Limited voting

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Limited voting (also known as partial block voting) is a voting system in which electors have fewer votes than there are positions available. The positions are awarded to the candidates who receive the most votes. In the special case in which the voter may vote for only one candidate and there are two or more posts, this system is called the single non-transferable vote or sometimes the strictly limited vote. [1]

Contents

Example

The town of Voterville makes up an electoral district. It elects three representatives to the legislature. At the election, the ballot paper appears thus:

Brian BlueBlue PartyX
Beryl BlueBlue PartyX
Boris BlueBlue Party
Rory RedRed Party
Rachel RedRed Party

The voter has only two votes. In this case the voter has voted for Brian and Beryl Blue. They cannot cast a third although there are three seats being contested. Each vote counts as one towards the total for the candidate voted for.

Practice and issues

Limited Voting frequently enables minority groupings to gain representation – unlike first past the post or bloc voting systems. But it is not guaranteed to do this, since the effectiveness of a sectional vote may be altered depending on the number of candidates fielded and the manner in which votes are cast for party candidates.

For example, in Voterville 54% of electors support the Blue Party while 46% support the Red Party. Assuming an even distribution of support across the town, the Blue Party would win all three seats with either bloc voting or first past the post, and the Red Party would win no representation.

With limited voting the Red Party would usually win one seat.

Assuming 20,000 electors in the town cast two votes each and the Blue party getting 54 percent of the votes and the Red party getting 46 percent, the results might be:

Brian Blue9800 votesElected
Beryl Blue9600 votesElected
Boris Blue2200 votes
Rory Red9,200 votesElected
Rachel Red9,200 votes

Thus two parties obtain representation.

But the ability of a minority to get representation (at least one seat) under limited voting is limited. To be sure of winning one seat out of three when each voter has two votes and only two parties are in the contest, it is necessary to get the votes of a full two-fifths of the voters. In the above case the Red party had support from just more than two-fifths of the voters. In cases where there are more than two parties running candidates and voters cast their two votes along party lines, the smaller of the two largest parties must have 40 percent of the total valid votes, or 40 percent of the valid votes of the largest and second-largest parties combined, to be sure to take a seat, and then might elect both of its candidates. If voters do not cast their votes along party lines or do not cast both votes, the smaller of the two largest parties can take a seat only if its most-popular candidate is more popular than the least-popular candidate of the largest party. [2]

If the largest party runs three candidates hoping to take all the seats, it may suffer from vote splitting and take just one seat. (It could happen that both parties would each run three candidates and suffer vote splitting and then the outcome could be conjectured In countless ways.)

If the larger party runs three candidates and the smaller runs two, it is possible for the larger party to win all three seats.

But it is also possible for the least-popular of the two parties to win more seats than the other. The Blue Party, even if it is the most-popular party, may win only one of the available seats if it attempts to win all three and overreaches itself.

Since the Blue party has nearly 60% of the vote, it may be tempted to try to win all three seats. To do this, it must field three candidates. The Red Party, aware of its relative weakness, is likely to choose only to run two and thus not to disperse its vote. (With each voter having two votes, there is no reason to run only one candidate.)

Assuming 20,000 electors in the town cast two votes each, the results might thus be:

Brian Blue8600 votesElected
Beryl Blue8000 votes
Boris Blue5000 votes
Rory Red9,200 votesElected
Rachel Red9,200 votesElected

By fielding three candidates the Blue Party split their vote and lost out, despite having a clear majority of voter support in the town.

As can be seen from this example, limited voting does not always produce proportional representation.

Another way in which the system may fail to achieve fair representation is if the largest party is very well organised and can arrange the distribution of its supporters' vote for maximum advantage, while other parties are not so well organized.

In Spain, where limited voting was used for most elections until 1936 and where it is still used today for the Senate, this practice was known as ir al copo (from the verb copar, 'to fulfill'). In both 1977 and 1979 Spanish general elections, the Union of the Democratic Centre won all three seats in the constituency of Gran Canaria.

In this next example, a party first secured a one-party sweep of a district's seats and then manipulated the vote so as to methodically sweep the seats again. In the 1880 election for the three Members of Parliament for the English city of Birmingham, electors cast one or two votes. Liberal candidates filled all three seats, leaving the Conservatives without representation. This is despite the Liberal vote being split among three candidates. Thus the limited vote did not produce mixed representation. The Conservative party may have had only about 15,000 supporters and the Liberal candidates may have had support from about 31,000 so the unfairness of the result is not as stark as it seems from seeing 29,000 Conservative votes disregarded. (The Conservatives' voter support in Birmingham was less than the 40 percent threshold for guaranteed representation mentioned above.)

But due to Limited Voting, it could have been that Conservative candidates received one vote from 29,000 voters and Liberal candidates received at least one vote from all 47,000 voters. Judging the fairness of elections results (and perceiving the portion of voters who saw their choice elected) is much easier when each voter has just one vote.

General Election 1880: Birmingham (3 seats); each voter casting one or two votes
PartyCandidateVotes%±%
Liberal Philip Henry Muntz 22,96924.27N/A
Liberal John Bright 22,07923.33N/A
Liberal Joseph Chamberlain 19,54420.65N/A
Conservative F.G. Burnaby15,73516.63N/A
Conservative Hon. A.C.G. Calthorpe14,30815.12N/A

Total votes cast = 94,635.

Estimated number of voters who voted = 47,318 (or more)

Eligible electors = 63,398

Turn-out = 74.6 percent [3]

Charles Seymour in Electoral Reform in England and Wales explained the reaction of the Liberals of Birmingham after the limited vote was enacted.

The Liberals of Birmingham realized that if they were to retain the third seat, their vote must be divided economically between the three candidates. To prevent waste of votes, an organization must be built up which could control absolutely the choice of the elector; and each elector must vote invariably as he was told. The success of the Birmingham organization, which soon became known as the Caucus, was unbroken and no Conservative candidate was returned. It was copied in many other constituencies and inaugurated a new era in the development of party electoral machinery, the effect of which upon the representative system has been profound.

Under single voting in 3-seat district (such as Single non-transferable voting), with the same (likely) voting behavior -- 31,000 Liberal voters and 15,000 Conservative voters -- it seems likely that the Conservatives would have filled one seat if they had run just one candidate. If the Conservative party ran two candidates, it is likely Liberals would win all three seats as under Limited voting.

Types of Limited Voting

An PR expert described the two types of limited voting:

-Limited vote (ordinary form) where each voter has a number of votes equivalent to more than half the seats being filled. An example of this is the Birmingham 1880 election described above. Two parties at most are likely represented, and never more than the number of seats.

-Limited vote (special form) where each voter has a number of votes equivalent to less than half the seats being filled. An example of this occurred In Japan during the US-led Allied occupation. In the first post-war election in 1946: in districts with ten or fewer representatives each voter had two votes; in districts with ten or fewer representatives each voter had three votes in districts with more than ten representatives. [5] In that election, with district magnitude mostly ranging from 6 to 23, many parties (usually 4 to 7 or more) elected representatives in almost every district.

History and current use

Historic
Current

'Fixed Ratio' or closed-list version of Limited Vote

The electoral system whereby two seats are assigned to the leading party-list and one seat to the second-placed party-list normally has the same result as limited vote with two votes per voter for three seats. It is used for the Senate of Argentina and 96 out of 128 seats for the Senate of Mexico, as well as the Senate of Bolivia until 2005. [11] A similar system was used for the Bolivian Constituent Assembly elections of 2 July 2006. [12]

See also

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References

  1. ↑ Enid Lakeman & James Labert (1955). Voting in democracies. London: Faber.
  2. ↑ Hoag and Hallett (1926). Proportional representation. pp. 43–45.
  3. ↑ Birmingham (UK Parliament constituency)
  4. ↑ Craig, British Parliamentary Election Results 1832–1885
  5. ↑ Tyson, Robert. ""Various voting methods"". Arena (Jan. 1908): 60.
  6. ↑ Pedro Tavares de Almeida; Margarida Lopes & João Samouqueiro (2006). "Legislação Eleitoral - REPÚBLICA.doc" (PDF). Retrieved 18 January 2025.{{cite web}}: CS1 maint: multiple names: authors list (link)
  7. ↑ Pedro Tavares de Almeida; Margarida Lopes & João Samouqueiro (2006). "Legislação Eleitoral - MONARQUIA CONSTITUCIONAL.doc" (PDF). Retrieved 18 January 2025.{{cite web}}: CS1 maint: multiple names: authors list (link)
  8. ↑ Bernard Grofman, Evald Mikkel & Rein Taagepera (1999). "Electoral System Change in Estonia" (PDF). Retrieved 24 November 2020.
  9. ↑ Parliamentary Guide 1900
  10. ↑ "Black candidate for Euclid school board to test new voting system - Cleveland.com". Archived from the original on 8 October 2012. Retrieved 28 February 2020.
  11. ↑ The electoral system in the new Constitution, used since the elections of 2009, is 4 seat list-PR (D'Hondt) per department
  12. ↑ "Ciao!: Brief review of constituent assembly electoral system".
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