Hare quota

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The Hare quota (also known as the simple quota) is a formula used under some forms of the Single Transferable Vote (STV) system and the largest remainder method of party-list proportional representation. In these voting systems 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 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.^[1] 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 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.^[2] 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 system has effectively become a multi-member single-vote system in the territory.^[3]^[4]

In 1868 Henry Richmond Droop (1831–1884) invented the Droop quota 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:

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

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

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
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 transferred to Carter, as specified on the ballots. The tallies therefore now become:

Carter: 24
Brad: 26

Although Brad has not reached the quota, he is declared elected since only two candidates remain and he has more votes than Carter. The winners are therefore Andrea and Brad.

Comparison with the Droop quota

Main article: 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 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 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
In an STV election in which there is only one seat to be filled (in other words an Instant Run-off Voting election) the Hare and Droop quotas are equivalent, as when there are 2 remaining candidates, the candidate with the least votes would be eliminated.

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

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

References

↑ (Portuguese) Brazilian Electoral Code, (Law 4737/1965), Articles 106 to 109.
↑ Tsang, Jasper Yok Sing: Divide then conquer, South China Morning Post, Page A17, 11 March 2008
↑ (traditional Chinese) Ma, Ngok, 港式比例代表制議會四分五裂, Ming Pao, Page A31, 25 July 2008
↑ (traditional Chinese (HK)) Choy, Ivan Chi Keung, 港式選舉淪為變相多議席單票制, Ming Pao, Page A29, 31 July 2008

Types of majority

Single member	Plurality Majority Supermajority Double majority

Multi-member (election threshold)	Hare quota Droop quota Imperiali quota Hagenbach-Bischoff quota

Voting systems

Part of the Politics and Election series

Single-winner voting system	Approval voting Borda count Bucklin voting Contingent vote Coombs' method Copeland's method Exhaustive ballot First-past-the-post voting Instant-runoff voting Kemeny–Young method Simple majoritarianism Minimax Condorcet Nanson's method Plurality Positional voting system Range voting Ranked pairs Schulze method Two-round system

Proportional representation	Mixed-member Party-list Single transferable vote Schulze STV CPO-STV Highest averages method Sainte-Laguë D'Hondt Largest remainder method Alternative vote Plus Closed list Open list Overhang seat Underhang seat

Semi-proportional representation	Parallel voting Single non-transferable vote Cumulative voting Limited voting Proportional approval voting Sequential proportional approval voting Satisfaction approval voting

Usage	Table of voting systems by country

Voting system criterion	Condorcet criterion Condorcet loser criterion Consistency criterion Independence of clones Independence of irrelevant alternatives Independence of Smith-dominated alternatives Later-no-harm criterion Majority criterion Majority loser criterion Monotonicity criterion Mutual majority criterion Pareto efficiency Participation criterion Plurality criterion Resolvability criterion Reversal symmetry Smith criterion

Voting system quotas	Droop quota Hagenbach-Bischoff quota Hare quota Imperiali quota

Other	Ballot Vote counting system Election threshold First-preference votes Spoilt vote Sortition

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