Hare quota

# Hare quota

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Encyclopedia
The Hare quota is a formula used under some forms of the Single Transferable Vote
Single transferable vote
The single transferable vote is a voting system designed to achieve proportional representation through preferential voting. Under STV, an elector's vote is initially allocated to his or her most preferred candidate, and then, after candidates have been either elected or eliminated, any surplus or...

(STV) system and the largest remainder method
Largest remainder method
The largest remainder method is one way of allocating seats proportionally for representative assemblies with party list voting systems...

of party-list proportional representation
Party-list proportional representation
Party-list proportional representation systems are a family of voting systems emphasizing proportional representation in elections in which multiple candidates are elected...

. In these voting system
Voting system
A voting system or electoral system is a method by which voters make a choice between options, often in an election or on a policy referendum....

s the quota is the minimum number of votes required for a party or candidate to capture a seat.

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, one of the earliest supporters of STV.

In Brazil
Brazil
Brazil , officially the Federative Republic of Brazil , is the largest country in South America. It is the world's fifth largest country, both by geographical area and by population with over 192 million people...

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
D'Hondt method
The d'Hondt method is a highest averages method for allocating seats in party-list proportional representation. The method described is named after Belgian mathematician Victor D'Hondt who described it in 1878...

. 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. Thus in Hong Kong
Hong Kong
Hong Kong is one of two Special Administrative Regions of the People's Republic of China , the other being Macau. A city-state situated on China's south coast and enclosed by the Pearl River Delta and South China Sea, it is renowned for its expansive skyline and deep natural harbour...

the use of the Hare quota has prompted political parties to nominate their candidates on separate tickets, as under this system this may increase the number of seats they obtain. The Democratic Party
Democratic Party (Hong Kong)
The Democratic Party is a pro-democracy political party in Hong Kong. It was established on 2 October 1994. The party is currently the second largest party in the Legislative Council, headed by Chairman Albert Ho Chun-yan and, following the November 2008 merger with the Frontier, had around 745...

, for example, filled 3 separate tickets in the 8-seat New Territories West constituency in the 2008 Legislative Council elections. In Hong Kong the Hare quota system has effectively become a multi-member single-vote system
Single non-transferable vote
The single non-transferable vote or SNTV is an electoral system used in multi-member constituency elections.- Voting :In any election, each voter casts one vote for one candidate in a multi-candidate race for multiple offices. Posts are filled by the candidates with the most votes...

in the territory.

In 1868 Henry Richmond Droop
Henry Richmond Droop
Henry Richmond Droop * was an English mathematician. He is widely credited with devising the Droop quota that is used today in the common voting system known as the Single Transferable Vote. He also may have been the first to write down what later became known as Duverger's Law, in 1869.He married...

(1831–1884) invented the Droop quota
Droop Quota
The Droop quota is the quota most commonly used in elections held under the Single Transferable Vote system. It is also sometimes used in elections held under the largest remainder method of party-list proportional representation . In an STV election the quota is the minimum number of votes a...

as a fairer alternative to the Hare quota, and the Hare quota is today rarely used with STV.

## Formula

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.

## An example of use in STV

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, Carter and Brad. There are 100 voters as follows:
 60 voters Andrea Carter 14 voters Carter 26 voters Brad Andrea

There are 100 voters and 2 seats. The Hare quota is therefore:

To begin the count the first preferences cast for each candidate are tallied and are as follows:
• Andrea: 60
• 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
Single transferable vote
The single transferable vote is a voting system designed to achieve proportional representation through preferential voting. Under STV, an elector's vote is initially allocated to his or her most preferred candidate, and then, after candidates have been either elected or eliminated, any surplus or...

to Carter, as specified on the ballots. The tallies therefore become:
• Carter: 24

Result: The elected candidates are Andrea and Brad.

## Comparison with the Droop quota

The Droop quota
Droop Quota
The Droop quota is the quota most commonly used in elections held under the Single Transferable Vote system. It is also sometimes used in elections held under the largest remainder method of party-list proportional representation . In an STV election the quota is the minimum number of votes a...

is smaller than the Hare quota, and is more efficient when counting ballots since a candidate needs only the smaller quota to be elected. Overall the two quotas give somewhat similar results since a candidate is bound to be elected once they achieve the Droop quota, however the results often differ, particularly with regard to the allocation of the last seat, based on the transfer of preferences. In the above example, using the Droop quota, Carter would be allocated the second seat in preference to Brad, by 40 votes to 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.
• In an open list
Open list
Open list describes any variant of party-list proportional representation where voters have at least some influence on the order in which a party's candidates are elected...

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 favours the Droop quota
• In an STV election in which there is only one seat to be filled (in other words an Instant Run-off Voting
Instant-runoff voting
Instant-runoff voting , also known as preferential voting, the alternative vote and ranked choice voting, is a voting system used to elect one winner. Voters rank candidates in order of preference, and their ballots are counted as one vote for their first choice candidate. If a candidate secures a...

election) the Hare quota is inapplicable, as the quota would be 100% of the votes cast.

The difference between the two quotas comes down to what the quota implies. Winners elected under a Hare system represent that proportion of the electorate; winners under a Droop system were elected by that proportion of the electorate.

The Droop quota is today the most frequently used quota for STV elections.