A Discussion of
Different Electoral Systems
“lifted” from the Australian Electoral Commission webpage:
http://www.aec.gov.au/pubs/electoral_systems.htm
Plurality systems are the simplest of all electoral systems. The plurality system awards the seat to the candidate who receives the most votes regardless of whether the candidate receives a majority of votes. The plurality system is almost always used in conjunction with single member constituencies, but can be adapted for multi-member constituencies.
The plurality system or First-Past-The-Post
system awards the seat to the candidate with the most votes. In the following
illustration candidate B wins the seat although not obtaining a majority.
|
Candidate |
Votes |
% |
|
A |
5 000 |
31.2 |
|
B |
7 500 |
46.9 |
|
C |
3 500 |
21.9 |
|
Total |
16 000 |
100 |
Plurality systems are widely used but are largely restricted to the United Kingdom, Canada and the Unites States of America. Plurality systems are commonly used for the election of Heads of State where only one candidate is to be elected.
The first-past-the-post system is widely seen to be unfair and many attempts have been made to improve or replace it in countries where it is in use. However, the system does have a number of advantages. First, when operated with single member constituencies it provides for a direct relationship between the member of the legislature and the local constituency. Second, because elections are contested at the constituency level there can be a degree of local control over the party's choice of candidate and parties must take some account of the constituency's wishes when selecting a candidate. Third, the system elects the candidate who receives the largest number of votes. Candidates cannot be elected as a result of the transfer of a third or fourth preference, thus defeating the candidate with the largest number of first preference votes. Fourth, the system is straightforward and easy to understand. Electors are not required to choose from vast lists of candidates or to exercise preferences they may not have. The system is uncomplicated and produces a speedy outcome. Fifth, the system allows electors to directly choose the government and not be subject to backroom wheeling and dealing that can occur when a large number of parties are elected to the legislature. Sixth, there is less opportunity for minority parties to be given power disproportionate to their electoral support. Seventh, there is less likelihood of a proliferation of minor parties which may make the formation of stable governments difficult. Finally, because elections are contested at the constituency level there is a greater possibility of outstanding candidates being elected regardless of party support.2
The main criticisms of the first-past-the-post systems are that it cannot be relied upon to provide a legislature reflecting the various shades of opinion expressed at the election and it does not necessarily place in power a government supported by the majority of the electorate.
The first-past-the-post
system is a winner take all system that can deny representation in the
legislature to quite substantial levels of minority opinion and can provide
large differences in the number of representatives elected with only a small
difference in the number of votes obtained through the operation of the winning
bonus. The Liberal Party in the United Kingdom has fought a singularly
unsuccessful campaign against the first-past-the-post system in that country.
The reason for the campaign is easily understood when the following results are
possible. In the 1987 general election the Liberal Social Democratic Alliance
polled 22.6% of the vote but received only 3.4% of the seats in the House of
Commons. The 1987 general election results demonstrated both the under
representation of minority parties and the effect of the winning bonus.
|
UK House of Commons Election 1987 |
|||
|
Party |
Votes % |
Seats No |
Seats % |
|
Conservatives |
42.2 |
375 |
57.7 |
|
Labour |
30.8 |
229 |
35.2 |
|
Liberal Social Democratic Alliance |
22.6 |
22 |
3.4 |
|
Others |
4.4 |
24 |
3.7 |
|
Total |
100.0 |
650 |
100.0 |
Source: The Times Guide to the House of Commons, June 1987, Times Books Ltd, London 1987.
In 1987 the Conservative Party was the recipient of the winning bonus characteristic of the first-past-the-post system and the Liberal Social Democratic Alliance was the victim of the under-representation of minor parties. The other parties shown in the above table are primarily located in Northern Ireland. This result demonstrates a quirk of the first-past-the-post system that allows minor parties to gain representation commensurate with their level of support if that support is concentrated in a specific area rather than spread over the whole country.
The first-past-the-post
system can also result in the election of a government that does not receive
support from a majority of the electorate, or even by the largest number of
votes. In countries with a strictly two party system there is a reasonable
chance that the first-past-the-post system will result in the party receiving
the majority of votes being elected to government. However, where significant
third parties are present this possibility becomes remote. The situation can
also occur where the party receiving the largest number of votes does not win
sufficient seats to form a government. In New Zealand the Labour Party has been
the victim on at least two recent occasions, 1978 and 1981.
|
NZ House of Representatives Elections, 1978 and 1981 |
||||
|
Party |
1978 |
1981 |
||
|
% Votes |
% Seats |
% Votes |
% Seats |
|
|
Labour Party |
40.4 |
43.5 |
39.0 |
46.7 |
|
National Party |
39.8 |
55.4 |
38.8 |
51.1 |
|
Others |
19.8 |
1.1 |
22.3 |
2.2 |
Source: T. Mackie and R. Rose, The International Almanac of Electoral History, 2nd ed, Facts on File Inc. New York 1982.
A further consequence of the first-past-the-post system is the tendency of the system to limit the range of candidates available through fear of splitting the vote. Thus two separate political parties with similar, but not the same policies, might decide to divide the constituencies between them rather than contesting all constituencies and splitting the vote. This tendency can provide a limitation to the choices facing an electorate.
Majoritorian Systems
Majoritorian systems as the name suggests require the winning candidate to receive a majority (more than half) of the vote to ensure election. This can be achieved either through a second ballot or by means of preference voting (Alternative Vote). The second ballot systems are restricted to electing members from single member constituencies while the alternative vote system can be used for both single and multi-member electorates.
In the Second Ballot system a second election is held a short time after the first election if no candidate gains more than 50% of the votes in the first election. Where second ballot systems are used the number of candidates eligible to enter the second election is restricted either by number - the two candidates who receive the highest vote - or by some threshold - only candidates receiving over a set percentage of the vote. Second ballot systems are more likely to be used in presidential elections rather than for legislative elections. Of the six Western European countries with a directly elected Head of State, three, including Austria, France and Portugal, use the second ballot system.
The second ballot system prevents the election of any candidate without a majority of the vote, thus overcoming one of the main criticisms of plurality systems. However, the second ballot system introduces a complication into the voting system. The requirement for a second ballot results in greater expense for the candidates and parties involved, greater inconvenience to the electors and delays the result of the election causing uncertainty. The requirement for a second ballot may also influence the final result as electors may use the first ballot as a form of protest vote.
The Alternative Vote system is familiar to all Australians as it is the system used to elect members to the House of Representatives and the lower houses of all State Parliaments except Tasmania. The alternative vote system removes the cumbersomeness of the second ballot system by asking the voter to indicate how he would vote if his first choice candidate were defeated and he had to choose again from the remaining candidates.
The system operates by asking voters to number the candidates in order of their choice. If no candidate receives a majority, more than 50% of first preference votes, then the candidate with the lowest first preference vote is eliminated and his votes are redistributed to the remaining candidates on the basis of the second choices. Further candidates are eliminated until one candidate reaches a majority.
In the following example
no candidate receives a majority of first preference votes. Candidate B
received the lowest number of first preference votes and is eliminated first
and his preferences are distributed to the two remaining candidates. Candidate
C is elected as he receives a majority of votes, after the distribution of
Candidate B's preferences, even though he did not receive the highest number of
first preference votes.
|
Alternative Vote System |
|||
|
|
First Preference Votes |
Distribution of Candidate B |
Total |
|
Candidate A |
10 000 |
500 |
10 500 |
|
Candidate B |
4 000 |
.. |
.. |
|
Candidate C |
8 000 |
3 500 |
11 500 |
|
Total |
22 000 |
4 000 |
22 000 |
In Australia the Alternative Vote system is not only used in single member constituencies. The system was used for multi-member constituencies to elect members of the Senate prior to 1949. The Alternative Vote system does not work well when applied to multi-member constituencies because of the propensity of the system to return members of the same party to all positions. In multi-member electorates the Alternative Vote system requires electors to indicate an order of preference for all candidates. If a candidate receives a majority of first preference votes he is elected. If no candidate receives a majority then the candidate with the lowest vote is eliminated and his votes are distributed. Candidates are eliminated until one candidate receives a majority.
The votes of the first elected candidate are then distributed (all votes being used again) and if no candidate receives a majority then the process of elimination starts over again. The process continues until all vacancies are filled. The system can result in the election of members of the one party to all positions as the votes used to elect the first member are used again to elect the second and subsequent members.
In the following example,
simplified by assuming that one candidate receives a majority of first
preference votes, all three vacancies are filled by members of the same party.
|
Alternative Vote - Multi-Member Constituency |
|||||
|
|
First Vacancy |
Second Vacancy |
Third Vacancy |
||
|
Distributed from Candidate A1 |
Total |
Distributed from Candidate A2 |
Total |
||
|
Party A |
|
|
|
|
|
|
Candidate A1 |
200 000 |
.. |
.. |
|
|
|
Candidate A2 |
5 000 |
195 000 |
200 000 |
.. |
|
|
Candidate A3 |
2 000 |
1 000 |
3 000 |
194 000 |
197 000 |
|
Party B |
|
|
|
|
|
|
Candidate B1 |
180 000 |
3 000 |
183 000 |
4 000 |
187 000 |
|
Candidate B2 |
4 000 |
500 |
4 500 |
1 000 |
5 500 |
|
Candidate B3 |
1 000 |
500 |
1 500 |
1 000 |
2 500 |
|
Total |
392 000 |
200 000 |
392 000 |
200 000 |
392 000 |
Under the Alternative Vote system representation in the Senate was grossly unequal. On three occasions 1925, 1934, and 1943 all Senators elected were from the same party or coalition of parties. In every other election there were large discrepancies between support for individual parties and the number of Senators elected from each party. The system was changed in 1949 to the current Single Transferable Vote form of proportional representation.
The main advantage of the alternative vote system (for single member constituencies) over plurality systems is that it requires the winning candidate to secure a majority of the vote. It thus avoids the situation where a candidate can be elected on a little over one third of the vote, where there are three relatively evenly supported candidates. The system also overcomes the problem of vote splitting.
With the alternative vote system voters can exercise a choice between two similar candidates without the fear that a third, unacceptable, candidate may be elected. Thirdly the alternative vote system provides some dampener on the plurality system's characteristics of concentrating party representation on a geographical basis and of providing exaggerated majorities. Although party representation under the alternative vote system is more clearly aligned to voter support than under plurality systems the alternative vote system still produces working majorities and thus provides for stable government. The alternative vote system is relatively easy to understand and can produce relatively speedy results.
The principle disadvantage of the alternative vote system, and of plurality systems, is that the system does not necessarily reflect the wishes of the electorate. The degree of proportionality (i.e. members elected in proportion to voter support) is greater under alternative vote than under plurality but does not achieve the degree of proportionality of proportional representation systems. The system is still subject to the winning bonus phenomenon and can also result in the party winning the highest number of votes not receiving the largest number of seats. Although this factor is largely dependent upon the geographic spread of party support and on the mix of parties contesting the election.
The alternative vote system can often be capricious in its practical application and can result in the election of the least unfavoured rather than the most popular candidate. In a political situation consisting of a left, right and centre party, the centre party could receive preferences of both the left and right parties on the basis of being the least unfavourable option available.
The capriciousness of the alternative vote system can often be witnessed in Australia in what are termed three cornered contests. Here the winning party is often more dependent upon which party polls the least first preference votes rather than which party polls the most.
In the following example
Lusher, National Party, was eliminated first and his preferences elected Fife,
Liberal Party. However, if approximately 550 voters had changed their first
preference vote from Fife to Lusher, then Lusher would have been elected. Thus,
in this example the main contest was between which party would be placed second
and which third.
|
House of Representatives Election 1984, Hume Electoral Division |
|||||
|
|
|
First Preference Votes |
After Distribution of Lusher's Preferences |
||
|
|
|
No |
% |
No |
% |
|
Milliken |
ALP |
24 342 |
39.3 |
26 221 |
42.3 |
|
Lusher |
NP |
18 245 |
29.5 |
.. |
.. |
|
Fife |
LIB |
19 331 |
31.2 |
35 695 |
57.7 |
Source: Australian Electoral Commission, Election Statistics 1984: House of Representatives: Full Distribution of Preferences, AGPS Canberra 1985.
The Alternative Vote system has also been criticised because it requires voters to express a preference for candidates where the voter may not wish to do so. This situation can be overcome by allowing voters the option of not expressing preferences if they so desire. The optional preferential system has been used for New South Wales Legislative Assembly elections since 1981.
Proportional Representation
To overcome the proportionality problems associated with single member constituencies using either plurality or majoritorian systems a bewildering number of proportional representation systems have been developed. Proportional representation systems are widely used in Europe, and in Australia for upper houses.
Proportional representation systems attempt to relate the allocation of seats as closely as possible to the distribution of votes. By definition, this requires more than one vacancy, so multi-member constituencies are necessary. Constituencies can range from the whole Country or State to parts of the Country.
Proportional representation systems can be broadly grouped into two categories: List systems and the Single Transferable Vote system. List systems can be further divided into Largest Remainder and Highest Average categories. List systems may or may not allow the elector to choose between candidates of the same party. List systems can be either closed; allowing no choice at all; flexible, where the voter can vote for the party or a candidate; open, where there is no party vote but candidates listed in order; or free where the candidates are not placed in any order by the parties.
The basic concept of proportional representation systems is to allocate seats in the legislature in a proportional relationship with the votes cast at the election. To achieve this requirement a number of different and quite complex computational arrangements have been devised. These may or may not include the use of a quota. A quota in this context is the number of votes required to obtain a seat.
The simplest method of determining a quota is to divide the number of valid votes by the number of seats to be allocated. This method is often referred to as the Hare3 quota. Three alternatives to the Hare quota exist; The Hagenbach-Bischoff quota, in which the number of votes is divided by the number of seats plus one; the Droop4 quota, in which the number of votes is divided by the number of seats plus one and adding one to the quotient; and the Imperiali quota, in which the number of votes is divided by the number of seats plus two. In the following examples 60000 valid votes are cast and 5 seats are to be allocated.
Quotas
|
Hare = |
Votes |
= 60 000 |
= 12
000 |
|
|
Seats |
5 |
|
|
Hagenbach-Bischoff
= |
Votes |
= 60 000 |
= 10
000 |
|
|
Seats + 1 |
6 |
|
|
Droop =
|
Votes + 1 |
= 60 000 + 1 |
= 10
001 |
|
|
Seats + 1 |
6 |
|
|
Imperiali
= |
Votes |
= 60 000 |
= 8 571 |
|
|
Seats + 2 |
7 |
|
The simplest method of
allocating seats under proportional representation is the Largest Remainder
system. Under this system a quota is established, usually Hare quota, and is
used to determine each party's allocation. A seat is allocated for each quota
that the party obtains. However, this system does not always provide for the
allocation of all seats as a number of votes will be left over after the
allocation of full quotas and some small parties will not gain sufficient votes
to obtain a full quota. The remaining seat or seats are allocated on the basis
of the largest remaining votes after the allocation of full quotas. In the
following example five seats are to be allocated but only three parties receive
a full quota. The remaining seats are allocated on the basis of the highest
remaining votes.
|
Largest Remainder |
||||||
|
Party |
Votes |
Hare Quota |
Seats |
Remainder |
Seats |
Total Seats |
|
A |
8700 |
4800 |
1 |
3900 |
1 |
2 |
|
B |
6800 |
4800 |
1 |
2000 |
0 |
1 |
|
C |
5200 |
4800 |
1 |
400 |
0 |
1 |
|
D |
3300 |
- |
0 |
3300 |
1 |
1 |
|
Total |
24000 |
|
|
5 |
|
|
Source: T. Mackie and R. Rose, op.cit.
The above example demonstrates one of the limitations of the largest remainder system in ensuring proportionality of representation. In the example Party D receives the same representation as Parties B \ C even though its vote is substantially lower, and in the case of Party B only half. The Largest Remainder system favours smaller parties over larger parties when using the Hare quota. The relative importance of remainders in the allocation of seats can be reduced by the use of a lower quota (Hagenbach-Bischoff or Droop). Lower quotas result in more seats being allocated on the basis of parties receiving a full quota and less being allocated by remainders. However, the use of a lower quota does not always overcome the proportionality problem of the Largest Remainder system. Using the example above the Droop quota produces exactly the same result as the Hare quota.
To overcome problems associated with the Largest Remainder system the Highest Average system was devised.5 The object of the highest average system is to ensure that when all seats have been allocated the average number of votes required to win one seat shall be as near as possible the same for each party. The Highest Average system can be used with or without a quota. When used with a quota the system is sometimes referred to as a Hagenbach-Bischoff system. The system derives its name from the method of allocation of seats to parties. Under the system each party's votes are divided by a series of divisors to produce an average vote. The party with the highest average vote after each stage of the process is allocated a seat. After a party has been allocated a seat its votes are then divided by the next divisor. The Highest Average system has a number of different variations, depending upon the divisors used and whether a quota is used or not.
The d'Hondt version uses
the numbers one, two, three, four etc as its divisions. In the following
example the d'Hondt is used without a quota. As in the previous example five
seats are to be allocated.
|
D'Hondt Version Highest Average System |
|||||||
|
Party |
Votes |
1st Seat Division |
2nd Seat Division |
3rd Seat Division |
4th Seat Division |
5th Seat Division |
Total |
|
A |
8700 |
8700(1) |
4350 |
4350 |
4350(4) |
2225 |
2 |
|
B |
6800 |
6800 |
6800(2) |
3400 |
3400 |
3400(5) |
2 |
|
C |
5200 |
5200 |
5200 |
5200(3) |
2600 |
2600 |
1 |
|
D |
3350 |
3350 |
3350 |
3350 |
3350 |
3350 |
0 |
|
Total |
24000 |
|
|
|
|
|
5 |
Source: T. Mackie and R. Rose, op.cit.
In the above example the
first seat divisor is one for all parties. Party A has the highest vote and is
allocated a seat. In the second round, votes for Party A are divided by two,
while all others are divided by one. Party B has the highest vote and is allocated
the second seat. The process continues with the divisor for a party increasing
by one each time that party is allocated a seat. The above example illustrates
the highest average concept of the d'Hondt version. An alternative presentation
of the above, that is easier to comprehend, is shown below. In this example
votes of all parties are divided by the series of divisors. From the resultant
matrix, seats are allocated to parties with the highest votes.
|
Alternative Presentation of the d'Hondt Version |
|||||
|
|
Party A |
Party B |
Party C |
Party D |
Total |
|
Votes |
8700 |
6800 |
5200 |
3350 |
24000 |
|
Divide by 1 |
8700(1) |
6800(2) |
5200(3) |
3350 |
|
|
Divide by 2 |
4350(4) |
3400(5) |
2600 |
1675 |
|
|
Divide by 3 |
2900 |
2267 |
1733 |
1117 |
|
|
Seats |
2 |
2 |
1 |
0 |
|
A comparison of the examples shown under the d'Hondt version of the Highest average system and the Largest Remainder shows a different distribution of seats and illustrates a characteristic of the d'Hondt version to favour major parties at the expense of minor parties. This can be modified by choosing different divisors. The Sainte-Lague version and the Modified Sainte-Lague versions increase the size of the divisors, thus making it more difficult for a party to win each additional seat. The Sainte-Lague divisors are odd numbers beginning at one (eg 1,3,5,7, etc.). The modified Sainte-Lague numbers are 1.4,3,5,7,9. The Sainte-Lague divisors make it harder for major parties to gain each additional seat while the modified Sainte-Lague divisors maintain this characteristic as well as making it more difficult for smaller parties to gain representation through the 1.4 first divisor.
The following examples
illustrate the Sainte-Lague characteristics of making it more difficult for
major parties to obtain additional seats.
|
Sainte-Lague Version |
|||||
|
|
Party A |
Party B |
Party C |
Party D |
Total |
|
Votes |
8700 |
6800 |
5200 |
3350 |
24000 |
|
Divide by 1 |
8700(1) |
6800(2) |
5200(3) |
3350(4) |
|
|
Divide by 3 |
2900(5) |
2267 |
1733 |
1117 |
|
|
Divide by 5 |
1740 |
1360 |
1040 |
670 |
|
Source:
T. Mackie and R. Rose, op.cit.
|
Modified Sainte-Lague Version |
|||||
|
|
Party A |
Party B |
Party C |
Party D |
Total |
|
Votes |
8700 |
6800 |
5200 |
3350 |
2400 |
|
Divide by 1.4 |
6214(1) |
4857(2) |
3714(3) |
2393(5) |
|
|
Divide by 3 |
2900(4) |
2267 |
1733 |
1117 |
|
|
Divide by 5 |
1740 |
1360 |
1040 |
670 |
|
Source: T. Mackie and R. Rose, op.cit.
In the above example both the Sainte-Lague and modified Sainte-Lague versions produce the same distribution of seats. However, the two versions provide representation for the smallest party at the expense of the second largest party.
In addition to varying the first divisor to make the election of smaller parties more difficult a threshold can also be used in list systems to achieve the same result. Thresholds require a party to achieve a certain percentage of the vote before they can be eligible to have members elected.
List systems of one variety or another are used widely throughout Western Europe. (See Table 2). Australia's first exposure to list systems occurred with the ACT Legislative Assembly elections in March 1989. The system used, termed modified d'Hondt, is described in greater detail in Appendix 3. The system used d'Hondt divisors with a Droop quota as a threshold and a flexible list. However, the ACT system was complicated by the use of a single transferable vote system (Senate system) to determine the individual candidates elected. The single transferable vote addition to the d'Hondt system was employed to overcome one of the main criticisms of the list systems ie the reliance of party lists to elect individual candidates rather than voter choice. However, in attempting to overcome this problem the system became so complex that voters had difficulty in understanding it and the scrutiny took two months to produce a result.
The form of proportional representation familiar to most Australians is the Single Transferable Vote system used in elections for the Senate, the Legislative Councils of New South Wales, South Australian and Western Australia and the Tasmanian House of Assembly. The Tasmanian system, referred to as Hare-Clark6, differs from the system used for the Senate and States' Upper Houses in a number of ways. However, the basic concepts are the same.
In the single transferable vote system voters are required to rank individual candidates according to their preference. A candidate must receive a Droop quota in order to be elected. Any candidates whose first preference votes equal or exceed the quota are declared elected. Votes surplus to the quota cast for successful candidates are transferred amongst the remaining candidates according to the second preferences recorded by the voter. The questions of which votes actually elect the first elected candidate and which votes are surplus and hence distributed can either be resolved by sampling or conducting a full count to determine the proportions favouring particular candidates. The proportions are then applied to the first preference votes of the successful candidate. As each candidate receives a quota he is elected and his surplus votes are distributed. If all surplus votes have been distributed and not all vacancies have been filled then the candidate with the smallest number of votes is eliminated and his votes distributed. This process continues until all vacancies are filled. (See Appendix 1 for a detailed explanation of the Senate system and Appendix 2 for a detailed explanation of the Hare-Clark system).
The single transferable vote system can be explained simply in the following terms. If a voter wished to vote for a particular candidate but the candidate was either so popular as to have no need for his vote or so unpopular as to have no chance of election, then the vote was not wasted but used to elect the voters' second choice candidate.7
The need for the Droop quota in the single transferable vote system may require some explanation. The Droop quota represents the smallest numbers of votes that will ensure election. This can best be illustrated in the case of an election for one vacancy with two candidates. One candidate is required to poll only one more vote than half to ensure election. Thus with 100 votes, 51 votes would ensure election. This can be expressed in the following formula:
|
Quota =
|
Votes + 1 |
= 100 + 1 |
= 51 |
|
|
Vacancies + 1 |
1 + 1 |
|
Similarly, in a five member constituency, six candidates can each receive one-sixth of the vote, but only five can get any more votes; therefore any candidate who polls one more vote than one-sixth of the total must be elected.8
|
Quota =
|
100 + 1 |
= 17 |
|
|
|
5 + 1 |
|
|
If five candidates receive 17 votes (85 votes in total) then the remaining candidate must receive 15 votes. Thus 17 votes is the smallest number of votes that ensure election.
A simplified example of the operation of the single transferable vote system is shown below. In this example four candidates are standing to fill three vacancies. The quota is 76. Candidates A1 and A2 are from the same party. Candidate A1 receives a quota on first preferences. He is elected and his surplus votes are distributed. Candidate A2 receives the vast majority of Candidate A1's surplus and also achieves a quota, and is elected. Candidate A2's surplus is distributed and results in the