A simulation of a proposed three-phase method for proportional representation in South Africa

Abstract

In October 1922 the President's Council of the Republic of South Africa approved a report on a proportional polling system for the country in a new constitutional dispensation. A three-phase method is proposed to ensure that there is not only proportionality with respect to the electoral regions of the country, but also on a party basis with respect to the votes cast in the election. A lower house of parliament with 400 seats is proposed. In the first phase 300 of the seats are made available to the various regions in proportion to the number of eligible voters in the respective regions. In the election the various parties compete for these 300 seats in the different regions. The second phase consists of allocating the seats to the parties on the basis of the actual votes cast for them in the regions. Because of factors such as variable percentage polls and support for the parties in the separate regions, it could happen that a particular party's portion of the 300 seats is not in accordance with the votes that it receives nationally. In the third phase the remaining 100 seats are used to rectify such situations. On the basis of the votes cast, these 100 seats are used for compensatory purposes, so that the final allocation of the 400 seats to the parties should be proportional to the support for the parties in the election. Fixed regional party lists of candidates for the election and the Jefferson allocation method are used in the applicable phases. We translate the pose of the President's Council report into formal mathematical descriptions of the proposed methods. Several hypothetical examples are used to illustrate the methods and to point out possible problems. A computer program which implements the methods is described briefly and is used to simulate various elections. These simulations show that 100 compensatory seats should be sufficient for the purpose for which they were introduced. We hope that our descriptions and analyses will contribute to the debate on an acceptable and practical electoral system in a new South Africa.