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. Eaeh seat is allocated in turn to a party which, after the allocation of an extra seat, will have the highest average number of votes per seat. In the first round, when no party has yet won aseat, the party with a plurality of votes has the highest average, so the first seat goes to Party A. (The order in wh ich the seats are assigned to a party is indieated in braekets in Table 3). After the allocation of a seeond seat Party B would have the highest average and therefore gains the seat. In the next round Party C has the highest average, then A and the last seat goes to party B.
Table 3: DISTRIBUTION OF SEATS BY THE D'HONDT HIGHEST AVERAGE SYSTEM WITHOUT AN INITIAL ALLOCATION BY QUOT A
1st seat 2nd seat 3rd seat 4th seat 5th seat Party Votes Divisor Divisor Divisor Divisor Divisor Total
A 8,700 8,700(1) 4,350 4,350 4,350(4) 2,900 2 B 6,800 6,800 6,800(2) 3,400 3,400 3,400(5) 2 C 5,200 5,200 5,200 5,200(3) 2,600 2,600 1 D 3,300 3,300 3,300 3,300 3,300 3,300 0
24,000 5
(iii) Highest average system (Sainte-Lague version). This system is identieal to d'Hondt exeept that the divisors used are odd numbers; instead of being 1,2,3,4 ete. they are 1,3,5, 7 ete. Beeause the inerease in the size of the divisor is greater under the Sainte-Lague system it is more diffieult for a party, onee it has been sueeessful, to win eaeh further seat. It is therefore more favourable to smaller parties than the d'Hondt system. In Table 4 parties A, Band C have eaeh passed the quota of 4,800 in the first round and have eaeh been awarded one seat. Their divisor in the next round is therefore three. Party D, whieh has not yet won a seat still has a divisor of one. In the seeond round D wins a seat with a highest average of 3,350. In the final round the divisor is three for all the parties, so the last seat goes to the party with a plurality of votes, Party A.
506 Appendix
Table 4: DISTRIBUTION OF SEATS BY TIIE SAINTE-LAGUE HIGHEST AVERAGE SYSlEM
First Round Second Round ThirdRound Party Votes Hare Seats Divisor Average Seats Divisor Average Seats Total Quota Won Won Won Seats Won
A 8,700 4,800 I 3 2,900 0 3 2,900 1 2 B 6,800 4,800 1 3 2,267 0 3 2,267 0 1 C 5,200 4,800 1 3 1,733 0 3 1,733 0 1 D 3,350 4,800 0 1 3,350 1 3 1,117 0 1
Total 24,000 5
When a full quota is required to win aseat, it can result in not all the seats in a constituency being allocated. In Table 4 only three parties, A, B, and C have as many votes as a Hare quota of 4,800. Since no party has as many votes as two full quotas, only three seats can be allocated on the basis of full quotas, and two seats remain. With a Hagenbach-Bischoff quota of 4,000 or an Imperiali quota of 3,429, Party A would be awarded two seats because its total vote is more than twice the quota, but one seat would still not be allocated. If the quota is combined with either the largest remainder or one of the versions of the highest average system, then all the seats in a constituency can be shared out. In some cases however this second stage calculation is carried out in a regional or even anational grouping. This tends to advantage smaller parties whose support is geographically widespread and whose votes may not be sufficient to reach a constituency quota. Unallocated seats are shared out in this way in Austria, Belgium, Greece and Italy. In three countries, Denmark, Germany and Sweden, some seats in the parliament are allocated in a nationwide constituency. The seats that the parties have won at constituency level are deducted from the national total, thus compensating for constituency-Ievel disproportionality. Threshold clauses may limit the parties which can participate in the higher-level allocation. For instance, in Germany a party must win either five per cent of the national vote or three single-member constituency seats and in Sweden a party must win four per cent of the national vote or 12 per cent of the vote in one constituency to be included in the nationwide distribution. The final stage in a proportional representation system is the allocation of seats to particular candidates. In some countries the elector can vote only for the party list, and the ranking of the candidates on the list is determined by the political party. The voter chooses a closed party list and the party list determines the order in which individual candidates can be elected. In many systems electors are able to cast one or more preference votes for individual candidates (Katz, 1986). In Finland, for example, a voter must actually vote for an individual candidate. Votes are then summed according to the candidates' parties and seats allocated proportionately to parties, and within a party, in accord with individual vote totals. More commonly,
507 Appendix the elector must choose a party list and then has the option of expressing a preference for individual candidates within that list. In a few cases voters may vote for candidates on different party lists (panachage). In the Single Transferable Vote system, used in Ireland, Malta and elections to the Australian Senate, the voter ranks the individual candidates rather than voting for a party list. In elections to the Irish Dail, a candidate must receive a Droop quota in order to be elected in a multi-member constituency (Gallagher, 1978). Any candidate whose flrst preference votes equal or exceed the Droop quota is declared elected. As there usua11y remain several seats to be mIed, a second count is held. Votes surplus to the quota cast for the successful candidates are transferred amongst the remaining candidates according to the second preferences recorded by the voter. This is calculated by counting all the second preference votes recorded on the ballots of the successful candidate and dividing them in proportion to the number of surplus votes. Any candidate who has now achieved a Droop quota is declared elected. If at any count no candidate is elected the candidate with the smallest number of votes is excluded and all his or her next preference votes are a110cated to other candidates. This procedure continues until a11 the seats have been mIed or the number of candidates remaining without a quota is one more than the seats remaining to be fl11ed. Then, the candidate with the least votes is eliminated and the top candidate or candidates are elected without a quota. A country's electoral law may combine features of several systems. For instance Germany overall achieves a proportional representation distribution, but half the members of the Bundestag are elected by a plurality in single-member constituencies. Table 5 records the main features of the electoral systems operating today in the countries included in this Almanac. The country chapters provide a historical summary of changes in the electoral systems and further details of national variations. The index of proportionality (Table 5) shows that the proportionality of electoral systems is a maUer of degree (Rose, 1983: 49ff; Lijphart, 1990). The degree of proportionality, according to this index, ranges from 79 per cent in the United Kingdom to 100 per cent in Malta. The index of proportionality ranges from 83 per cent in Spain to 100 per cent among PR systems and among plurality systems from 79 per cent to 94 per cent in the United States Congress. Thus, it is empirica11y possible for a plurality system to produce a more proportional result than a PR system. On average, a PR system scores 94 per cent on the index, and a plurality system, 86 per cent.
508 Table5 BASIC FEATURES OF ELECTORAL SYSTE~S 1
Compulsory VOling Work or TumoutCS) SealS Consuluencies Voting Age Rest Day % ~ :-<
Australia Yes 18 Rest 89.2 148 148 2 Austria No (2) 19 Rest 88.8 183 9(13)
Belgium Yes 18 Rest 87.2 212 30(14) 4 Canada No 18 Work 74.9 295 295
Denmark No 18 Wode 85.1 175(8) 18 a) Con stituency 135 17 b) National 40 1 6 Finland No 18 Sunday & Monday 71.7 200 15
7 France No 18 Rest 64.9 555 (9) 555 8 Germany No 18 Rest 83.5 496(0) 249 a) Constituency 248 248 b) National 248
9 Greece Yes 18 Rest 82.6 300 560S)
10 Iccland No 18 Rest 89.1 63 9 a) Constituency 50 8 b) National 13
11 lrcland No 18 Wode 67.7 166 41 12 Israel No 18 Rest 78.9 120 1
13 llaly Yes(3) 18 Sunday & Monday 84.6 630 32 (6) 14 Japan N;, 20 Rest 69.9 512 131
15 Luxemboorg Yes 18 Rest 82.5 60 4
16 Malla No 18 Wode 95.5 65 13 17 Netherlands No· (4) 18 Wode 85.5(6) 150
18 New Zea1and No 18 Rest 86.6 97 97 19 Norway No 18 Sunday & Monday 83.9 157 19
20 Portugal No 18 Rest 71.0 246(1) 20 21 Spatn No 18 Wode 69.1 350 52
22 Sweden No 18 Rest 84.9 349 29 a) Constituency 310 28 b) ~ational 39 1 23 Switz.erland No 20 Rest 46.1 200 26
24 U niled Kingdom No 18 Wode 75.3 650 650 25 United Slates Congress No 18 Wode 48.2(7) 435 (12) 435
1 Al mosl recent election for lower house of nalional parliamem. 2 Compulsory voting in Carinthia. Styria, Tyrol and Vorarlberg. 3 VOling is nol legally compulsory. but is regarded OS a civic duty and failure 10 vole is recorded for five years on an eleClOr's identity card. 4 VOling was compulsory from 1917 10 1967. 5 Al lalesl eleclion reported in this book. 6 Voting was compulsory umil 1971. From 1946 10 1967 tumout averaged 94.7 per cent.
509 SealS per BeelO" per Constituency Higher Level Candidale Choiee Index of (11» ConslIluency Represenlalive Seat Allocation Seal Allocation PropoTtionaI ny Ave"'ie Range (11)
0 69,954 Allernative V OIe Yes: individual 87 20 6-39 29,844 PR: Hare quota d'lIondl highe'l avg. Yes: fr 7 2-34 33,346 PR: Hare quota d·Hondl highesl avg. Ye, frorn pany li,l 92 0 59,793 Plurality Yes: individual 86 4 Yes: fr 0 65,973 Two-ballot plura1ity Yes: individual 81 7 99 8 0 182,774 P1urality LargeS! remainder Yes: individual 248 0 182,774 No: slriel pany list 5 2-32 24,607 PR: Hagenbaeh- LargeS! remainder Yes: f r 4 3-5 14,752 PR: smgle Iransferable vote Yes: individual 95 11 120 0 24,119 PR: d·Hondl higheS! avg. No: slriel pany 1iS! 94 12 20 2-53 PR: imperiali quOla Largest rem.inder Yes: rr 15 7·23 3,649 PR: Hagenbach- Yes: rrom pany Iists 91 15 Bischoff highesl avg. (paNlcllag.) (\9) 0 3,789 PR: single Iransferable vote Yes: individual 100 16 150 0 71,518 PR: d'Hondl higheS! aVI. Yes: fr 0 21,801 Pluralily Yes: indiVIdual candidale 88 18 4-15 19,748 PR: Sie Lague highesl Yes: from pany Iists 91 19 average (1) 12 3-56 30,965 PR: dllondl highest aVI. So: strici pany liS! 91 20 7 2-33 84,582 PR: dllondl highe .. avg. So: strict pany Iisl 87 21 Yes: rr 0 66,432 Pluralily Yes: indiVIdual 79 24 0 403,630 Pluralily Yes: indiVIdual 94 25 Percentage tumout of citizen population of voting age. Excludes four seats for representatives from the F aroe Islands and Greenland. Excludes 22 seats for the overseas departments and territories. 10 Exc1udes the representatives of West Berlin. Total number of seats in the Bundestag may be more than 496, because parties who win more single-member constituency seats than they would have been allocated by nationwide PR (überhangmandate) are allowed to keep the additional seals. 510 11 Exc1udes four sealS for representatives of Portugese citizens resident abroad. 12 Excludes the non-voting representatives of the Distriet of Columbia, Puerto Rico, the U.S. Virgin Islands, Guam, and American Samoa. 13 Each of Austria's nine provinces forms a constituency. SealS not allocated at the constituency stage are allocated in two regions, one comprising Vienna, Lower Austria and Burgenland, and the other the remaining six provinces. 14 SealS not allocated at the constituency level are allocated within groups of constituencies matching Belgium's nine provinces. 15 SealS not allocated at the constituency level are allocated in 13 regional groupings of constituencies. 16 Any sealS not aIlocated at the constituency level are allocated at the national level. 17 Range excludes a number of single-member distrielS in predominantly proportional representation systems, namely: Finland (Aland Islands), Greece (Evrytania, Kefallinia, LefIcas, Samos and Zakynthos), Italy (Val d'Aosta), Japan (Amami-Oshima Islands), Spain (Ceuta and Melilla) and Switzerland (Appenzell Inner-Rhoden, Glarus, Nidwalden, Obwalden and Uri). 18 A modified version of the Ste Lagui! system with an initial divisor of 1.4 instead of one. 19 Electors may vote for more than one candidate including those on the Iists of different parties. 20 The Index of Proportionality is calculated by sununing the difference between each party's percentage share of sealS and ilS share of votes, dividing by two and subtracting the result from 100. The formula is applied to the latest election reported in this book. Sourees: D. Fisichella, 'The double-ballot system as a weapon against anti-system parties', in A. Lijphart and B. Grofman (eds.) Choosing an Electoral System (New York: Praeger, 1984) 181-90 M. Gallagher, 'Party solidarity, exclusivity and inter-party relationships in Ireland : 1922-1977' Economic and Social Review 10,1 (1978) 1-22 R. Katz, 'Intraparty preference voting' in B. Grofman and A. Lijphart (eds.), Electoral Laws and their Political Consequences (New York: Agathon, 1986) A. Lijphart, 'The Political Consequences of Electoral Laws, 1945-85', American Political Science Review 85,2 (1990) 481-96 A. Lijphart, R. Lopez Pintor and Y. Sone, 'The limited vote and the single nontransferable vote', in B. Grofman and A. Lijphart (eds.), Electoral Laws and their Political Consequences (New York: Agathon, 1986) 154-169 W.J.M. Mackenzie, Free Elections (London: George Allen & Unwin, 1956) R. Rose, 'Elections and electoral systems: choices and alternatives', in V. Bogdanor and D. Butler (eds.), Democracy and Elections (Cambridge: Cambridge University Press, 1983) 20-45 J.F.H. Wright, 'Australian experience with majority-preferential and quota preferential systems', in B. Grofman and A. Lijphart, (eds.), Electoral Laws and their Political Consequences (New York: Agathon, 1986) 124-138 511