].<ref>{{in lang|pt}} [http://www.planalto.gov.br/ccivil_03/Leis/L4737.htm Brazilian Electoral Code, (Law 4737/1965), Articles 106 to 109.]</ref> This procedure is used for the Federal Chamber of Deputies, State Assemblies, Municipal and Federal District Chambers.
+In [[Brazil]]'s largest remainder system the Hare quota is used to set the basic number of seats allocated to each party or coalition. Any remaining seats are allocated according to the [[D'Hondt method]].<ref>{{in lang|pt}} [http://www.planalto.gov.br/ccivil_03/Leis/L4737.htm Brazilian Electoral Code, (Law 4737/1965), Articles 106 to 109.]</ref> This procedure is used for the Federal Chamber of Deputies, State Assemblies, Municipal and Federal District Chambers.
-Compared to some similar methods, the use of the Hare quota with the largest remainder method tends to favour the smaller parties at the expense of the larger ones.
-But the opposite was expected in Hong Kong in 1997. For geographical constituencies, the SAR government adopted proportional representation using the largest remainder method with Hare quota in replacement of the first-past-the-post system introduced in 1995. The use of this system was designed to reward the weaker pro-Beijing candidates and dilute the electoral strength of the majority democrats.<ref>Diamond, Larry; Myers, Ramon H. (2001). Elections and Democracy in Greater China. OUP Oxford. pp. 1985–6</ref>
-The Hare-based system did not work as expected and this reality prompted political parties to start to nominate their candidates on separate tickets, as under the system in use that maneuvre may increase the number of seats they obtain.<ref>{{cite news |last=Tsang |first=Jasper Yok Sing |author-link=Jasper Tsang |date=11 March 2008 |title=Divide then conquer |page=A17 |newspaper=[[South China Morning Post]] |location=Hong Kong}}</ref> The [[Democratic Party (Hong Kong)|Democratic Party]], for example, filled three separate tickets in the 8-seat [[New Territories West constituency]] in the [[2008 Hong Kong legislative election|2008 Legislative Council elections]]. In the [[2012 Hong Kong legislative election|2012 election]], no candidate list won more than one seat in any of the six PR constituencies (a total of 40 seats). In Hong Kong the Hare quota system has effectively become a [[Single non-transferable vote|multi-member single-vote system]] in the territory.<ref>{{cite news |author=Ma Ngok |date=25 July 2008 |script-title=zh:港式比例代表制 議會四分五裂 |language=zh-hk |trans-title=Hong Kong-style proportional representation is divided |page=A31 |newspaper=[[Ming Pao]] |location=Hong Kong}}</ref><ref>{{cite news |last=Choy |first=Ivan Chi Keung |date=31 July 2008 |script-title=zh:港式選舉淪為變相多議席單票制 |language=zh-hk |trans-title=Hong Kong-style elections become a multi-seat multi-seat single-vote system |page=A29 |newspaper=[[Ming Pao]] |location=Hong Kong}}</ref> This formula also rewards political alliances and parties of small-to-moderate size and discourages broader unions which led to the fragmentation of the political parties and electoral alliances rather than expanding them.<ref name="Carey">{{cite journal |last=Carey |first=John M. |title=Electoral Formula and Fragmentation in Hong Kong |url=http://sites.dartmouth.edu/jcarey/files/2016/07/Hong-Kong-PR-Formula-Carey-June-2016.pdf}}</ref>
-==Comparison with the Droop quota==
-{{Main|Comparison of the Hare and Droop quotas}}
-The [[Droop quota]] is smaller than the Hare quota, and is considered more efficient when counting ballots—since a candidate needs only the smaller quota to be elected, the winners are often determined with fewer counting rounds. Overall the two quotas give mostly similar results. However the results often differ, particularly with regard to the allocation of the last seat, which is determined after vote transfers. In the above example, using the Droop quota (34), more of Andrea's votes would be transferred with some going to Carter and Carter would win the second seat by having about 34 votes, which would be more than Brad's 26.
-*In a multi-winner election, the Hare quota is kinder to small parties than the Droop quota because they have a slightly better chance to win the final seat, the previous winner's votes being wasted in un-transferred surplus votes. (As well, Droop is smaller than Hare so a small party may have enough votes to pass the Droop quota but not Hare if it had been used.)
-*In an [[open list]] multi-winner election under the Hare quota it is possible for a party supported by a clear majority of voters to receive only a minority of seats if the votes are not dispersed relatively evenly across all the party's candidates. Thus the principle of majority rule favors the Droop quota. {{dubious|date=March 2016}} Single Transferable Voting using either Hare or Droop, being district-level systems that do not guarantee overall proportionality of representation, can see a party that has majority of the votes not take a majority of the seats and see a party with a minority of the votes take a majority of the seats overall (but it happens less often than under [[first-past-the-post voting]]) and the degree of mis-representation is much less than can happen under {{first-past-the-post voting]]).<ref>{{cite web|url=https://www.ourcommons.ca/content/Committee/421/ERRE/Brief/BR8550163/br-external/McCullochStephen-e.pdf |access-date=14 April 2023|website=ourcommons.ca|title=Seven Ways that the Canadian Electoral system is UNFAIR}}</ref>
-*In an Alternative Voting ([[Instant-runoff voting]]) election, an election using preferential voting where there is only one seat to be filled, bare majority (Droop quota) is used. There is no transfer of surplus votes. When the seat has not been filled and there are only two remaining candidates, the candidate with more votes (a majority) is elected.
-As shown in the example, quota does not enter it once the field of candidates is thinned to just one more than the number of remaining open seats. Brad's election would have been the same whether Droop or Hare had been used.
-The Droop quota is today the most frequently used quota for STV elections.
-==Criticisms==
-The Hare quota is often criticised for favouring the smaller parties at the expense of the larger ones.{{citation needed|date=September 2020}}
-Under certain circumstances, the Hare quota can also lead to a situation in which the outcome of the election depends on the order in which the votes were counted. If a candidate fulfils the quota, it is not obvious which of their single transferable votes should be distributed and which should get "used up" electing the candidate. This problem can be eliminated by fully distributing fractional votes rather than partially distributing full votes, as in the [[Counting single transferable votes|Gregory system]], which is used in [[Irish Senate]] elections.
-=== The Hare quota in Hong Kong's largest remainder system, 1998–2012 ===
-In some cases, it leads to the fragmentation and infighting of the electoral alliances. In Hong Kong, the [[1998 Hong Kong legislative election|1998 Legislative Council election]], [[pro-democracy camp]] organization [[The Frontier (Hong Kong)|The Frontier]] fails to co-ordinate two former legislators (1995–1997) [[Lee Cheuk-yan]] and [[Leung Yiu-chung]] into a two-candidate list running for [[New Territories West (constituency)|New Territories West (NT West) 5-seat constituency]], and Leung left The Frontier, running as Nonpartisan candidate with the support of [[Neighbourhood and Worker's Service Centre]] in NT West and Lee running as Frontier candidate in NT West. Lee and Leung won the last two seats by around 10% votes (Lee 12.45% and Leung 10.30%), in case they ran in a single list with same election result(12.45% + 10.30% = 22.75%), they would win the first seat by full quota (20% as a 5-seat constituency) and the remainder(2.75%) is smaller than the candidate list standing for [[Indigenous inhabitants of the New Territories]], which leaded by [[vice-chairman]] of the [[Heung Yee Kuk]] - [[Daniel Lam|Lam Wai-keung]] (6.91%), this election result mean "infighting" may benefit the political alliance.
+=== In Hong Kong ===
-In [[2000 Hong Kong legislative election]], the second legislative election using the Hare quota largest remainder method, fragmentation and infighting within the parties and camps were shown because political parties began to split their lists in order to waste fewer votes as purchasing seats with remainder votes is always more efficient than purchasing them with full quotas under the Hare quota.<ref name="Carey"/> For instance, the [[Democratic Party (Hong Kong)|Democratic Party]] ran multiple lists by filling two lists in [[New Territories East (constituency)|New Territories East]] and three lists in [[New Territories West (constituency)|New Territories West]], in which incumbent [[Lee Wing-tat]]'s list was lost to his party colleague [[Albert Chan]]'s list in the latter constituency.<ref name="Carey"/> In 2004, the [[HKADPL|ADPL]] joined the Democrats by splitting lists in [[Kowloon West (1998 constituency)|Kowloon West]].
+For geographical constituencies, the SAR government adopted weakly-proportional representation using the largest remainder method with Hare quota in 1997{{Cn|date=February 2024}}. Typically, largest remainders paired with the Hare quota produces unbiased results that are difficult to manipulate.<ref name=":0" /> However, the combination of extremely small districts, no [[Electoral threshold|electoral thresholds]], and low  led to a system that parties could manipulate using careful vote management.
+By running candidates on separate tickets, Hong Kong parties aimed to ensure they received no seats in the first step of apportionment, but still received enough votes to take several of the remainder seats when running against a divided opposition.<ref>{{cite news |last=Tsang |first=Jasper Yok Sing |author-link=Jasper Tsang |date=11 March 2008 |title=Divide then conquer |page=A17 |newspaper=[[South China Morning Post]] |location=Hong Kong}}</ref> The [[Democratic Party (Hong Kong)|Democratic Party]], for example, filled three separate tickets in the 8-seat [[New Territories West constituency]] in the [[2008 Hong Kong legislative election|2008 Legislative Council elections]]. In the [[2012 Hong Kong legislative election|2012 election]], no candidate list won more than one seat in any of the six PR constituencies (a total of 40 seats). In Hong Kong, the Hare quota has effectively created a [[Single non-transferable vote|multi-member single-vote system]] in the territory.<ref>{{cite news |author=Ma Ngok |date=25 July 2008 |script-title=zh:港式比例代表制 議會四分五裂 |language=zh-hk |trans-title=Hong Kong-style proportional representation is divided |page=A31 |newspaper=[[Ming Pao]] |location=Hong Kong}}</ref><ref>{{cite news |last=Choy |first=Ivan Chi Keung |date=31 July 2008 |script-title=zh:港式選舉淪為變相多議席單票制 |language=zh-hk |trans-title=Hong Kong-style elections become a multi-seat multi-seat single-vote system |page=A29 |newspaper=[[Ming Pao]] |location=Hong Kong}}</ref><ref name="Carey">{{cite journal |last=Carey |first=John M. |title=Electoral Formula and Fragmentation in Hong Kong |url=http://sites.dartmouth.edu/jcarey/files/2016/07/Hong-Kong-PR-Formula-Carey-June-2016.pdf}}</ref>
-In [[2008 Hong Kong legislative election|2008]], [[pro-Beijing camp|pro-Beijing]] [[DABHK|DAB]] and [[Regina Ip|Savantas Policy Institute]] candidate lists aimed to win 2 seats for their list in 6-seat [[Hong Kong Island (1998 constituency)|Hong Kong Island constituency]], however due to high popularity between two lists in pro-Beijing camp, both lists got around 19% votes, which lost the "third" seat of pro-Beijing camp to [[Civic Party]](26.4% votes) [[Audrey Eu]] who won the seat by the remainder(26.4% = 16.6% + 9.8% which is larger than 19% = 16.6% + 2.4%), the "meaningful" pro-Beijing camp strategy would be trying to win 3 seats by distributing the votes evenly into 3 candidate lists.
+== Mathematical properties ==
-In [[2012 Hong Kong legislative election|2012]], the [[pro-Beijing camp|pro-Beijing]] [[DABHK|DAB]] deployed multiple lists for the first time. As a result, of the 34 seats captured by lists from the two major camps, only three were won by full quota.<ref name="Carey"/> Due to strong network of pro-Beijing camp with its affiliated grassroots and community organisations, pro-Beijing camp was able to split the votes evenly to get more candidates to be elected with fewer votes, pro-Beijing camp won the last seats in 4 out of 5 constituencies and total 17 of 35 geographical Constituency seats with 42.66% shares of votes, compared with Pan-democrats 56.24% shares of votes winning 18 seats.
+In situations where parties' total share of the vote varies randomly, the Hare quota is the unique [[Seat bias|unbiased]] quota for an electoral system based on vote-transfers or quotas.<ref name=":0" /> However, if the quota is used in small [[constituencies]] with no [[electoral threshold]], it is possible to manipulate the system by running several candidates on separate lists, allowing each to win a remainder seat with less than a full quota. This can make the method behave like the [[single nontransferable vote|single non-transferable vote]] in practice, as has happened in [[Hong Kong]].<ref name="Carey" /> By contrast, [[Droop quota]] cannot be manipulated in the same way, as it is never possible for a party to gain seats by splitting.<ref name=":0" /><!--
+=== In Hong Kong ===
-The Hare quota used in Hong Kong's largest remainder system also encourages the multiplication of political parties and nonpartisan candidates.<ref name="Carey"/> The vote share of the largest party Democratic Party dropped significantly, from 43 per cent in 1998 to 29 per cent in 2000, to 21 per cent in 2004, rising slightly to 20 per cent in 2008 and falling again to 14 per cent in 2012.<ref name="Carey"/> As under the Hare quota largest remainder method the broad alliance wins little or no seat bonus, whereas much smaller lists win larger bonuses in the elections, politicians and potential allies are motivated to diverge rather than to coalesce.<ref name="Carey"/> On the other hands, candidate with radical stand won seats starting from 2004, which expanded the exposure of radical stand among Hong Kong general public.
+In the [[1998 Hong Kong legislative election|]], [[pro-democracy camp]] organization [[The Frontier (Hong Kong)|The Frontier]] fails to co-ordinate two former legislators (1995–1997) [[Lee Cheuk-yan]] and [[Leung Yiu-chung]] into a two-candidate list running for [[New Territories West (constituency)|New Territories West (NT West) 5-seat constituency]], and Leung left The Frontier, running as Nonpartisan candidate with the support of [[Neighbourhood and Worker's Service Centre]] in NT West and Lee running as Frontier candidate in NT West. Lee and Leung won the last two seats by around 10% votes (Lee 12.45% and Leung 10.30%), in case they ran in a single list with same election result(12.45% + 10.30% = 22.75%), they would win the first seat by full quota (20% as a 5-seat constituency) and the remainder(2.75%) is smaller than the candidate list standing for [[indigenous inhabitants of the New Territories]], which led by [[vice-chairman]] of the [[Heung Yee Kuk]] - [[Daniel Lam|Lam Wai-keung]] (6.91%).
+In [[2000 Hong Kong legislative election]], the second legislative election using the Hare quota largest remainder method, fragmentation and infighting within the parties and camps were shown because political parties began to split their lists in order to waste fewer votes as acquiring seats with remainder votes can be more efficient than purchasing them with full quotas under the Hare quota.<ref name="Carey"/> For instance, the [[Democratic Party (Hong Kong)|Democratic Party]] ran multiple lists by filling two lists in [[New Territories East (constituency)|New Territories East]] and three lists in [[New Territories West (constituency)|New Territories West]], in which incumbent [[Lee Wing-tat]]'s list was lost to his party colleague [[Albert Chan]]'s list in the latter constituency.<ref name="Carey"/> In 2004, the [[HKADPL|ADPL]] joined the Democrats by splitting lists in [[Kowloon West (1998 constituency)|Kowloon West]].
-The adoption of the Hare quota system by the Beijing government on the eve of the transfer of sovereignty of Hong Kong was seen as the measure to curb the dominance of the [[pro-democracy camp]] who dominated in the [[1995 Hong Kong legislative election|1995 elections]] with [[single-member district]] (SMD) plurality system, winning 17 of the 20 directly elected seats. [[Lau Siu-kai]], political scientist who served as the convenor of the Subgroup on Electoral Methods for the First Legislature (SEMFL) appointed by [[National People's Congress]] explained the reason behind the Beijing installation of the Hare quota largest remainder method:<ref name="Carey"/>
+In [[2012 Hong Kong legislative election|2012]], the [[pro-Beijing camp|pro-Beijing]] [[DABHK|DAB]] deployed multiple lists for the first time. As a result, of the 34 seats captured by lists from the two major camps, only three were won by full quota.<ref name="Carey"/> Due to strong network of pro-Beijing camp with its affiliated grassroots and community organisations, pro-Beijing camp was able to split the votes evenly to get more candidates to be elected with fewer votes, pro-Beijing camp won the last seats in 4 out of 5 constituencies and total 17 of 35 geographical Constituency seats with 42.66% shares of votes, compared with pan-democrats 56.24% shares of votes winning 18 seats.
-{{blockquote|The Communist regime...realized full well that the appearance of political parties was inevitable whenever there were elections, particularly popular elections. It nevertheless did not want to see the rise of anti-Communist political parties in Hong Kong. Nor could China tolerate the domination of the legislature by a powerful political party, which then could use the veto powers at the legislature's disposal to 'blackmail' the executive or to bring about stalemate between the executive and legislative branches...In devising the electoral arrangements for the first legislature of the HKSAR, therefore, China strove to impede the development of local political parties, particularly those with pro-democratic and anti-Communist inclinations.<ref name="Carey"/>}}
+The Hare quota used in Hong Kong's largest remainder system also encourages the multiplication of political parties and nonpartisan candidates.<ref name="Carey"/> The vote share of the largest party Democratic Party dropped significantly, from 43 per cent in 1998 to 29 per cent in 2000, to 21 per cent in 2004, rising slightly to 20 per cent in 2008 and falling again to 14 per cent in 2012.<ref name="Carey"/> As it is only possible to win a single remainder seat, politicians and potential allies can be motivated to diverge rather than to coalesce.<ref name="Carey"/>
-By installing the [[single non-transferable vote]] (SNTV) system, Beijing ensured the pro-Beijing politicians who received only roughly 40 per cent of the support and were defeated by the pro-democratic candidates in 1995 could return a corresponding number of seats in the legislature.<ref name="Carey"/>
+-->
 ==References==
-{{Reflist}}{{Majorities and quotas}}{{voting systems}}
+{{Reflist}}
+{{Majorities and quotas}}
+{{voting systems}}
 {{DEFAULTSORT:Hare Quota}}
 [[Category:Electoral system quotas]]
 [[Category:Single transferable vote]]
+[[Category:Apportionment methods]]

v t e Types of majority and other electoral quotas
Single winner (majority)	Plurality Majority Absolute majority Supermajority Double majority
Electoral quotas	Hare quota Droop quota Imperiali quota (pseudoquota)
Other	Electoral threshold