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Voting Systems or Electoral
Formulas
Additional Member System
A mixed system, with some single-member
constituencies (using First Past the Post), and some multi-member
constituencies (using closed lists) across a wider grouping
of constituencies. Voters mark an 'X' next to their favourite
candidate in the constituency, and then choose a party list
in the wider region. In the constituencies, the candidate
with the most votes wins. In the list section, the number
of seats already won by each party in the relevant constituencies
is taken into account, and an electoral formula is used to
distribute the remaining seats amongst the parties.
Alternative Vote
Single member constituencies. Voters rank
as many candidates as they wish in order of preference (1,
2, 3 etc). If one candidate gets 50% or more of first preferences,
s/he is elected. If not, the candidate with the least votes
is excluded, and the ballot papers are transferred to the
second (or next available) preferences . This process continues
until one candidate has 50% of the votes and is declared elected.
First-Past-the-Post
Usually in single-member constituencies,
though multi-member constituencies are also possible. 'X'
vote for a candidate, or multiple 'X's for several candidates
(voters are entitled to cast as many 'X's as there are places
to be filled). The winner is the candidate with the greatest
number of votes.
The Limited Vote
Very similar to First-Past-the-Post in multi-member
constituencies, except that voters are entitled to cast one
'X' less than the places to be filled (i.e. maximum of 3 'X's
where there are 4 places to be filled).
List Systems:
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Closed Lists
Multi-member constituencies. Each party puts
forward a list of candidates. Voters choose one list.
Seats are distributed to parties, in proportion to the
votes cast, by means of an electoral formula. Candidates
are elected in the order in which they appear on their
party's list. Voters are not able to influence the order
in which candidates are elected.
Semi-Open Lists
Multi-member constituencies. Each party puts
forward a list of candidates. Voters choose one list,
or they have the option of choosing a particular candidate
(or candidates) from a party list. Seats are distributed
to parties, in proportion to the votes cast, by means
of an electoral formula. Candidates are elected in the
order in which they appear on their party's list - but
some candidates may get elected sooner because they
have won 'personal' votes. Voters have some influence
over the order in which candidates are elected.
Open Lists
Multi-member constituencies. Each party puts
forward a list of candidates. Voters choose a particular
candidate (or candidates) from a party list. Seats are
distributed to parties, in proportion to the votes cast,
by means of an electoral formula. Candidates are elected
in the order dictated by the votes cast. Voters have
absolute influence over the order in which candidates
are elected.
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Single Transferable Vote
Multi-member constituencies. Similar to
the Alternative Vote, in that voters rank as many candidates
as they wish in order of preference (1, 2, 3 etc). A quota
is calculated - if any candidates have enough first preferences
to reach the quota, they are elected. If there are still places
to be filled, the surplus votes of elected candidates are
transferred to the next available preferences. If there are
still places to be filled, the candidate with the fewest votes
is excluded, and the ballot papers are transferred to the
next available preferences. This process continues until all
places are filled.
Supplementary Vote
Single-member constituencies. Voters place
an 'X' in one column for their first choice, and another 'X'
in a second column for their second choice. If a candidate
gets 50% or more of the first choices, s/he is elected. If
not, all candidates are excluded except the two with the greatest
number of votes. All ballot papers from the excluded candidates
are transferred to the second choice, if that candidate remains
in the contest. The candidate with the greatest number of
votes after this distribution is the winner.
Two-Round System
Usually single-member constituencies. Similar
to the Supplementary Vote, except that instead of two choices
on a single ballot paper, voters vote for their first choice
of candidate by marking an 'X'. If a candidate gets 50% or
more of the votes, s/he is elected. If not, all candidates
are excluded except the two with the greatest number of votes.
Then there is a second round of voting, and voters choose
between the two remaining candidates by marking another 'X'.
The candidate with the greatest number of votes is the winner.
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| Glossary:
Electoral Formulas |
Electoral formulas are used for distributing
seats with proportional voting systems. They can be divided
into two basic categories:
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Highest
average methods - these work by taking a party's
total number of votes and repeatedly dividing the total
by a fixed series of numbers; the party which has the
highest figure at each stage once this division has
been done is entitled to a seat |
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Quota
methods - these work by working out a quota
(based on the total number of valid votes cast and the
number of seats to be filled), which is equivalent to
the number of votes a party needs to win a seat. Usually
(though not always) any places which remain to be elected
when no party has a complete quota left, are distributed
to the parties with the highest remaining fraction of
a quota. |
1. Highest average methods
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1.1 d'Hondt
With the d'Hondt method, each party's total
number of votes is divided by the following series of
numbers: 1, 2, 3, 4, 5, 6 etc.
1.2 Pure Sainte Laguë
With the Pure Sainte Laguë method, each
party's total number of votes is divided by the following
series of numbers: 1, 3, 5, 7, 9 etc. This method is
very rare.
1.3 Modified Sainte Laguë
With the Modified Sainte Laguë method,
each party's total number of votes is divided by the
following series of numbers: 1.4, 3, 5, 7, 9 etc. This
method is far more common than Pure Sainte Laguë.
1.4 Danish method
With the Danish method, each party's total
number of votes is divided by the following series of
numbers: 1, 4, 7, 10, 13 etc. This method is called
the Danish method because it is used nowhere other than
Denmark.
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2. Quota methods
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2.1 Hare
The Hare quota is calculated by dividing
the total number of valid votes by the number of seats
to be filled.
2.2 Droop
The Droop quota is calculated by dividing
the total number of valid votes by one more than the
number of seats to be filled. Sometimes, as in the Republic
of Ireland, the resulting figure is rounded up to the
next whole number, even if it is already a whole number.
2.3 Imperiali
The Imperiali quota is calculated
by dividing the total number of valid votes by two more
than the number of seats to be filled.
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3. Other methods
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3.1 Hagenbach-Bischoff
The Hagenbach-Bischoff method is a
variant of the Droop quota. It uses the Droop quota
in the initial stages, and then rather than distributing
remaining seats to the parties with the highest remaining
fraction of a quota, it uses the d'Hondt method to distribute
these remaining seats.
3.2 (Hare)-Niemeyer
The Hare-Niemeyer or Niemeyer method
has exactly the same effect as the Hare quota. However,
it is done in a different way: the number of seats to
be filled is multiplied by the number of votes won by
a party. The result of this calculation is divided by
the total number of valid votes. This gives the number
of seats to be allocated to the party. This method is
used only in Germany.
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© 2004 Electoral
Reform Society