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Measuring Electoral Bias: Australia, 1949–93


Electoral systems translate citizens' votes into seats in the legislature, and are thus critical components of democracies. But electoral systems can be unfair, insulating incumbents from adverse electoral trends, or biasing the mapping of votes to seats in favour of one party. I assess methods for measuring bias and responsiveness in electoral systems, highlighting the limitations of the popular ‘multi-year’ and ‘uniform swing’ methods. I advocate an approach that incorporates constituency-level and jurisdiction-wide variation in party's vote shares. I show how this method can be used to elaborate both the extent and consequences of malapportionment. I then present election-by-election estimates of partisan bias and responsiveness for ninety-three state and federal elections in Australia since 1949. The empirical results reported show that the coalition parties have generally ‘out-biased’ the Australian Labor party, despite some notable pro-ALP biases. The overall extent of partisan bias in Australian electoral systems, however, has generally diminished in magnitude over time.

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1 See Arrow Kenneth J., Social Choice and Individual Values, 2nd edn (New Haven, Conn.: Yale University Press, 1963); Mueller Dennis C., Public Choice (Cambridge: Cambridge University Press, 1979); Riker William H., Liberalism Against Populism: A Confrontation Between the Theory of Democracy and the Theory of Social Choice (Prospect Heights, Ill.: Waveland Press, 1982).

2 Rae Douglas, The Political Consequences of Electoral Laws (New Haven, Conn.: Yale University Press, 1967); Grofman Bernard and Lijphart Arend, eds, Electoral Laws and their Political Consequences (New York: Agathon Press, 1986).

3 For instance, Tufte Edward R., ‘The Relationship between Seats and Votes in Two-Party Systems’, American Political Science Review, 67 (1973), 540–54; King Gary and Browning Robert X., ‘Democratic Representation and Partisan Bias in Congressional Elections’, American Political Science Review, 81 (1987), 1251–73; Taagepera Rein and Shugart Matthew Soberg, Seats and Votes: The Effects and Determinants of Electoral Systems (New Haven, Conn.: Yale University Press, 1989).

4 I have in mind here choices among the following features of electoral systems: single-member versus multi-member constituencies, proportional representation with or without gatekeeping, transferable preferences (the ‘alternative vote’), majority versus plurality rule, etc.

5 See Griffith Elmer C., The Rise and Development of the Gerrymander (New York: Scott, Forseman, 1907).

6 Useful summaries include Coaldrake Peter, Working the System: Government in Queensland 1983–1989 (St Lucia: University of Queensland Press, 1989); Fitzgerald Ross, From 1915 to the Early 1980s: A History of Queensland (St Lucia: University of Queensland Press, 1984); Lunn Hugh, Joh: The Life and Political Adventures of Sir Johannes Bjelke-Petersen, 2nd edn (St Lucia: University of Queensland Press, 1984).

7 Jaensch Dean, ‘A Functional “Gerrymander” – South Australia, 1944–1970’, Australian Quarterly, 42, No. 4 (1910), 96101.

8 Butler David and Cain Bruce, Congressional Redistricting: Comparative and Theoretical Perspectives (New York: Macmillan, 1992), pp. 122–3.

9 Gelman Andrew and King Gary, ‘Estimating the Electoral Consequences of Legislative Redistricting’, Journal of the American Statistical Association, 85 (1990), 274–82.

10 In this brief summary I do not provide a comprehensive survey of the complexities of Australian constitutionalism, federalism and its political and electoral history. My aim here is merely to introduce enough detail so as to render my substantive focus on electoral manipulation accessible to readers unfamiliar with the Australian political system. Standard textbook introductions to Australian politics include Aitkin Don, Jinks Brian and Warhurst John, Australian Political Institutions, 4th edn (Melbourne: Pitman, 1989); Mayer Henry and Nelson Helen, eds, Australian Politics: A Fifth Reader (Melbourne: Longman Cheshire, 1980); and Crisp L. F., Australian National Government, 5th edn (Melbourne: Longman Cheshire, 1983).

11 The territories are subsequent creations of the federal government. Constitutional amendments and federal legislation since 1973 have gradually granted the territories more representation in the federal parliament, though the Northern Territory has had an elected member of the House of Representatives since 1922.

12 However, as I point out below, Australia's federal system creates many important exceptions to this general principle. Some observers find the term ‘Washminster’ more appropriate in describing Australia's mix of Westminster and federalist political institutions. See Jaensch Dean, Getting Our Houses in Order (Ringwood, Victoria: Penguin, 1986).

13 See Thomson James A., ‘State Constitutions and Institutional Systems’, in Galligan Brian, ed., Australian State Politics (Longman Cheshire: Melbourne, 1986), pp. 177–93.

14 Common law and Westminster conventions fill some of the constitutional breach. Grey areas persist, particularly over the status of the remaining legal and constitutional ties to the British monarchy, still the head-of-state in Australian jurisdictions: a ‘Governor’ for each state, and a ‘Governor-General’ for the Commonwealth. In November 1975, after failing to pass its budget through the opposition-controlled Senate, a federal Labor government was removed from office and parliament dissolved by the then Governor-General.

15 For example, Melbourne Corp v. Commonwealth (1947) 74 CLR 31; Victoria v. Commonwealth (1971) 122 CLR 353; Queensland Electricity Commission v. Commonwealth (1985) 159 CLR 192. See also the discussion in Lumb R. D., The Constitution of the Commonwealth of Australia Annotated, 4th edn (Sydney: Butterworth, 1986).

16 This principle was affirmed as recently as 1992 in Australian Capital Television Pty. Ltd. and others v. Commonwealth (No. 2) 108 ALR 577.

17 For example, sections 24, 27, 29 of the Commonwealth Constitution. Contrast the United States, where the state legislatures are responsible for redistricting of their respective congressional districts.

18 See, for example, the 1980s and 1990s amendments to the Commonwealth Electoral Act 1918; the Queensland Electoral Act 1992; and the 1991 amendments to the South Australian Constitution Act 1934 (see also fn. 60 below).

19 Redistricting of a state's House of Representatives constituencies begins ‘automatically’ when for a period of three months more than a one-third of the state's constituencies deviate from the average constituency enrolment by more than 10 per cent, or if more than seven years has passed since the last redistricting. Federal politicians, however, did legislate themselves an election year reprieve: redistricting under these provisions cannot take place within the last year of the federal parliament's three-year term. See Commonwealth Electoral Procedures (Canberra: Australian Electoral Commission, 1992) and Butler and Cain , Congressional Redistricting. p. 122.

20 For example, Queensland's Electoral Districts Act 1985 malapportioned the state via four ‘zones’ with enrolment quotas ranging from 9,186 for constituencies in the Western and Far Northern zone to 19,357 for constituencies in the South-Eastern zone. See Coaldrake 's Working the System, chap. 2.

21 Aitkin , Jinks and Warhurst , Australian Political Institutions, pp. 37, 146.

22 A good elementary introduction to Australia's electoral systems is Stevens Bron, Elections: How? Why? When? (Sydney: Rigby, 1984). A more advanced summary is Wright Jack F. H., ‘Australian Experience with Majority-Preferential and Quota-Preferential Systems’, in Grofman and Lijphart , Electoral Laws and their Political Consequences, pp. 124–38. Useful histories include Wright Jack F. H., Mirror of the Nation's Mind: Australia's Electoral Experiments (Sydney: Hale and Iremonger, 1980). and (for the Commonwealth) Reid Gordon S. and Forrest Martyn, Australia's Commonwealth Parliament, 1901–1988 (Melbourne: Melbourne University Press, 1989).

23 As of 1992 the line for failing to enrol for federal elections was up to $50; for failing to vote ‘without a valid and sufficient reason’. $20; and if the matter is dealt with in court, a tine of up to $50 (Commonwealth Electoral Procedures, p. 59). Fines vary at the state level, and voting is compulsory in local elections as well.

24 Though, of course, the alternative vole reduces to simple majority rule when only two candidates contest a seat.

25 Malcolm Mackerras is generally attributed with introducing two-party preferred vote totals to the study of Australian elections. For a review see Rydon Joan, ‘Two-Party Preferred: The Analysis of Voting Figures under Preferential Voting’. Politics, 21 (1986), 6874.

26 Gudgin Contrast G. and Taylor P., Seats, Votes, and the Spatial Organisation of Elections (London: Pion, 1979), pp. 165–9.

27 Except the 1983 elections for the Western Australian Legislative Assembly for which I was unable to obtain 2PP data.

28 369 U.S. 186(1962).

29 McKay Robert B., Reapportionment: The Law and Politics of Equal Representation (New York: Clarion, 1965); Polsby Nelson, Reapportionment in the 1970s (Berkeley: University of California Press, 1971).

30 Kendall M. G. and Stuart A., ‘The Law of Cubic Proportion in Election Results’, British Journal of Sociology, 1 (1950), 183–97. An early statement of the ‘cube law’ is in Edgeworth F. Y.'s paper presented to the Royal Statistical Society in 1898, ‘Miscellaneous Application of the Calculus of Probabilities’, Journal of the Royal Statistical Society, 61 (1898), 534–42. The Right Hon. J. Parker Smith, a Fellow of the Royal Society from 1891 and a four-term member of the House of Commons, cited Edgeworth's work and presented applications of the ‘cube law’ for British elections between 1885 and 1906 to a Royal Commission on Systems of Election (House of Commons Sessional Papers, 26 (1910), 7981). The Commission heard evidence on many different electoral systems operating in Europe and the Australian states at the time and makes fascinating reading.

31 Examples include McHenry Dean, ‘The Australian General Election of 1954’, Australian Quarterly, 27, No. 1 (1955), 1423; Rydon Joan, ‘The Relation of Votes to Seats in Elections for the Australian House of Representatives, 1949–1954’, Political Science, 9, No. 2 (1957), 4961; Warhurst John, ‘State Elections: Queensland and South Australia’, Politics, 13 (1978), 121–30.

32 Tufte , ‘The Relationship between Seats and Votes in Two-Party Systems’; Schrodt Phillip A., ‘A Statistical Study of the Cube Law in Five Electoral Systems’, Political Methodology, 7 (1981), 3153; King and Browning , ‘Democratic Representation and Partisan Bias in Congressional Elections’; cf. Gudgin and Taylor , Seats, Votes, and the Spatial Organisation of Elections.

33 Gudgin and Taylor , Seats, Votes, and the Spatial Organisation of Elections, Appendix One.

34 Debates as to the functional form of the error term are reviewed in Linehan William J. and Schrodt Phillip A., ‘A New Test of the Cube Law’, Political Methodology, 4 (1978), 353–67, and King and Browning , ‘Democratic Representation and Partisan Bias in Congressional Elections.’

35 Variously attributed to Niemi Richard and Fett Patrick, ‘The Swing Ratio: An Explanation and an Assessment’, Legislative Studies Quarterly, 11 (1986), 7590.

36 Niemi Richard and Jackman Simon, ‘Bias and Responsiveness in State Legislative Redistricting’, Legislative Studies Quarterly, 16 (1991), 183202.

37 Compulsory voting ensures that this particular confounding variable (differential turnout) is far less an issue in Australia than in the United States or the United Kingdom.

38 Butler David E., ‘Appendix III: The Relation of Seats to Votes’, in McCallum R. B. and Readman Alison, The British General Election of 1945 (London: Oxford University Press, 1947).

39 Gudgin and Taylor , Seats, Votes, and the Spatial Organisation of Elections, pp. 1420.

40 See Gudgin and Taylor , Seats, Votes, and the Spatial Organisation of Elections, p. 16.

41 The literature on this question is mammoth. Malcolm Mackerras has made the case for uniform swing in various articles, replies and rejoinders: see ‘Uniform Swing: Analysis of the 1975 Election’, Politics, 11 (1976), 41–6; ‘No Change: Analysis of the 1977 Election’, Politics, 13 (1978), 131–8; ‘Rejoinder to Campbell Sharman’, Politics, 13 (1978), 339–42. Clive Bean and David Butler are also impressed with the uniformity of swings in Australian elections – see their ‘Uniformity in Australian Electoral Patterns: The 1990 Federal Election in Perspective’, Australian Journal of Political Science, 26 (1991), 127–36. For contrary arguments and evidence, see Rydon Joan, ‘Swings and Predictions: The Analysis of Australian Electoral Statistics’, in Mayer Henry, ed., Labor to Power (Sydney: Angus and Robertson, 1973); Sharman Campbell, ‘Swing and the Two-Party Preferred Vote: A Comment on Malcolm Mackerras’, Politics, 13 (1978), 336–9; Austen Brian, Uniformity and Variation in Australian Electoral Behavior: State Voting Patterns in House of Representatives Elections 1946–1975, Occasional Monograph No. 1 (Hobart: Department of Political Science, University of Tasmania, 1977); Austen Brian, ‘A Comment on Malcolm Mackerras’, Politics, 13 (1978), 342–4; Hughes Owen, ‘Uniform Swing Revisited: Further Comments on Mackerras’, Politics, 19 (1984), 111–18; Peetz D., ‘Donkeys, Deserters and Targets: Causes of Swing in Electorates in the 1987 Federal Election’, Australian Quarterly, 61 (1989), 468–80; Fischer Alistair, ‘Swings and Gerrymanders’, Electoral Studies, 10 (1991), 299312; Leithner Christian, ‘The Geographic Configuration of the Vote: New Results and Interpretations from Australian Data’ (paper presented to the Annual Meetings of the Australasian Political Studies Association, Australian National University, Canberra, 1992).

42 Fischer's ‘Swings and Gerrymanders’ is a notable exception among the ‘uniform swing’ literature cited in the previous footnote.

43 The uniform swing line in Figure 6 was estimated using restricted least squares, the restriction being that the slope parameter equal one. The unrestricted intercept parameter indicates the size and direction of the fitted uniform swing. The unrestricted slope estimate is 0.91 (s.e. = 0.03), and the root mean square error of the unrestricted model is marginally under 4 per cent, suggesting a slight improvement over the uniform swing model.

44 Bean and Butler , ‘Uniformity in Australian Electoral Patterns’, p. 133.

45 Though even in this application uniform swing is of dubious value. See the interesting review in Maley Michael and Medew Rodney, ‘Some Approaches to Election Night Forecasting in Australia’, Australian Journal of Political Science, 26 (1991), 5162.

46 For examples, see Rydon Joan, ‘“Malapportionment” – Australian Style’, Politics, 3 (1968), 133–47; Kelly James, ‘Vote Weightage and Quota Gerrymanders in Queensland, 1931–1971’, Australian Quarterly, 43 (1971), 3954; and Hughes Colin A., A Handbook of Australian Government and Politics, 1975–1984 (Sydney: Australian National University Press, 1986), Appendix A.

47 Strictly speaking, uniform swing does indeed yield standard errors, though they are always constrained to zero, implying an infinite level of confidence in the bias and responsiveness estimates. Garand Contrast James C. and Parent T. Wayne, ‘Representation, Swing, and Bias in US Presidential Elections, 1872–1988’, American Journal of Political Science, 35 (1991), 1011–31, where Equation (4) is fit to the step-functions generated by uniform swing (e.g., Figures 4 and 5).

48 One particular source of constituency-specific variation that has been modelled in this way is ‘incumbency advantage’. For example, see King Gary, ‘Representation through Legislative Redistricting: A Stochastic Model’, American Journal of Political Science, 33 (1989), 787824; King Gary and Gelman Andrew, ‘Systemic Consequences of Incumbency Advantage in the US House’, American Journal of Political Science, 35 (1991), 110–38; Gelman Andrew and King Gary, ‘A General Method for Evaluating Electoral Systems and Redistricting Plans’, American Journal of Political Science, 38 (1994), forthcoming.

49 Gelman and King , ‘Estimating the Electoral Consequences of Legislative Redistricting.’

50 In this article I have opted for a broad approach, analysing as many state and federal Australian elections as practical, rather than a detailed analysis of a smaller group of elections. Gathering constituency-level covariates for the large group of elections I analyse here is beyond my scope in this article. If such data are available I recommend use of an alternative model proposed by Gelmari and King (‘A General Method for Evaluating Electoral Systems and Redistricting Plans’), which can easily be implemented with their free computer program ‘Judgelt’.

51 By making ‘guesses’ about variance parameters deliberately high I offset any undue ‘over-confidence’ in my guesses about means. The data overwhelmingly dominate the distribution of constituency-level influences on vote shares I ultimately settle on for each election.

52 Soper C. S. and Rydon Joan, ‘Under-Representation and Electoral Prediction’, Australian Journal of Politics and History, 4 (1958), 94106. Subsequent applications include Rydon Joan, ‘A Note on Voting and ALP Under-Representation in the 1958 Federal Elections’, Australian Journal of Politics and History, 5 (1959), 84–6; Rydon Joan, ‘Some Aspects of Voting in the 1961 Elections’, Australian Journal of Politics and History, 8 (1962), 98101; Rydon Joan, ‘The South Australian “Gerrymander”’, Australian Journal of Politics and History, 9 (1963), 86–7; Jaensch , ‘A Functional “Gerrymander” – South Australia, 1944–1970’; Gudgin and Taylor , Seats, Votes, and the Spatial Organisation of Elections, pp. 57–8. Contrast uses of Gini coefficients and differences between median and mean constituency-level vote shares. See Hughes Colin A., ‘Fair and Equal Constituencies: Australia, Jamaica and the United Kingdom’, Journal of Commonwealth and Comparative Politics, 16 (1978), 256–71, and ‘A Close-Run Thing’, in Penniman Howard E., ed., Australia at the Polls: The National Elections of 1980 and 1983 (American Enterprise Institute, Washington, DC: George Allen & Unwin, 1983).

53 In the pathological case of equal numbers of voters in all constituencies (wi = 1, for all i), the covariance term in Equation (10) is zero because wi, is invariant: i.e., no malapportionment is possible.

54 I use the sum of the Labor and non-Labor 2PP votes as a proxy for constituency size, since compulsory voting helps ensure that voter turnout is consistently high in Australian elections. Any biases introduced by this proxy are unlikely to be substantial nor bear heavily on my later conclusions.

55 Taking the product of the correlation between votes and constituency size and Gini coefficient results in weighting down elections with strong correlations but relatively equally sized constituencies (e.g., NSW 1988, VIC 1985). This product is a close approximation to the covariance term in Equation (10), and has the advantage that both correlation and Gini coefficients have well-defined and easily interpreted metrics.

56 No 2PP data is available for the 1957 Queensland election, held under plurality voting at the height of the ALP ‘split’.

57 Mackerras Malcolm, ‘A Revisionist Interpretation of the Impact of Queensland's Electoral Scheme’, Australian Journal of Political Science, 25 (1990), 339–49.

58 See the Report of the Electoral Districts Boundaries Commission (Adelaide: Government Printer, 1991), p. 2, and note B.2 below.

59 The ‘loess’ curves in Figures 11 and 12 are locally weighted regression fits to the data, as described in Cleveland William S., Grosse Eric and Shyu William M., ‘Local Regression Models’, in Chambers John M. and Hastie Trevor J., eds, Statistical Models in S (Pacific Grove, Calif.: Wadsworth and Brooks, 1992).

60 Amendments to the South Australian Constitution (Constitution Act 1991) provide, inter alia that ‘83. (1) … the Commission must ensure, as far as practicable, that … if candidates of a particular group attract more than 50 per cent of the popular vote (determined by aggregating vote cast throughout the State and allocating preferences to the necessary extent), they will be elected in sufficient numbers to enable a government to be formed.’ Such requirements obviously require a consideration of many of the issues I raise above. Further, South Australia's ‘50 percent rule’ comes close to a constitutional mandate for the very measures of electoral bias I employ here.

61 ‘One wonders whether this [malapportionment] might be best for the party itself; without vigorous and effective criticism from outside can it maintain its record of efficiency?’ These reflections refer, not a little ironically, to the ALP in Queensland during the 1950s. See Morrison A. A., ‘The Queensland Electoral System’, Australian Quarterly, 28 (1956), 80–5.

62 Formally known as the ‘Commission of Inquiry Into Possible Illegal Activities and Associated Police Misconduct’ (19871989), the Fitzgerald Inquiry had far-reaching political consequences in Queensland. Labor resumed office in the 1989 election after thirty-two years in opposition, in the wake of the Commission's findings of high-level corruption in Queensland public life. Among Fitzgerald's recommendations was the creation of an independent electoral commission in Queensland. See the Report of the Commission and discussions in Coaldrake 's Working the System: Government in Queensland, and Whitton Evan, The Hillbilly Dictator: Australia's Police State (Crows Nest: ABC Enterprises, 1989). Mackerras Contrast, ‘A Revisionist Interpretation of the Impact of Queensland's Electoral Scheme’, p. 347.

63 Key V. O., Southern Politics in State and Nation (New York: Knopf, 1949; 2nd reprinting, Knoxville: University of Tennessee, 1986), chap. 14.

64 For an introduction see Stine Robert, ‘An Introduction to Bootstrap Methods: Examples and Ideas’, in Fox John and Long J. Scott, eds, Modern Methods of Data Analysis (Newbury Park, California: Sage, 1990).

65 Gelman and King , ‘Estimating the Electoral Consequences of Legislative Redistricting’.

66 See Hughes , ‘Fair and Equal Constituencies’, p. 262.

67 This estimate is obtained by substituting the estimate of σ in the following expression:

recalling that σ is on the logit scale, and that logit (0.5) = 0.

68 King Gary, Unifying Political Methodology (New York: Cambridge University Press, 1989), p. 82.

69 For details on the properties of these distributions see Johnson Norman L. and Kotz Samuel, Distributions in Statistics: Continuous Univariate Distributions I and II (New York: Wiley, 1970). Algorithms for generating random samples from these distributions can be found in Devroye Luc, Non-Uniform Random Variate Generation (New York: Springer-Verlag, 1986) and Narayanan A., ‘Computer Generation of Dirichlet Random Vectors’, Journal of Statistical Computation and Simulation, 36(1990), 1930.

70 Tanner Martin A. and Wong Wing Hung, ‘The Calculation of Posterior Distributions by Data Augmentation’, Journal of the American Statistical Association, 82 (1987), 528–40. This method is a special case of what is known as ‘Gibbs sampling’ in the statistics literature. See Tanner Martin A., Tools for Statistical Inference: Observed Data and Data Augmentation Methods (New York: Springer Verlag, 1991), the review in Gelman Andrew and Rubin Donald B., ‘Inference from Iterative Simulation Using Multiple Sequences’, Statistical Science, 7 (1992), 457511, and the essays in Bernardo J. M., Berger J. O., Dawid A. P. and Smith A. F. M., eds, Bayesian Statistics 4 (Oxford: Oxford University Press, 1992).

71 See Dempster A. P., Laird N. M. and Rubin D. B., ‘Maximum Likelihood from Incomplete Data via the EM Algorithm’, Journal of the Royal Statistical Association, Series B.39, No. 1 (1977), 122; Aitkin Murray and Wilson Granville T., ‘Mixture Models, Outliers, and the EM Algorithm’, Technometrics, 22 (1980), 325–31; Rubin D. B. and Little R., Statistical Analysis with Missing Data (New York: Wiley, 1987); and McLachlan Geoffrey J. and Basford Kaye E., Mixture Models: Inference and Applications to Clustering (New York: Marcel Dekker, 1988).

* Woodrow Wilson School of Public and International Affairs, Princeton University (visiting), and Department of Political Science, University of Rochester. Larry Bartels, John Londregan and Gary King patiently helped my understanding of many of the issues addressed here. A report of this research was presented to the Annual Meetings of the Australasian Political Studies Association, Australian National University, Canberra, October 1992. Alistair Fischer, Colin Hughes and Gillian Weiss made useful comments on an earlier draft. Many people helped me acquire data and other materials. I thank Doug Arnold, A. K. Becker and the staff of the South Australian State Electoral Department, Beverley Brill, Brian Costar, David Gow, Colin Hughes, Therese Iverach (New South Wales State Electoral Office), Maureen Jackman, Christian Leithner, Malcolm Mackerras, Roland McMillan, Gerard Newman (Parliamentary Research Service), Paul Reynolds, Glenn Rhodes and the staff of the Queensland Electoral Commission, Gina Roach (Social Science Data Archives), Fabian Uzaraga and the staff of the Western Australian Electoral Commission, Katrina Von Wieldt, Trevor Willson (Australian Electoral Commission), and Claire Wrighton. I make extensive use of the data collection ‘Australian Two-Party Preferred Votes, 1949–82’, available from the Social Science Data Archives, Australian National University and originally published under the auspices of the Australasian Political Studies Association. Errors and omissions remain my responsibility.

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