Jump to content

Hare quota

From Wikipedia, the free encyclopedia

In the study of apportionment, the Hare quota (sometimes called the simple quota or Hamilton quota) is the number of voters represented by each legislator under a system of proportional representation. In these voting systems, 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.

The Hare quota was used in the original proposal for a single transferable vote (STV-Hare) system, but has since been almost entirely supplanted for this use by the more mathematically-accurate Droop quota.

However, 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 use cases, the Hare quota gives unbiased apportionments that favor neither large nor small parties.[1]


The Hare quota may be given as:


  • 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[edit]

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.[2]

The Hare quota was devised by Thomas Hare, the first to identify of STV. In 1868, Henry Richmond Droop (1831–1884) invented the Droop quota as an alternative to the Hare quota. The Droop quota , the Hare quota today being 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.[3]


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:

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 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 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 and 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[edit]

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.[4] This procedure is used for the Federal Chamber of Deputies, State Assemblies, Municipal and Federal District Chambers.

In Hong Kong[edit]

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.[5] 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.[6][7] This situation rewards political alliances and parties of small-to-moderate size and discourages broader unions, leading to the fragmentation of political parties and electoral alliances.[8]

Comparison with the Droop quota[edit]


The Hare quota is often criticised for favouring the smaller parties at the expense of the larger ones.[citation needed]

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. Under the whole vote method of transferring surplus votes, when a candidate fulfils the quota, it is not obvious which of their votes should be distributed as surplus votes and which should get "used up" electing the candidate, staying with the candidate as the quota. Rather than partially distributing full votes, as under the whole vote method, one can fully distribute fractional votes as in the Gregory system, which is used in Irish Senate elections. The whole vote method used in Ireland's lower house elections sorts transfers by next usable preference. STV used in Cambridge (Mass.) transfers randomly which more or less reflects the make-up of the successful candidate's overall votes.

The Hare quota in Hong Kong's largest remainder system, 1998–2012[edit]

In some cases, it leads to the fragmentation and infighting of the electoral alliances. In Hong Kong, the 1998 Legislative Council election, pro-democracy camp organization 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 (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 - Lam Wai-keung (6.91%), this election result means "infighting" may benefit the political alliance.

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.[8] For instance, the Democratic Party ran multiple lists by filling two lists in New Territories East and three lists in 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.[8] In 2004, the ADPL joined the Democrats by splitting lists in Kowloon West.

In 2008, pro-Beijing DAB and Savantas Policy Institute candidate lists aimed to win 2 seats for their list in 6-seat 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.

In 2012, the pro-Beijing 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.[8] 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.

The Hare quota used in Hong Kong's largest remainder system also encourages the multiplication of political parties and nonpartisan candidates.[8] 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.[8] 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.[8] 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.

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 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:[8]

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.[8]

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.[8]


  1. ^ a b 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. ^ Baily, PR in large constituencies (1872) (hathitrust online)
  3. ^ Baily, PR in large constituencies (1872) (hathitrust online)
  4. ^ (in Portuguese) Brazilian Electoral Code, (Law 4737/1965), Articles 106 to 109.
  5. ^ Tsang, Jasper Yok Sing (11 March 2008). "Divide then conquer". South China Morning Post. Hong Kong. p. A17.
  6. ^ 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.
  7. ^ 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.
  8. ^ a b c d e f g h i j Carey, John M. "Electoral Formula and Fragmentation in Hong Kong" (PDF). {{cite journal}}: Cite journal requires |journal= (help)