
Limited voting

Limited voting (also known as the limited vote method) 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.
Although it frequently enables minority groupings to gain representation – unlike first past the post or bloc voting systems – it is not guaranteed to do this, since the effectiveness of a sectional vote may be altered depending on the number of candidates fielded.
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. With limited voting the Red Party would usually win one seat.
However, it is possible for the Blue Party to overreach itself and win only one of the available seats. 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 is not a proportional electoral system.
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. A 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.
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.
'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 96 of 128 seats of the Senate of Mexico, and for the Senate of Argentina. Until 2005, for the Senate of Bolivia. A similar system was used for the Bolivian Constituent Assembly elections of 2 July 2006.