The rationale underpinning all proportional representation (PR) systems is to consciously reduce the disparity between a party's share of the national vote and its share of the parliamentary seats. If a major party wins forty percent of the votes, it should win approximately forty percent of the seats, and a minor party with ten percent of the votes should also gain ten percent of the parliamentary seats. The use of party lists helps to achieve proportionality, whereby political parties present lists of candidates to the voters on a national or regional basis (see List PR). However, it can be achieved just as easily if the proportional component of an MMP system compensates for any disproportionality arriving out of the majoritarian district results (see Mixed Member Proportional). But preferential voting can work equally well: the Single Transferable Vote, where voters rank-order candidates in multi-member districts, is another well-established proportional system (see Single Transferable Vote).
PR systems are a common choice in many new democracies. Over twenty established democracies, and just under half of all 'free' democracies, use some variant of PR (see The Global Distribution of Electoral Systems). PR systems are dominant in Latin America and Western Europe, and make up a third of all the systems in Africa. While seats are often allocated within regionally-based multi-member districts, in a number of countries (e.g. Germany, Namibia, Israel, Netherlands, Denmark, South Africa, and New Zealand) the parliamentary seat distribution is effectively determined by the overall national vote.
The formula used to calculate the allocation of seats after the votes have been counted can have a marginal effect on PR electoral outcomes. Formulae can be either by 'highest average' or 'largest remainder' methods (see Transforming Votes to Seats). However, district magnitudes (see District Magnitude) and the threshold for representation are of more importance to overall PR results (see Thresholds). The greater the number of representatives to be elected from a district, and the lower the required threshold for representation in the legislature, the more proportional the electoral system will be, and the greater chance small minority parties will have of gaining representation. In Israel, the threshold is 1.5 percent, while in Germany it is 5 percent. In the Seychelles a ten percent threshold is imposed for the twenty-three PR seats. In South Africa in 1994, there was no legal threshold for representation, and the African Christian Democratic Party won two seats out of 400, with only 0.45 percent of the national vote. Other important choices involve the drawing of district boundaries (see Boundary Delimitation); the way parties constitute their PR lists (see Open, Closed and Free Lists); the complexity of the ballot paper (e.g. the range of choice given to the voter - between parties, or between candidates and parties - see Way of Voting); arrangements for formal or informal 'vote-pooling'; and the scope for agreements between parties, such as that provided by systems which use apparentement (see Apparentement).
