¹ See Arrow, Kenneth J., Social Choice and Individual Values, 2nd edn (New Haven, Conn.: Yale University Press, 1963)Google Scholar; Mueller, Dennis C., Public Choice (Cambridge: Cambridge University Press, 1979)Google Scholar; 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).Google Scholar

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

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

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).Google Scholar

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

⁷ Jaensch, Dean, ‘A Functional “Gerrymander” – South Australia, 1944–1970’, Australian Quarterly, 42, No. 4 (1910), 96–101.CrossRefGoogle Scholar

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

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

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)Google Scholar; Mayer, Henry and Nelson, Helen, eds, Australian Politics: A Fifth Reader (Melbourne: Longman Cheshire, 1980)Google Scholar; and Crisp, L. F., Australian National Government, 5th edn (Melbourne: Longman Cheshire, 1983).Google Scholar

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).Google Scholar

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

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

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)Google Scholar and Butler, and Cain, , Congressional Redistricting. p. 122.Google Scholar

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.Google Scholar

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

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

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. 59Google Scholar). 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), 68–74.CrossRefGoogle Scholar

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

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)Google Scholar; Polsby, Nelson, Reapportionment in the 1970s (Berkeley: University of California Press, 1971).Google Scholar

³⁰ Kendall, M. G. and Stuart, A., ‘The Law of Cubic Proportion in Election Results’, British Journal of Sociology, 1 (1950), 183–97CrossRefGoogle Scholar. 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), 534–42Google Scholar. 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), 79–81Google Scholar). 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), 14–23Google Scholar; Rydon, Joan, ‘The Relation of Votes to Seats in Elections for the Australian House of Representatives, 1949–1954’, Political Science, 9, No. 2 (1957), 49–61CrossRefGoogle Scholar; Warhurst, John, ‘State Elections: Queensland and South Australia’, Politics, 13 (1978), 121–30.CrossRefGoogle Scholar

³² Tufte, , ‘The Relationship between Seats and Votes in Two-Party Systems’Google Scholar; Schrodt, Phillip A., ‘A Statistical Study of the Cube Law in Five Electoral Systems’, Political Methodology, 7 (1981), 31–53Google Scholar; King, and Browning, , ‘Democratic Representation and Partisan Bias in Congressional Elections’Google Scholar; cf. Gudgin, and Taylor, , Seats, Votes, and the Spatial Organisation of Elections.Google Scholar

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

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), 353–67Google Scholar, and King, and Browning, , ‘Democratic Representation and Partisan Bias in Congressional Elections.’Google Scholar

³⁵ Variously attributed to Niemi, Richard and Fett, Patrick, ‘The Swing Ratio: An Explanation and an Assessment’, Legislative Studies Quarterly, 11 (1986), 75–90.CrossRefGoogle Scholar

³⁶ Niemi, Richard and Jackman, Simon, ‘Bias and Responsiveness in State Legislative Redistricting’, Legislative Studies Quarterly, 16 (1991), 183–202.CrossRefGoogle Scholar

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).Google Scholar

³⁹ Gudgin, and Taylor, , Seats, Votes, and the Spatial Organisation of Elections, pp. 14–20.Google Scholar

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

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), 41–6Google Scholar; ‘No Change: Analysis of the 1977 Election’, Politics, 13 (1978), 131–8Google Scholar; ‘Rejoinder to Campbell Sharman’, Politics, 13 (1978), 339–42Google Scholar. 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), 127–36Google Scholar. 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)Google Scholar; Sharman, Campbell, ‘Swing and the Two-Party Preferred Vote: A Comment on Malcolm Mackerras’, Politics, 13 (1978), 336–9CrossRefGoogle Scholar; 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)Google Scholar; Austen, Brian, ‘A Comment on Malcolm Mackerras’, Politics, 13 (1978), 342–4CrossRefGoogle Scholar; Hughes, Owen, ‘Uniform Swing Revisited: Further Comments on Mackerras’, Politics, 19 (1984), 111–18CrossRefGoogle Scholar; Peetz, D., ‘Donkeys, Deserters and Targets: Causes of Swing in Electorates in the 1987 Federal Election’, Australian Quarterly, 61 (1989), 468–80CrossRefGoogle Scholar; Fischer, Alistair, ‘Swings and Gerrymanders’, Electoral Studies, 10 (1991), 299–312CrossRefGoogle Scholar; 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).Google Scholar

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.Google Scholar

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), 51–62.CrossRefGoogle Scholar

⁴⁶ For examples, see Rydon, Joan, ‘“Malapportionment” – Australian Style’, Politics, 3 (1968), 133–47CrossRefGoogle Scholar; Kelly, James, ‘Vote Weightage and Quota Gerrymanders in Queensland, 1931–1971’, Australian Quarterly, 43 (1971), 39–54CrossRefGoogle Scholar; and Hughes, Colin A., A Handbook of Australian Government and Politics, 1975–1984 (Sydney: Australian National University Press, 1986), Appendix A.Google Scholar

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), 1011–31CrossRefGoogle Scholar, 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), 787–824CrossRefGoogle Scholar; King, Gary and Gelman, Andrew, ‘Systemic Consequences of Incumbency Advantage in the US House’, American Journal of Political Science, 35 (1991), 110–38CrossRefGoogle Scholar; Gelman, Andrew and King, Gary, ‘A General Method for Evaluating Electoral Systems and Redistricting Plans’, American Journal of Political Science, 38 (1994), forthcoming.CrossRefGoogle Scholar

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

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’)Google Scholar, 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), 94–106CrossRefGoogle Scholar. 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), 84–6CrossRefGoogle Scholar; Rydon, Joan, ‘Some Aspects of Voting in the 1961 Elections’, Australian Journal of Politics and History, 8 (1962), 98–101CrossRefGoogle Scholar; Rydon, Joan, ‘The South Australian “Gerrymander”’, Australian Journal of Politics and History, 9 (1963), 86–7CrossRefGoogle Scholar; Jaensch, , ‘A Functional “Gerrymander” – South Australia, 1944–1970’Google Scholar; Gudgin, and Taylor, , Seats, Votes, and the Spatial Organisation of Elections, pp. 57–8Google Scholar. 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), 256–71CrossRefGoogle Scholar, 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).Google Scholar

⁵³ In the pathological case of equal numbers of voters in all constituencies (w_i = 1, for all i), the covariance term in Equation (10) is zero because w_i, 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.CrossRefGoogle Scholar

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

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).Google Scholar

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.Google Scholar

⁶² Formally known as the ‘Commission of Inquiry Into Possible Illegal Activities and Associated Police Misconduct’ (1987–1989)Google Scholar, 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 QueenslandGoogle Scholar, and Whitton, Evan, The Hillbilly Dictator: Australia's Police State (Crows Nest: ABC Enterprises, 1989)Google Scholar. Mackerras, Contrast, ‘A Revisionist Interpretation of the Impact of Queensland's Electoral Scheme’, p. 347.Google Scholar

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

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).Google Scholar

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

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

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.Google Scholar

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)Google Scholar. Algorithms for generating random samples from these distributions can be found in Devroye, Luc, Non-Uniform Random Variate Generation (New York: Springer-Verlag, 1986)CrossRefGoogle Scholar and Narayanan, A., ‘Computer Generation of Dirichlet Random Vectors’, Journal of Statistical Computation and Simulation, 36(1990), 19–30.CrossRefGoogle Scholar

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