Hare quota

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 1868 Henry Richmond Droop (1831-1884) invented the Droop quota as a replacement for the Hare quota and today, because it is considered to be technically inferior by some standards (not by all), 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:

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

:$frac\{100\}\{2\}\; =\; 50$

To begin the count the first preferences cast for each candidate are tallied and are as follows:

*Andrea: 60
*Carter: 19
*Brad: 21

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 become:

*Carter: 29
*Brad: 21

No candidate now has a quota so Brad, as the candidate with the fewest votes, is excluded. Carter is now the only remaining candidate. We might continue the count by 'transferring' Brad's votes to Carter. If this is done Carter will reach a quota. However Carter is the only candidate who can win so this step is not necessary.

Result: The elected candidates are Andrea and Carter.

Comparison with the Droop quota

The Droop quota is today the most popular quota for STV elections. The Droop quota is smaller than the Hare quota, and was first suggested because it is the smallest quota that, like the Hare quota, ensures that the number of candidates who reach the quota will not be greater than the number of seats to be filled.

In an STV election in which there is only one seat to be filled (in other words an Instant Run-off Voting election) it is possible to use the Hare quota, which will simply be equal to 100% of votes cast. However, it is more intuitive to use the Droop quota, which will be equal to an absolute majority of votes cast, meaning 50% plus one, and both quotas will achieve the same result. A similar logic governs why the Droop quota should be extended to STV elections with multiple winners as well, and replace the Hare quota. When voters have only one vote -- the single non-transferable vote system -- a candidate is sure to win if reaching the Droop quota.

The Hare quota is generally kinder to small parties than the Droop quota because they have a better chance to win the final seat. This can mean more proportional results for small parties. But this comes at the expense of preserving the principle of majority rule -- one reason that the Droop quota is used in all governmental STV elections. In an election held under the Hare quota it is possible for a group of candidates supported by a clear majority of voters to receive only a minority of seats if those voters do not disperse their vote relatively evenly across all their supported candidates. In contrast, such an outcome will not happen in an election held under the Droop quota unless voters in the majority do not rank all their preferred candidates or not enough preferred candidates seek office.