Appendix THE MECHANICS OF ELECTORAL SYSTEMS The conversion of votes cast in a parliamentary election into seats in a legislature involves a number of related but distinct stages; at each stage choices can be made between different ways of accomplishing this end (Rose, 1983). Electoral systems can conveniently be divided into two major categories. Majority systems award a seat to the candidate who gets the most votes in a given constituency, whether a plurality of votes or an absolute majority, that is, one vote more than half of the total. Proportional representation (PR) systems attempt to allocate seats in proportion to votes. There is more than one form of proportional representation; it is the most frequently used method in Western nations today. In plurality systems (often known as 'first past the post') the candidate with the largest number of votes wins, even if this is less than an absolute majority. In a single-member constituency, electors have one vote. In multi-member constituencies, electors usually have as many votes as there are seats and candidates are ranked in order of the number of votes until all the seats in the constituency have been filled. Variants of the plurality system have been employed in order to assist in the representation of minorities in multi-member constituencies. The limited vote, used in Spain and Portugal in the 19th and early 20th centuries and in 13 United Kingdom constituencies between 1868 and 1880, restricts the number of votes an elector may cast to less than the total number of seats in a multi-member constituency. The single non-transferable vote, used in Japan today, is aversion of the limited vote; the elector may cast only one vote regardless of the number of seats in the constituency (Lijphart et al., 1986). The alternative vote, used in elections to the Australian House of Representatives since 1918, ensures that the winning candidate has an absolute majority. An absolute majority may be obtained on the first count, but with three or more candidates this is by no means certain. Hence each elector is required to rank alternative candidates in order of preference 1, 2, 3 etc. If no majority is secured on the first count the candidate with the lowest number of votes is eliminated and his or her second preferences distributed among the remaining candidates. If this does not produce an absolute majority, then the next lowest candidate is eliminated and his or her second preferences distributed and so on until an absolute majority is secured (Wright, 1986). The two-ballot system, widely used in continental European countries in the 19th century and in the French Third and Fifth Republics, is a variant on the 503 Appendix alternative vote (Fisichella, 1984). Instead of voters marking their preference in order at a single point in time two ballots may be held. If no candidate wins an absolute majority on the first ballot a second vote takes place. A majority at the second ballot may be guaranteed by eliminating all but the two leading first round contenders (as in Imperial Germany or the presidential elections of the French Fifth Republic). If more than two candidates are allowed to survive in the second round, a plurality can suffice for victory, as in the legislative elections of the Third or Fifth Republic. In France today, a candidate's first round vote must amount to at least 12.5 per cent of the total electorate in order to proceed to the second round. In Third Republic France there were no restrictions on proceeding to the second round, and candidates could enter the second round even if they did not contest the first. Proportional representation systems are designed to ensure a high degree of correspondence between a party's share of the popular vote and its share of seats in the legislature. Whereas plurality systems may operate with either single or multi­ member constituencies, PR must employ multi-member constituencies so that seats can be shared amongst the panies. In a single-member constituency, the candidate with the most votes wins and there is no representation for those favouring other candidates. That is the consequence of the election of a single individual to a unique office, such as a President. In PR systems the initial step in allocating seats is the identification of the quota of votes required to win a seato In the simplest method of calculating a quota (often known as the Hare quota), the total number of valid votes is divided by the number of seats to be allocated. Three alternatives are the Hagenbach-Bischojfquota, in wh ich the number of votes is divided by the number of seats plus one; the Droop quota, in which the number of votes is divided by the number of seats plus one and adding one to the quotient, and the lmperiali quota, uSed in Italy, where the number of votes is divided by the number of seats plus two. Thus, in a constituency with 60,000 votes and five seats, the respective quotas would be: Hare 12,000; Hagenbach-Bischoff 10,000; Droop 10,001; Imperiali 8,572. After the electoral quota for a constituency has been determined, the next step is to allocate the seats between the parties. Three major systems are in use. (i) Largest remainder. The vote for each party is divided by the electoral quota. A seat is awarded to each pany for each bloc of votes equal to a quota. Smaller panies that have not been awarded any seat will have all their votes counted as a remainder, and a party that has won seats will have a remainder that is short of a full quota. There mayaIso be seats remaining unallocated on the basis of requiring the winner to have a full quota. These seats are then allocated in strict sequence to the parties with the largest remainders. This system enables a small party to win a seat in a constituency, even if its share of the vote is less than a quota, provided that its initial vote is more than the remainder of parties that have already won a seato In the example in Table 1 (adapted from Mackenzie, 1956: 77-79), 24,000 valid votes have been cast in a five-member constituency. The Hare quota is therefore 24,000/5 = 4,800. In the first stage parties A, B and C each secure aseat, but pany D does not because its total vote is less than the quota. Two seats remain to be 504 Appendix allocated at the se~ond stage. One quota is subtracted from the votes cast for parties A, B and C, because they have each won aseat; party D's vote remains unchanged. Since Party A has the largest remainder and party D the second largest remainder they are awarded the two remaining seats. Table 1: DISTRffiUTION OF SEATS BY TIIE LARGEST REMAINDER SYSTEM Party First Round Rare Seats Second Round Seats Total Votes Quota Remainder Seats A 8,700 4,800 1 3,900 1 2 B 6,800 4,800 1 2,000 0 1 C 5,200 4,800 1 400 0 1 D 3,300 0 3,300 1 1 Total 24,000 5 (ii) Highest average system (d'Hondt version). In aseries ofrounds, each party's vote is divided by the number of seats it has been allocated in the ftrst mund quota plus one, then two, and so on. The remaining seats are allocated in turn to the party which has the highest average vote in each of these divisions. Table 2 considers a ftve-seat constituency contested by four parties, with the distribution of votes as in Table 1. In the ftrst mund parties A, B and C have been allocated one seat by passing the Rare quota of 4,800. Their divisor in the next mund is therefore two. Party D has not yet won a seat so its divisor is still one. In the second mund Party A, with an average of 4,350, has the highest average and therefore wins a seal. In the third and ftnal mund A's divisor is now three, because it has now won two seats, whereas the other parties' divisors remain the same. Party B, with 3,400 votes, now has the highest average, so it is awarded the last seato Table 2: DISTRffiUTION OF SEATS BY TIIE D'HONDT HIGHEST AVERAGE SYSTEM First Round Second Round ThirdRound Party Votes Rare Seats Divisor Average Seats Divisor Average Seats Total Quota Won Won Won Seats Won A 8,700 4,800 1 2 4,350 1 3 2,900 0 2 B 6,800 4,800 1 2 3,400 0 2 3,400 1 2 C 5,200 4,800 1 2 2,600 0 2 2,600 0 1 D 3,300 4,800 0 1 3,300 0 1 3,300 0 0 Total 24,000 5 505 Appendix Another method of eomputation for allocating seats under the highest average system (which produees an identieal outeome) uses the Hagenbaeh-Bisehoff quota. Beeause this quota is smaller than the Hare quota, a larger number of seats may be allocated initially. For the ease quoted in Table 2, the Hagenbaeh-Bisehoff quota would be 4,000, and thus four seats would be allocated in the first round, including two to party A, with a vote more than twiee the size of the quota. A third alternative under the d'Hondt system is to allocate seats simply by the highest average without any use of a quota.