Quota

A quota is a number of votes (obtained by formula) often relevant to deciding who wins and how ballots are evaluated or modified in proportional voting methods.

The following quotas are listed from largest to smallest.

Hare quota

The Hare quota may be given as:

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

Where:

• ${\text{total votes}}$ = the total valid poll; that is, the number of valid (unspoiled) votes cast in an election.
• ${\text{total seats}}$ = the total number of seats to be filled in the election.

When there are 5 seats to be filled and 100 votes cast, the Hare quota is (100/5) = 20 votes.

Droop quota

Sources differ as to the exact formula for the Droop quota. As used in the Republic of Ireland the formula is usually written:

$\left({\frac {\text{total valid poll}}{{\text{seats}}+1}}\right)+1$

but more precisely

$\operatorname {Integer} \left({\frac {\text{total valid poll}}{{\text{seats}}+1}}\right)+1$

where:

• ${\text{total valid poll}}$ = Total number of valid (unspoiled) votes cast in an election.
• ${\text{seats}}$ = total number of seats to be filled in the election.
• $\operatorname {Integer} ()$ refers to the integer portion of the number, sometimes written as $\operatorname {floor} ()$

One reason Droop quotas are used more often than Hare Quotas for ranked PR methods is because not only do they often help reduce the amount of vote-counting necessary, but they almost entirely eliminate the possibility of a majority of voters receiving a minority of seats compared to Hare Quotas. The Droop Quota is the smallest possible quota that guarantees that there will be as many quotas as there are winners desired.

When there are 5 seats to be filled and 100 votes cast, the Droop quota is 17 votes, which is calculated as: Integer((100/(5+1)) + 1) = Integer((100/6) + 1) = Integer(~16.667 + 1) = Integer(~17.667) = 17 votes.

Hagenbach-Bischoff quota

The Hagenbach-Bischoff quota (HB quota) (known by a few other names as well) is:

$\left({\frac {\text{total valid poll}}{{\text{seats}}+1}}\right)$

Some sources call the HB Quota a Droop Quota instead. There will always be either exactly one more HB quota than seats to be filled. Because of this, it will on rare occasion be necessary to break a tie between various candidates to decide who should win with PR methods that use the HB quota.

When there are 5 seats to be filled and 100 votes cast, the HB quota is (100/(5+1)) = ~16.667 votes.