¹ The relationship between the decline in competitive seats and the rise in incumbency advantage is not, however, as straightforward as it might at first seem, insofar as there is evidence that the likelihood of incumbent defeat can rise even if the average margin of victory for incumbents is rising, and conversely. Probability of incumbent defeat is affected by electoral volatility, among other factors (see Jacobson, G. C., ‘Strategic Politicians and the Dynamics of House Elections’ (paper presented at the annual meeting of the American Political Science Association, Washington, DC, 1988)Google Scholar; cf. Ansolabehere, S., Brady, S. and Fiorina, M., ‘The Marginals Never Vanished?’ (unpublished manuscript, Stanford University Graduate School of Business, 1988)Google Scholar. The discussion in this Note does not directly address the incumbency advantage issue (see the references cited above and King, Gary and Gelman, Andrew, ‘Systematic Consequences of Incumbency Advantage in US House Elections’ (unpublished manuscript, Department of Government, Harvard University, 1989).Google Scholar

² In the nineteenth century some House members were elected from multi-member districts which could distort the results. We ran the data both ways, excluding and including these districts, and there was no significant difference. The results reported exclude multi-member districts.

³ In general, constituencies are larger than clusters of voters; that is, districts contain more than one socially homogeneous area.

⁴ The competitiveness of Northern congressional elections falls most after the period of Wilsonian progressivism, and House elections continue less competitive through the periods of Republican control and Democratic New Deal dominance; competition declines again after the 1958 Democratic landslide, and there is a further decline in the 1960s (data omitted). See Brady, D., Critical Elections and Congressional Policy Making (Stanford, Calif.: Stanford University Press, 1988) for further details.Google Scholar

⁵ Tufte, E. R., ‘The Relationship Between Seats and Votes in Two-Party Systems’, American Political Science Review, 67 (1973), 540–7CrossRefGoogle Scholar; Grofman, B., ‘Declarations in Badham v. Eu’ (excerpts), Political Science (1985), 544–9, 573–4Google Scholar; Niemi, R. G. and Fett, P., ‘The Swing Ratio: An Explanation and Assessment’, Legislative Studies Quarterly, 11 (1986), 75–90.CrossRefGoogle Scholar

⁶ Tufte, , ‘The Relationship Between Seats and Votes in Two-Party Systems’Google Scholar; see also Campagna, J. and Grofman, B., ‘The Effects of Partisan Control of the Redistricting Process on Partisan Bias in 1980s Congressional Districting’, Journal of Politics (forthcoming, 1990).Google Scholar

⁷ Alternative logit or bilogit specifications are given in Linehan, W. J. and Schrodt, P., ‘A New Test of the Cube Law’, Political Methodology, 4 (1978), 353–67Google Scholar; Browning, R. X. and King, G., ‘Seats, Votes, and Gerrymandering: Estimating Representation and Bias in State Legislative Redistricting’, Law and Policy, 9 (1987), 305–22CrossRefGoogle Scholar; King, G. and Browning, R. X., ‘Democratic Representation and Partisan Bias in Congressional Elections’, American Political Science Review, 81 (1987), 1251–73CrossRefGoogle Scholar; and King, G., ‘Representation Through Legislative Redistricting: A Stochastic Model’, American Journal of Political Science, 33 (1989), 787–824CrossRefGoogle Scholar. The link between the procedure we use and the bilogit formula of King and his colleagues is discussed in Campagna, and Grofman, , ‘The Effects of Partisan Control of the Redistricting Process’Google Scholar.

⁸ Butler, D., The Electoral System in Britain 1918–1951 (London: Oxford University Press, 1953).Google Scholar

⁹ King, G., ‘Measuring Political Gerrymandering’ (unpublished manuscript, Department of Government, Harvard University, 1989).Google Scholar

¹⁰ Niemi, R. G. and Fett, P., ‘The Swing Ratio: An Explanation and Assessment’, Legislative Studies Quarterly, 11 (1986), 75–90.CrossRefGoogle Scholar

¹¹ Dahl, R. A., A Preface to Democratic Theory (Chicago: University of Chicago Press, 1956)Google Scholar; March, J. D., ‘Party Legislative Representation as a Function of Election Results’, Public Opinion Quarterly, 21 (1957), 521–42.CrossRefGoogle Scholar

¹² See especially Brady, , Critical Elections and Congressional Policy MakingGoogle Scholar; Grofman, B. N., ‘For Single-Member Districts, Random is Not Equal’, in Grofman, Bernard, Lijphart, Arend, McKay, Robert and Scarrow, Howard, eds, Representation and Redistricting Issues (Lexington, Mass.: Lexington Books, 1982), pp. 55–8Google Scholar; Gudgin, G. and Taylor, P. J., Seats. Votes and the Spatial Organisation of Elections (London: Pion, 1979)Google Scholar; Johnston, R. J., Political, Electoral and Spatial Systems: An Essay in Political Geography (Oxford: Clarendon Press, 1979).Google Scholar

¹³ See review in Grofman, B. N., ‘Measures of Bias and Proportionality in Seats-Votes Relationships’, Political Methodology, 9 (1983), 295–327.Google Scholar

¹⁴ Tufte, , ‘The Relationship Between Seats and Votes in Two-Party Systems’.Google Scholar

¹⁵ Niemi, R. G. and Deegan, J. Jr, ‘A Theory of Political Districting: Responsiveness and the Swing Ratio’, American Political Science Review, 72 (1978), 1304–23.CrossRefGoogle Scholar

¹⁶ Gudgin, and Taylor, , Seats, Votes and the Spatial Organisation of ElectionsGoogle Scholar; Johnston, , Political, Electoral and Spatial Systems, pp. 63–6.Google Scholar

¹⁷ E.g., Gross, D. and Garand, J. C., ‘Changes in the Vote Margins for Congressional Candidates: A Specification of Historical Trends’, American Political Science Review, 78 (1989), 17–31.Google Scholar

¹⁸ See especially Gudgin, and Taylor, , Seats, Votes and the Spatial Organisation of Elections, pp. 36ff.Google Scholar

¹⁹ Hicks, J. D., The Populist Revolt: A History of the Farmers' Alliance and the People's Party (Minneapolis: University of Minnesota Press, 1931)Google Scholar; Argersinger, P. H., Populism and Politics: William Alfred Peffer and the People's Party (Lexington: University of Kentucky Press, 1974).Google Scholar

²⁰ The competitiveness of Northern congressional elections fell most after the period of Wilsonian progressivism, and the House elections continued to be less competitive through the periods of Republican control and Democratic New Deal dominance. Competition declined again after the 1958 Democratic landslide, and there was a further decline in the 1960s (data omitted).

²¹ Cf. Grofman, B. and Handley, L., ‘The Effect of the Voting Rights Act on Black Success in Southern State Legislature and Congressional Districts’ (paper presented at the National Science Foundation Conference on the Voting Rights Act, Rice University, Houston, 1990).Google Scholar

²² King, and Gelman, , ‘Systematic Consequences of Incumbency Advantage in US House Elections’.Google Scholar

²³ King, and Gelman, , ‘Systematic Consequences of Incumbency Advantage’, Figure 9.Google Scholar

²⁴ However, pro-Democratic bias in particular states (e.g., California) might become invisible when we look at data aggregated to the regional level (see Grofman, B., ‘Declarations in Badham v. Eu (excerpts)’Google Scholar; Grofman, B. and Scarrow, H., ‘Current Issues in Reapportionment’, Law and Policy Quarterly, 4 (1982), 435–74CrossRefGoogle Scholar; Owen, G. and Grofman, B., ‘Optimal Partisan Gerrymandering’, Political Geography Quarterly, 7 (1988), 5–22)CrossRefGoogle Scholar. A state-level analysis of seats-votes relationships is a topic which must, however, be left to a subsequent paper. Disaggregated analyses of the sort that we regard as appropriate are found in Cain, B., ‘Assessing the Partisan Effects of Redistricting’, American Political Science Review, 79 (1985), 320–33CrossRefGoogle Scholar, for California congressional seats; and in Glazer, A., Grofman, B. and Robbins, M., ‘Partisan and Incumbency Effects of 1970's Congressional Redistricting’, American Journal of Political Science, 30 (1987), 680–701CrossRefGoogle Scholar, for congressional redistricting in the 1970s.

²⁵ King, and Gelman, 's innovative but unpublished paper, ‘Systematic Consequences of Incumbency Advantage’Google Scholar, seeks to disentangle the issue of partisan bias from the question of incumbency advantage.