Hare quota

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.

Hamilton method

The Hamilton method, also known as the method of largest remainders, uses the Hare quota to allocate seats in proportion to votes.

Steps:

1. Calculate the Hare quota.
2. Divide each party's total votes by the Hare quota to get a raw seat count.
3. Assign each party the whole number part of their seat count.
4. Distribute any remaining seats to parties with the largest fractional remainders.

This method ensures a more proportional allocation of seats and is commonly used in electoral systems based on vote shares.

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.

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.

Example

Suppose an STV election using the Hare quota has 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:

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, Brazil, and Guyana use the Hare quota in largest-remainder systems. Costa Rica uses a modified Hare quota for its Legislative Assembly.

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. 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. Typically, largest remainders paired with the Hare quota produces unbiased results that are difficult to manipulate. However, the combination of extremely small districts, no electoral thresholds 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. 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.

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. 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. By contrast, rules based on the Droop quota cannot be manipulated in the same way, as it is never possible for a party to gain seats by splitting.

In Hong Kong

In the , 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%).

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. 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. In 2004, the ADPL joined the Democrats by splitting lists in Kowloon West.

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. 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. 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. As it is only possible to win a single remainder seat, politicians and potential allies can be motivated to diverge rather than to coalesce.

References

References

1. Pukelsheim, Friedrich. (2017). "Favoring Some at the Expense of Others: Seat Biases". Springer International Publishing.
2. Humphreys, Proportional Representation (1911), p. 138
3. Pukelsheim, Friedrich. (2017). "Quota Methods of Apportionment: Divide and Rank". Springer International Publishing.
4. Baily, PR in large constituencies (1872) (hathitrust online)
5. Baily, PR in large constituencies (1872) (hathitrust online)
6. {{in lang. pt [http://www.planalto.gov.br/ccivil_03/Leis/L4737.htm Brazilian Electoral Code, (Law 4737/1965), Articles 106 to 109.]
7. Pukelsheim, Friedrich. (2017). "Proportional Representation". SpringerLink.
8. Tsang, Jasper Yok Sing. (11 March 2008). "Divide then conquer". [[South China Morning Post]].
9. Ma Ngok. (25 July 2008)
10. Choy. Ivan Chi Keung. (31 July 2008)
11. Carey, John M.. "Electoral Formula and Fragmentation in Hong Kong".