Designing electoral institutions: STV systems and their consequences

Political Studies

Volumn 44, Issue 1, 1996, Pages 24-43

  Farrell, David M ^a   Mackerras, Malcolm ^a   McAllister, Ian ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030094172     PISSN: 00323217     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-9248.1996.tb00755.x     Document Type: Article

References (102)

1. A. Lijphart and B. Grofman, 'Choosing an electoral system' in A. Lijphart and B. Grofman (eds). Choosing an Electoral System: Issues and Alternatives (New York, Praeger, 1984), p. 6.
2. In France over this period the system has changed from majoritarian (second-ballot), to PR-list and back again to majoritarian.
3. R. Taagepera, 'The Baltic States', Electoral Studies, 9 (1990), 303-11; P. Wilder, 'The Estonian elections of 1992: proportionality and party organization in a new democracy', Representation: Journal of Electoral Record and Comment, 31 (1993), 72-6.
4. R. Taagepera, 'The Baltic States', Electoral Studies, 9 (1990), 303-11; P. Wilder, 'The Estonian elections of 1992: proportionality and party organization in a new democracy', Representation: Journal of Electoral Record and Comment, 31 (1993), 72-6.
5. For a small selection, see V. Bogdanor, What is Proportional Representation? A Guide to the Issues (Oxford, Martin Robertson, 1984); E. Lakeman, How Democracies Vote: a Study of Majority and Proportional Electoral Systems (London, Faber and Faber, 3rd ed. 1970); T. Newman, Hare-Clark in Tasmania: Representation of all Minorities (Tasmania, Joint Library Committee of the Parliament of Tasmania, 1992); R. Taagepera and M. S. Shugart, Seat and Votes: the Effects and Determinants of Electoral Systems (New Haven, Yale University Press, 1989); J. F. H. Wright, Mirror of the Nation's Mind: Australia's Electoral Experiments (Sydney, Hale and Iremonger, 1980).
6. For a small selection, see V. Bogdanor, What is Proportional Representation? A Guide to the Issues (Oxford, Martin Robertson, 1984); E. Lakeman, How Democracies Vote: a Study of Majority and Proportional Electoral Systems (London, Faber and Faber, 3rd ed. 1970); T. Newman, Hare-Clark in Tasmania: Representation of all Minorities (Tasmania, Joint Library Committee of the Parliament of Tasmania, 1992); R. Taagepera and M. S. Shugart, Seat and Votes: the Effects and Determinants of Electoral Systems (New Haven, Yale University Press, 1989); J. F. H. Wright, Mirror of the Nation's Mind: Australia's Electoral Experiments (Sydney, Hale and Iremonger, 1980).
7. For a small selection, see V. Bogdanor, What is Proportional Representation? A Guide to the Issues (Oxford, Martin Robertson, 1984); E. Lakeman, How Democracies Vote: a Study of Majority and Proportional Electoral Systems (London, Faber and Faber, 3rd ed. 1970); T. Newman, Hare-Clark in Tasmania: Representation of all Minorities (Tasmania, Joint Library Committee of the Parliament of Tasmania, 1992); R. Taagepera and M. S. Shugart, Seat and Votes: the Effects and Determinants of Electoral Systems (New Haven, Yale University Press, 1989); J. F. H. Wright, Mirror of the Nation's Mind: Australia's Electoral Experiments (Sydney, Hale and Iremonger, 1980).
8. For a small selection, see V. Bogdanor, What is Proportional Representation? A Guide to the Issues (Oxford, Martin Robertson, 1984); E. Lakeman, How Democracies Vote: a Study of Majority and Proportional Electoral Systems (London, Faber and Faber, 3rd ed. 1970); T. Newman, Hare-Clark in Tasmania: Representation of all Minorities (Tasmania, Joint Library Committee of the Parliament of Tasmania, 1992); R. Taagepera and M. S. Shugart, Seat and Votes: the Effects and Determinants of Electoral Systems (New Haven, Yale University Press, 1989); J. F. H. Wright, Mirror of the Nation's Mind: Australia's Electoral Experiments (Sydney, Hale and Iremonger, 1980).
9. For a small selection, see V. Bogdanor, What is Proportional Representation? A Guide to the Issues (Oxford, Martin Robertson, 1984); E. Lakeman, How Democracies Vote: a Study of Majority and Proportional Electoral Systems (London, Faber and Faber, 3rd ed. 1970); T. Newman, Hare-Clark in Tasmania: Representation of all Minorities (Tasmania, Joint Library Committee of the Parliament of Tasmania, 1992); R. Taagepera and M. S. Shugart, Seat and Votes: the Effects and Determinants of Electoral Systems (New Haven, Yale University Press, 1989); J. F. H. Wright, Mirror of the Nation's Mind: Australia's Electoral Experiments (Sydney, Hale and Iremonger, 1980).
10. There are, of course, particular technical problems associated with STV which have prevented its adoption in certain cases (or, at least, have been used as an excuse not to adopt it). For example, the British Labour Party's Plant Commission rejected STV partially on the grounds that it is non-monotonic (for criticisms, see Editorial, 'Lack of monotonicity', Representation: Journal of Electoral Record and Comment, 31 (1993), 70-1).
11. B. Chubb, 'Going about persecuting public servants: the role of the Irish parliamentary representative', Political Studies, 11 (1963), 272-86; M. Bax, Harpstrings and Confessions: Machine-Style Politics in the Irish Republic (Assen, Netherlands, Van Gorcum, 1976); P. M. Sacks, The Donegal Mafia: an Irish Political Machine (New Haven, Yale University Press, 1976).
12. B. Chubb, 'Going about persecuting public servants: the role of the Irish parliamentary representative', Political Studies, 11 (1963), 272-86; M. Bax, Harpstrings and Confessions: Machine-Style Politics in the Irish Republic (Assen, Netherlands, Van Gorcum, 1976); P. M. Sacks, The Donegal Mafia: an Irish Political Machine (New Haven, Yale University Press, 1976).
13. B. Chubb, 'Going about persecuting public servants: the role of the Irish parliamentary representative', Political Studies, 11 (1963), 272-86; M. Bax, Harpstrings and Confessions: Machine-Style Politics in the Irish Republic (Assen, Netherlands, Van Gorcum, 1976); P. M. Sacks, The Donegal Mafia: an Irish Political Machine (New Haven, Yale University Press, 1976).
14. Z. Baranski and R. Lumley, Culture and Conflict in Postwar Italy (London, Macmillan, 1990); M. Gallagher, 'Does Ireland need a new electoral system?', Irish Political Studies, 2 (1987), 27-48.
15. Z. Baranski and R. Lumley, Culture and Conflict in Postwar Italy (London, Macmillan, 1990); M. Gallagher, 'Does Ireland need a new electoral system?', Irish Political Studies, 2 (1987), 27-48.
16. A. Lijphart, 'The demise of the last Westminster system? Comments on the report of New Zealand's Royal Commission on the electoral system', Electoral Studies, 6 (1987), p. 100.
17. Taggepera, 'The Baltic States'; Wilder, 'The Estonian elections of 1992: proportionality and party organization in a new democracy'.
18. Taggepera, 'The Baltic States'; Wilder, 'The Estonian elections of 1992: proportionality and party organization in a new democracy'.
19. Lijphart, 'The demise of the last Westminster system? Comments on the report of New Zealand's Royal Commission on the electoral system'; M. Mackerras, 'Reform of New Zealand's voting system, 1985-96', Representation: Journal of Electoral Record and Comment, 32 (1994), 36-40; V. Bogdanor, The People and the Party System: the Referendum and Electoral Reform in British Politics (Cambridge, Cambridge University Press, 1981), p. 105. Bogdanor refers to one other example which is not consistent with Lijphart's law. As is well known, STV was developed coincidently by Thomas Hare (1806-91) in England and Carl Andrae (1812-93) in Denmark, neither aware of the other's ideas. Andrae was a government minister. In 1855 he applied his system to Danish federal elections, making this 'the first occasion on which the single transferable vote system was applied to a national legislature'.
20. Lijphart, 'The demise of the last Westminster system? Comments on the report of New Zealand's Royal Commission on the electoral system'; M. Mackerras, 'Reform of New Zealand's voting system, 1985-96', Representation: Journal of Electoral Record and Comment, 32 (1994), 36-40; V. Bogdanor, The People and the Party System: the Referendum and Electoral Reform in British Politics (Cambridge, Cambridge University Press, 1981), p. 105. Bogdanor refers to one other example which is not consistent with Lijphart's law. As is well known, STV was developed coincidently by Thomas Hare (1806-91) in England and Carl Andrae (1812-93) in Denmark, neither aware of the other's ideas. Andrae was a government minister. In 1855 he applied his system to Danish federal elections, making this 'the first occasion on which the single transferable vote system was applied to a national legislature'.
21. Lijphart, 'The demise of the last Westminster system? Comments on the report of New Zealand's Royal Commission on the electoral system'; M. Mackerras, 'Reform of New Zealand's voting system, 1985-96', Representation: Journal of Electoral Record and Comment, 32 (1994), 36-40; V. Bogdanor, The People and the Party System: the Referendum and Electoral Reform in British Politics (Cambridge, Cambridge University Press, 1981), p. 105. Bogdanor refers to one other example which is not consistent with Lijphart's law. As is well known, STV was developed coincidently by Thomas Hare (1806-91) in England and Carl Andrae (1812-93) in Denmark, neither aware of the other's ideas. Andrae was a government minister. In 1855 he applied his system to Danish federal elections, making this 'the first occasion on which the single transferable vote system was applied to a national legislature'.
22. R. Sinnott, 'The electoral system' in J. Coakley and M. Gallagher (eds), Politics in the Republic of Ireland (Dublin, Folens/PSAI, 2nd ed., 1993), p. 68.
23. For excellent histories, see D. Butler, The Electoral System in Britain Since 1918 (Oxford, Clarendon, 2nd ed., 1963); Bogdanor, The People and the Party System; J. Hart, Proportional Representation: Critics of the British Electoral System. 1820-1945 (Oxford, Clarendon, 1992).
24. For excellent histories, see D. Butler, The Electoral System in Britain Since 1918 (Oxford, Clarendon, 2nd ed., 1963); Bogdanor, The People and the Party System; J. Hart, Proportional Representation: Critics of the British Electoral System. 1820-1945 (Oxford, Clarendon, 1992).
25. For excellent histories, see D. Butler, The Electoral System in Britain Since 1918 (Oxford, Clarendon, 2nd ed., 1963); Bogdanor, The People and the Party System; J. Hart, Proportional Representation: Critics of the British Electoral System. 1820-1945 (Oxford, Clarendon, 1992).
26. Hart, Proportional Representation.
27. Hart, Proportional Representation, p. 210.
28. Bogdanor, The People and the Party System, p. 133.
29. Royal Commission, Report of the Royal Commission on the Electoral System: 'towards a Better Democracy' (Wellington, Government Publications, 1986), pp. 37-8.
30. R. L. Engstrom, 'Cincinnati's 1988 proportional representation initiative', Electoral Studies, 9 (1990), 217-25.
31. Lakeman, How Democracies Vote.
32. D. Rae, The Political Consequences of Electoral Laws (New Haven, Yale University Press, 1967).
33. A. Lijphart, Electoral Systems and Party Systems: a Study of Twenty-Seven Democracies, 1945-1990 (Oxford, Oxford University Press, 1994); Taagepera and Shugart, Seats and Votes.
34. A. Lijphart, Electoral Systems and Party Systems: a Study of Twenty-Seven Democracies, 1945-1990 (Oxford, Oxford University Press, 1994); Taagepera and Shugart, Seats and Votes.
35. See the discussion in M. Gallagher, 'Proportionality, disproportionality and electoral systems', Electoral Studies, 10 (1991), 33-51, and Lijphart, Electoral Systems and Party Systems.
36. See the discussion in M. Gallagher, 'Proportionality, disproportionality and electoral systems', Electoral Studies, 10 (1991), 33-51, and Lijphart, Electoral Systems and Party Systems.
37. A. Lijphart, 'Degrees of proportionality of proportional representation formulas' in B. Grofman and A. Lijphart (eds), Electoral Laws and Their Political Consequences (New York, Agathon, 1986), p. 171.
38. Taagepera and Shugart, Seats and Votes, p. 207; see also R. S. Katz, 'The single transferable vote and proportional representation' in A. Lijphart and B. Grofman (eds), Choosing an Electoral System: Issues and Alternatives (New York, Praeger, 1984).
39. Taagepera and Shugart, Seats and Votes, p. 207; see also R. S. Katz, 'The single transferable vote and proportional representation' in A. Lijphart and B. Grofman (eds), Choosing an Electoral System: Issues and Alternatives (New York, Praeger, 1984).
40. J. Blondel, An Introduction to Comparative Government (London, Weidenfeld and Nicolson, 1969), p. 191.
41. Lijphart, 'Degrees of proportionality of proportional representation formulas'.
42. M. Gallagher, 'Disproportionality in a proportional representation system: the Irish experience', Political Studies, 23 (1975), 501-13; P. Mair and M. Laver, 'Proportionality, PR and STV in Ireland', Political Studies, 23 (1975), 491-500.
43. M. Gallagher, 'Disproportionality in a proportional representation system: the Irish experience', Political Studies, 23 (1975), 501-13; P. Mair and M. Laver, 'Proportionality, PR and STV in Ireland', Political Studies, 23 (1975), 491-500.
44. Rae, The Political Consequences of Electoral Laws, p. 38.
45. Rae, The Political Consequences of Electoral Laws, p. 111.
46. Lijphart, 'Degrees of proportionality of proportional representation formulas', p. 175.
47. M. Gallagher, 'Comprising proportional representation electoral systems: quotas, thresholds, paradoxes and majorities', British Journal of Political Science, 22 (1992), 480. As Gallagher observes, this assumption may have some credence in Malta (as we shall see, also in the case of Australian Senate elections), 'but it should be made clear that this does not give a full picture of the way STV can operate in practice'.
48. Lijphart, 'Degrees of proportionality of proportional representation formulas' and Electoral Systems and Party Systems.
49. M. Gallagher, 'The political consequences of the electoral system in the Republic of Ireland', Electoral Studies, 5 (1986), 253-75. Gallagher has carried out the most detailed examination of this issue, and has found no reason to believe that proportionality is affected by particular transfer patterns in Irish elections.
50. R. S. Katz, A Theory of Parties and Electoral Systems (Baltimore MD, Johns Hopkins University Press, 1980).
51. Katz, A Theory of Parties and Electoral Systems, p. 108.
52. Taagepera and Shugart, Seats and Votes.
53. A related distinction is between those systems which have a consistent district magnitude (Malta on five and Tasmania on seven) and those which offer a range (all the rest).
54. In Ireland an 'X' is sufficient for a vote to be counted as valid. Similarly, in the case of Australian Senate 'ticket voting', an 'X' above the line is also counted.
55. This requirement was seen as a necessary reform when it was decided to readopt STV in Tasmania in 1907. The system had been abolished in 1901 (after a brief test since 1896), one reason being the apparent habit of voters to 'plump' for only one or two favoured candidates (Newman, Hare-Clark in Tasmania, pp. 43-61.
56. In reality a ballot paper which has most of the preferences completed (about 90 per cent) is accepted; however, this fact is not advertized and therefore not generally known.
57. N. Gow, 'The introduction of compulsory voting in the Australian Commonwealth', Politics, 6 (1971), 201-10; C A. Hughes, 'Compulsory voting', Politics, 1 (1966), 81-95; I. McAllister and T. Makkai, 'Institutions, society or protest? Explaining invalid votes in Australian elections', Electoral Studies, 12 (1993), 23-40.
58. N. Gow, 'The introduction of compulsory voting in the Australian Commonwealth', Politics, 6 (1971), 201-10; C A. Hughes, 'Compulsory voting', Politics, 1 (1966), 81-95; I. McAllister and T. Makkai, 'Institutions, society or protest? Explaining invalid votes in Australian elections', Electoral Studies, 12 (1993), 23-40.
59. N. Gow, 'The introduction of compulsory voting in the Australian Commonwealth', Politics, 6 (1971), 201-10; C A. Hughes, 'Compulsory voting', Politics, 1 (1966), 81-95; I. McAllister and T. Makkai, 'Institutions, society or protest? Explaining invalid votes in Australian elections', Electoral Studies, 12 (1993), 23-40.
60. Ballot paper design can also have important consequences for voters. The question here is which is fairer: a ballot paper which sorts by candidates (Ireland) where the voter has to work harder to find the relevant party labels, or a ballot paper which sorts by parties (all other systems), where the voter has to work harder to find the relevant candidates? For further discussion, see R. Darcy and M. Marsh, 'Decision heuristics: ticket-splitting and the Irish voter', Electoral Studies, 13 (1994), 38-49.
61. R. Darcy and I. McAllister, 'Ballot position effects', Electoral Studies, 9 (1990), 5-17.
62. Darcy and Marsh, 'Decision heuristics: ticket-splitting and the Irish voter'; J. Kelly and I. McAllister, 'Ballot paper cues and the vote in Australia and Great Britain: alphabetic voting, sex, and title', Public Opinion Quarterly, 48 (1984), 452-66; M. Mackerras, 'Preference voting and the "donkey vote"', Politics, 5 (1970), 69-76.
63. Darcy and Marsh, 'Decision heuristics: ticket-splitting and the Irish voter'; J. Kelly and I. McAllister, 'Ballot paper cues and the vote in Australia and Great Britain: alphabetic voting, sex, and title', Public Opinion Quarterly, 48 (1984), 452-66; M. Mackerras, 'Preference voting and the "donkey vote"', Politics, 5 (1970), 69-76.
64. Darcy and Marsh, 'Decision heuristics: ticket-splitting and the Irish voter'; J. Kelly and I. McAllister, 'Ballot paper cues and the vote in Australia and Great Britain: alphabetic voting, sex, and title', Public Opinion Quarterly, 48 (1984), 452-66; M. Mackerras, 'Preference voting and the "donkey vote"', Politics, 5 (1970), 69-76.
65. R. Darcy and M. Mackerras, 'Rotation of ballots: minimizing the number of rotations', Electoral Studies, 12 (1993), 77-82.
66. D. Jaensch, Getting our Houses in Order: Australia's Parliament: how it Works and the Need for Reform (Ringwood, Victoria, Penguin, 1986), p. 58.
67. M. Gallagher (ed.), Irish Elections 1922-44: Results and Analysis (Limerick, Political Studies Association of Ireland Press, 1993).
68. In general, see M. Gallagher and A. R. Unwin, 'Electoral distortion under STV random sampling procedures', British Journal of Political Science, 16 (1986), 243-68.
69. Ireland also represents one of the few cases of a PR system which incorporates by-elections. As a result of its recent electoral reforms, New Zealand is another example.
70. 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), pp. 135-6.
71. B. Farrell, 'Ireland: from friends and neighbours to clients and partisans' in V. Bogdanor (ed.), Representatives of the People? (Aldershot, Gower, 1985).
72. D. Farrell, 'Ireland: centralization, professionalization and campaign pressures' in R. Katz and P. Mair (eds), How Parties Organize: Adaptation and Change in Party Organizations in Western Democracies (London, Sage, 1994); M. Gallagher, 'Ireland: the increasing role of the centre' in M. Gallagher and M. Marsh (eds), Candidate Selection in Comparative Perspective: the Secret Garden of Politics (London, Sage, 1988); P. Mair, The Changing Irish Party System (London, Pinter, 1987).
73. D. Farrell, 'Ireland: centralization, professionalization and campaign pressures' in R. Katz and P. Mair (eds), How Parties Organize: Adaptation and Change in Party Organizations in Western Democracies (London, Sage, 1994); M. Gallagher, 'Ireland: the increasing role of the centre' in M. Gallagher and M. Marsh (eds), Candidate Selection in Comparative Perspective: the Secret Garden of Politics (London, Sage, 1988); P. Mair, The Changing Irish Party System (London, Pinter, 1987).
74. D. Farrell, 'Ireland: centralization, professionalization and campaign pressures' in R. Katz and P. Mair (eds), How Parties Organize: Adaptation and Change in Party Organizations in Western Democracies (London, Sage, 1994); M. Gallagher, 'Ireland: the increasing role of the centre' in M. Gallagher and M. Marsh (eds), Candidate Selection in Comparative Perspective: the Secret Garden of Politics (London, Sage, 1988); P. Mair, The Changing Irish Party System (London, Pinter, 1987).
75. D. Farrell, 'Campaign strategies' in M. Gallagher and M. Laver (eds), How Ireland Voted 1992 (Dublin, Folens/PSAI, 1993).
76. M. Gallagher, 'Comparing proportional representation electoral systems: quotas, thresholds, paradoxes and majorities'; Lakeman, How Democracies Vote; Wright, 'Australian experience with majority-preferential and quota-preferential systems'; for an exception, see A. S. Cohan, 'Rejoinder', British Journal of Political Science, 9 (1979), 369-70.
77. M. Gallagher, 'Comparing proportional representation electoral systems: quotas, thresholds, paradoxes and majorities'; Lakeman, How Democracies Vote; Wright, 'Australian experience with majority-preferential and quota-preferential systems'; for an exception, see A. S. Cohan, 'Rejoinder', British Journal of Political Science, 9 (1979), 369-70.
78. M. Gallagher, 'Comparing proportional representation electoral systems: quotas, thresholds, paradoxes and majorities'; Lakeman, How Democracies Vote; Wright, 'Australian experience with majority-preferential and quota-preferential systems'; for an exception, see A. S. Cohan, 'Rejoinder', British Journal of Political Science, 9 (1979), 369-70.
79. M. Gallagher, 'Comparing proportional representation electoral systems: quotas, thresholds, paradoxes and majorities'; Lakeman, How Democracies Vote; Wright, 'Australian experience with majority-preferential and quota-preferential systems'; for an exception, see A. S. Cohan, 'Rejoinder', British Journal of Political Science, 9 (1979), 369-70.
80. Gallagher, 'Comparing proportional representation electoral systems', p. 482.
81. R. J. Johnston, 'Friends-and-neighbours voting in Victoria: a note', Politics, 13 (1978), p. 152.
82. Rae, The Political Consequences of Electoral Laws.
83. S. Bowler and D. Farrell, 'Party loyalties in complex settings: STV and party identification', Political Studies, 39 (1991), 350-62; S. Bowler and D. Farrell, 'Voter behavior under STV-PR: solving the puzzle of the Irish party system', Political Behavior, 13 (1991), 303-20; Darcy and Marsh, 'Decision heuristics'.
84. S. Bowler and D. Farrell, 'Party loyalties in complex settings: STV and party identification', Political Studies, 39 (1991), 350-62; S. Bowler and D. Farrell, 'Voter behavior under STV-PR: solving the puzzle of the Irish party system', Political Behavior, 13 (1991), 303-20; Darcy and Marsh, 'Decision heuristics'.
85. S. Bowler and D. Farrell, 'Party loyalties in complex settings: STV and party identification', Political Studies, 39 (1991), 350-62; S. Bowler and D. Farrell, 'Voter behavior under STV-PR: solving the puzzle of the Irish party system', Political Behavior, 13 (1991), 303-20; Darcy and Marsh, 'Decision heuristics'.
86. Rae, The Political Consequences of Electoral Laws, p. 37.
87. F. A. Hermens, 'Representation and proportional representation' in A. Lijphart and B. Grofman (eds), Choosing an Electoral System: Issues and Alternatives (New York, Praeger, 1984), pp. 20-1.
88. Gallagher, 'Proportionality, disproportionality and electoral systems', p. 33.
89. Taagepera and Shugart, Seats and Votes.
90. Lijphart, Electoral Systems and Party Systems.
91. Lijphart, Electoral Systems and Party Systems, p. 13.
92. Since Malta3 is an unusual case, as a result of the contingent upper tier which was used in its 1987 election, we exclude it from the analysis.
93. The making of two new two-seater constituencies in the Australian territories in 1975 meant that average DM for full-Senate elections dropped from 10 to 8 (a 20 per cent change). The equivalent change for half-Senate elections (when both senators in the territories are also re-elected) was from 5 to 4.25 (only a 15 percent change). The increase in 1984 in state senatorial seats from 10 to 12 and from 5 to 6 respectively did not constitute a change of 20 per cent, when allowance is made for the territorial seats (which remained as two-seaters).
94. Lijphart, Electoral Systems and Party Systems, p. 30.
95. We exclude Israel and the Netherlands from these averages because they have very large DMs due to the fact that in both cases the entire nation is one constituency.
96. Rae, The Political Consequences of Electoral Laws.
97. J. Loosemore and V. Hanby, 'The theoretical limits of maximum distortion: some analytic expressions for electoral systems', British Journal of Political Science, 1 (1971), 467-77.
98. Gallagher, 'Proportionality, disproportionality and electoral systems'.
99. For comparisons with other electoral systems, see Lijphart, Electoral Systems and Party Systems, Appendix B.
100. Again directly comparable with Lijphart, Electoral Systems and Party Systems, Appendix B.
101. The estimates were also recalculated using the other three measures of disproportionality, producing substantially similar results.
102. Lijphart, Electoral Systems and Party Systems, p. 110.