Hare quota

In the study ofapportionment,theHarequota(sometimes called thesimple,ideal,orHamiltonquota) is the number of voters represented by each legislator under an idealized system ofproportional representation,where every legislatorrepresents an equal number of voters.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 asingle transferable votesystem, and is still occasionally used, although it has since been largely supplanted by theDroop quota.

The quota continues to be used in settingelectoral thresholds,as well as for calculatingapportionmentsby thelargest remainder method(LR-Hare) or otherquota-basedmethods ofproportional representation.In such use cases, the Hare quota gives unbiased apportionments that favor neither large nor small parties.

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 thefirst-past-the-post votingsystem) so the quota is a cue to the number of votes that are used to actually elect someone.

The Hare quota was devised byThomas Hare,the first to identify of STV. In 1868,Henry Richmond Droop(1831–1884) invented theDroop quotaas an alternative to the Hare quota. The he 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 thedistrict magnitudeof the district in conjunction with the number of valid votes cast.

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 aretransferredto 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 thereforeAndreaandBrad.

Use in party-list PR

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

InBrazil'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 theD'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, noelectoral 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.TheDemocratic Party,for example, filled three separate tickets in the 8-seatNew Territories West constituencyin the2008 Legislative Council elections.In the2012 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 amulti-member single-vote systemin the territory.

Comparison with the Droop quota

Main article:Comparison of the Hare and Droop quotas

Mathematical properties

In situations where parties' total share of the vote varies randomly, the Hare quota is the uniqueunbiasedquota for an electoral system based on vote-transfers or quotas.When the number of seats in eachconstituencyis large andvote managementbecomes impractical (as it requires an unrealistic degree of coordination of voters), the quota becomes fully unbiased.

However, if the quota is used in smallconstituencieswith noelectoral 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 transform the method into a de factosingle nontransferable votesystem, a situation that has been seen inHong Kong.By contrast,Droop's quotacannot be manipulated in the same way, as it is never possible for a party to gain seats by splitting.