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 absolutely. 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.
Example
The town of Voterville elects three representatives to the local legislature. At the election, the ballot paper appears thus:
The voter has only two votes, which they have cast 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 parties.
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.
However, it is still possible for one party to win all three seats or for the least popular of two parties to win more seats than the other.
It is possible for the Blue Party, even if it is the most popular party, to win only one of the available seats if it attempts to win all three and overreaches itself. Since they have nearly 60% of the vote, they may be tempted to try to win all three seats. To do this, they need only to field three candidates. The Red Party, aware of their relative weakness, choose only to contest two and thus to concentrate their vote.
Assuming 100,000 electors in the town casting two votes each, the results might thus be:
By fielding three candidates the Blue Party hopelessly split their vote, despite having a clear majority 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.
In Spain, where limited voting was used for most elections until 1936 (and it's 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 on the constituency of Gran Canaria.
Another historical example of this was the 1880 election for the three members of parliament for the English city of Birmingham. Electors could cast up to two votes. Liberal candidate 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. 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.
Total votes cast = 94,635.
Estimated number of voters who voted = 47,318 (or more)
Eligible electors = 63,398
Turn-out = 74.6 percent
Note: Turnout is based on estimated number of voters who voted, calculated by dividing votes cast by two. To the extent that electors did not use both their possible votes (and thus more voted than the number of votes cast divided by two), turnout will be underestimated.
Charles Seymour in Electoral Reform in England and Wales explained the reaction of the Liberals of Birmingham after the limited vote was enacted.