Voting systems are of two types, first past the post, and proportional representation. In the first past the post system, the party with the most votes in a district (or riding, etc.) gets the seat for that district, and the other parties get nothing for that district. This tends to result in minor parties getting a smaller share of the seats than their share of the votes. For example, a party which polled five percent of the vote would probably receive fewer than five percent of the seats, and might well receive no seats at all. The problem is that while the minor party may have significant support, if that support is evenly spread among the districts it will not be great enough in any given district to result in victory there. Proportional representation systems are designed to remedy this defect, bringing the share of seats into closer proportion to the vote share. They are of two types, the single transferrable vote, or party list systems.
Single transferrable vote
In this system the voter must number `1' the candidate she most wishes to elect, and then may number her next-best candidate `2', the next after that `3', and so on as far as she pleases. This instructs the returning officer that if the vote cannot help that voter's favourite candidate (either because that candidate already has enough votes or because that candidate has so few votes as to have no hope of winning), it shall be transferred to the candidate the voter has marked `2', and so on if necessary, until it reaches a candidate it can help elect. (In practice, most votes are effective for their first or second preference.) It is possible to compute a `quota', which is the number of votes a candidate must receive in order to be elected, given the number of people who voted and the number of seats. Voters are under no obligation to stick to party lines, although often they tend to choose candidates from their favourite party, ranking them according to their own preference.
Single transferrable vote is used for all public elections in the Republic of Ireland. In England it is used in elections for the Church Assembly, some trade unions, some committees, and was used in four univ. constituencies from 1918 to 1945.
The single transferrable vote used to fill one vacancy is called the alternative vote. It serves only to eliminate ties and is not a form of proportional representation. It is widely used in Australia. A similar technique called the second ballot was used in France before 1945 and after 1958.
In a party list system, the elector votes for a party and each party is alotted seats in proportion to its total votes. Seats may be filled by candidates in the order in which they are placed by the party in its list; more often, the voter is given some power to alter this order. Some of the countries in which this system has been used are listed in Everyman's Encyclopedia (1967):
Party list systems are used to elect the parliaments of the Scandinavian and Benelux countries, Switzerland, Israel, and Italy. Germany uses a mixed system, in which the disproportional results of voting by the British [first past the post] system are corrected by addition of members from party lists; France introduced party list proportional representation in 1945, but in 1951 modified it drastically to give Communists and Gaullists much less than their proportional share of seats. In 1958 she reverted to the second ballot.
Lakeman, E., and J. D. Lambert (1959). Voting in Democracies. (Cited by Everyman's Encyclopedia.)