¹ See, for example, Finer, S. E., ed., Adversary Politics and Electoral Reform (London: Anthony Wigram, 1975)Google Scholar and The Report of the Hansard Society Commission on Electoral Reform (Chmn. Lord Blake) (London: Hansard Society for Parliamentary Government, 1976).Google Scholar

² Schumpeter, J. A., Capitalism, Socialism and Democracy, 5th edn (London: George Allen and Unwin, 1976)Google Scholar, Chapters 21 and 22. See also the classical debate on the single transferable vote between Mill and Bagehot contained in Chapter 7 of the former's Representative Government (1861)Google Scholar and Chapter 4 of the latter's English Constitution (1867).Google Scholar

³ Schumpeter, , Capitalism, Socialism and Democracy, p. 250.Google Scholar

⁴ See fn. 17 below for the Northern Irish case, and more generally Gallagher, Michael, ‘Disproportionality in a Proportional Representation System: The Irish Experience’, Political Studies, XXIII (1975), 501–13.CrossRefGoogle Scholar

⁵ Schumpeter, , Capitalism, Socialism and Democracy, p. 269.Google Scholar

⁶ Sartori, Giovanni, Parlies and Parly Systems (Cambridge: Cambridge University Press, 1978), p. 192 (emphasis as in the original).Google Scholar

⁷ For further details see Lakeman, E., How Democracies Vote (London: Faber, 1970), pp. 215–16 (Italy)Google Scholar, and pp. 222–4 (France); Carstairs, A. M., A Short History of Electoral Systems in Western Europe (London: George Allen and Unwin, 1980), pp. 156, 159 (Italy), and pp. 180–2Google Scholar (France); and Nohlen, D., Wahlsysteme der Welt: Ein Handbuch (München: R. Piper, 1978), pp. 173–207Google Scholar (on these and several other examples of such systems).

⁸ The use of the single transferable vote for most Northern Ireland elections since 1973 has awakened that part of the United Kingdom to some of the wider debates about electoral systems. In this article, where differences in the recent political experience of Northern Ireland and the rest of the United Kingdom limit the validity of our comments to Great Britain, that term is deliberately used.

⁹ Hereafter, the term ‘leading’ or ‘major’ party refers to the Conservative and Labour parties. All other parties are referred to as ‘third’ or ‘minor’ parties.

¹⁰ In the context of the cube law, electoral bias refers to the ability of one of the two leading parties to win more seats than the other leading party for any given share of the two-party vote. As its existence would mean that the leading party which wins less than 50 per cent of the two-party vote could win a majority of seats (as happened in 1951 and February 1974) it can seriously distort the ability of the electorate to choose between alternative governments. Although there have been changes in the extent and direction of electoral bias since 1955, we have excluded consideration of this from the article. A full examination would add substantially to the article's length; the bias will be altered by the current boundary review, and its existence does not have any substantial implications for the likelihood of ‘hung’ parliaments.

¹¹ Butler, D. E., ‘An Examination of the Results’Google Scholar, in Nicholas, H. G., The British General Election of 1950 (London: Macmillan, 1951), p. 333Google Scholar. See also Butler, D. E., The Electoral System in Britain since 1918, 2nd edn (Oxford: Clarendon Press, 1963), pp. 194–204.Google Scholar

¹² Kendall, M. G. and Stuart, A., ‘The Law of Cubic Proportion in Election Results’, British Journal of Sociology, 1 (1950), 183–96.CrossRefGoogle Scholar

¹³ Gudgin, G. and Taylor, P. J., Seats, Votes and the Spatial Organisation of Elections (London: Pion, 1979), p. 28.Google Scholar

¹⁴ Butler, , Electoral System in Britain, pp. 201–2.Google Scholar

¹⁵ See Gudgin, and Taylor, , Spatial Organisation of ElectionsGoogle Scholar, passim. As their work demons trates, besides political cleavages the number and size of constituencies and the form of districting can also influence the operation of the system.

¹⁶ Downs, Anthony, An Economic Theory of Democracy (New York: Harper, 1957).Google Scholar

¹⁷ At the first Stormont election, in 1921, only 0·8 per cent of the votes were not cast for Unionist or for anti-Partition candidates. The 66·9:32·3 ratio between these two camps would, on strict proportionality, have divided the forty-eight seats into thirty-two and sixteen. In fact, the application of the single transferable vote form of proportional representation within nine multi-member constituencies turned this into thirty-six and twelve. When Northern Ireland was divided into forty-eight single-member constituencies, eleven proved to have a clear anti-Partition majority, and one other was winnable by a republican, so the change did not affect the ratio of representation at Stormont. If, however, the cube law had operated (using the 1921 election – no subsequent election was contested on such a clear-cut basis) anti-Partition representation would have been reduced to four seats out of forty-eight.

¹⁸ Thus Krejci, J. and Velimsky, V., Ethnic and Political Nations in Europe (London: Croom Helm, 1981)Google Scholar, state ‘in the regional parliament (Stormont) the single-member constituency method left the Catholics underrepresented’ (p. 186) and make no reference to the more significant effects of the method.

¹⁹ Mitchell, Austin, Labour and Electoral Reform (London: Labour Campaign for Electoral Reform, 1980).Google Scholar

²⁰ For example, writing before the launch of the Liberal–SDP Alliance, but after the 1979 election, one of the prominent critics of adversary politics described the operation of the British electoral system in terms of the ‘cube law’ (See Finer, S. E., The Changing British Party System, 1945–79 (Washington, D.C.: American Enterprise Institute, 1980), p. 37)Google Scholar. Current textbooks on British politics also still emphasize the ability of the electoral system to produce safe overall majorities (see, e.g., Rose, R., Politics in England: an Interpretation for the 1980s (London: Faber, 1980), pp. 246–54)Google Scholar. The modern rediscoverer of the cube law has, however, noticed a change; see the contribution of Butler, D. in Stuart, A., Webb, N. L. and Butler, D., ‘Public Opinion Polls (with discussion)’, Journal of the Royal Statistical Society, Series A, CXLII (1979), 443–67, pp. 456–7.Google Scholar

²¹ The only area to swing against the tide in either election was East Anglia with a slight swing to Labour in 1955 – a regional variation which bears no relation to the subsequent pattern.

²² See, e.g., Leonard, R. L., Guide to the General Election (London: Pan Books, 1964), pp. 149–50Google Scholar; Butler, D. and Stokes, D., Political Change in Britain, 2nd edn (London: Macmillan, 1974), pp. 121, 140ff.CrossRefGoogle Scholar

²³ These notional results are explained on p. 284 of Butler, D. E. and Kavanagh, Dennis, The British General Election of February 1974 (London: Macmillan, 1974)CrossRefGoogle Scholar. In a few cases the notional figures may be somewhat unreliable, but due to the method used these will be in groups of neighbouring constituencies and most such groups are probably within a single socio-geographic category. The notation 1974(F) and 1974(O) refers to the February 1974 and October 1974 elections respectively.

²⁴ A full analysis of the variation in swing at each election since 1955 is to be found in the statistical appendices to the Nuffield series of elections studies, namely, ‘Appendix II: A Commentary on the Figures’, in Butler, D. and Rose, R., The British General Election of 1959 (London: Macmillan, 1960), pp. 232–40Google Scholar; Steed, M., ‘An Analysis of The Results’, in Butler, D. and King, A., The British General Election of 1964 (London: Macmillan, 1965), pp. 337–59Google Scholar; Steed, M., ‘An Analysis of The Results’, in Butler, D. and King, A., The British General Election of 1966 (London: Macmillan, 1966), pp. 271–95Google Scholar; Steed, M., ‘An Analysis of The Results’, in Butler, D. and Pinto-Duschinsky, M., The British General Election of 1970 (London: Macmillan, 1971), pp. 386–415Google Scholar; Steed, M., ‘The Results Analysed’Google Scholar, in Butler, and Kavanagh, , General Election of February 1974, pp. 313–39Google Scholar; Steed, M., ‘The Results Analysed’, in Butler, D. and Kavanagh, D., The British General Election of October 1974 (London: Macmillan, 1975), pp. 330–56Google Scholar; Curtice, J. and Steed, M., ‘An Analysis of The Voting’Google Scholar, in Butler, D. and Kavanagh, D., The British General Election of 1979 (London: Macmillan, 1980), pp. 390–431CrossRefGoogle Scholar. All further references to these appendices are in the form author, dale, page number.

²⁵ The claim that these two cleavages are the most important discriminators of the variation in swing is upheld by regression analysis. A stepwise regression analysis of the swing between 1955 and 1970, and between 1970(NT) and 1979, conducted separately, was undertaken using the more popular census variables and other (mostly location-identifying) dummies. The first three variables to be entered into the equation for each period were (a) for 1955–70, percentage car-owners, South & Midlands (dummy variable) and percentage lower non-manual (socioeconomic groups 5 and 6); (b) for 1970(NT)–79, percentage car-owners, Scotland (dummy variable) and percentage employed in agriculture. Both equations explain just over 40 per cent of the variance. Car-ownership is generally higher in rural areas than in cities, and in the South of the country than in the North. Lower non-manual employees are also systematically spatially segregated, being concentrated in cities, especially in and around London.

²⁶ For further detail see Steed, , 1970, p. 396Google Scholar; Steed, 1974 (F), pp. 331–3.Google Scholar

²⁷ Two-party swing is used in this table and throughout this paper. It is defined as the change in the Conservative share of the combined Conservative and Labour (two-party) vote. There is thus a clear relationship between this measure of swing and the distribution of the two-party vote whose shape determines the operation of the electoral system. On all occasions in the paper where mean (two-party) swing between two elections is quoted, those seats in which, at either of the two elections, there was a split major party candidature or an absence of a Labour or Conservative candidate, are excluded from the calculation.

²⁸ A full list of these studies from 1959 onwards is given in fn. 24 above.

²⁹ Thus the conurbation category ranged from constituencies such as Bootle and Salford East, which are in the inner-city core of the Merseyside and Greater Manchester conurbations but outside the areas of Liverpool and Manchester county boroughs respectively, to constituencies on the semi-rural fringe of the West Yorkshire conurbation, which the Registrar General defines more widely than the other English conurbations.

³⁰ The 1965 electorates for both old and new constituencies were published in the Second Periodical Reports of the Boundary Commissions for England, Scotland and Wales (London and Edinburgh: HMSO, 1969)Google Scholar (Cmnd. 4084, 4085 and 4086). Since 1965 redevelopment has significantly reduced population density in inner urban areas and the cut-off points which were most appropriate for the 1965 figures would not necessarily be so for later years. The areas used in the calculation of electorate density were obtained, so far as 1970(NT)–79 constituencies were concerned, from Electoral Statistics 1979 (London: HMSO, 1980)Google Scholar, and for English and Welsh 1955–70 constituencies from the Registrar General's Statistical Review of England and Wales for the Year 1969 (Part II) (London: HMSO, 1971)Google Scholar. Equivalent figures for 1955–70 constituencies in Scotland are not available, and were derived from the 1971 Census County Reports for Scotland which provide data on the area of local authority districts and wards. In the case of some constituencies (especially in Glasgow and Edinburgh), where local authority boundaries and those of parliamentary constituency boundaries did not coincide, the figures derived were necessarily approximate, but none of the Scottish constituencies had an electorate density close to one of the cut-off points.

³¹ Constituencies with an electorate density of between two and six persons per hectare mostly consist of a main urban centre (population in the 40,000–80,000 range) plus some nearby smaller communities, or of straggling urban development (e.g. a Welsh mining valley); the urban component of constituencies with an electorate density of less than two persons per hectare usually consists of smaller towns. For purposes other than the analysis of the effects of long-term swing, it might well be appropriate to divide our ‘Mixed’ category into two.

³² This analysis of variance also reveals that the variation in swing between our categories is significant at the 0·1 per cent level of probability in both periods.

³³ See especially, Crewe, I., Särlvik, B. and Alt, J., ‘Partisan Dealignment in Britain, 1964–74’, British Journal of Political Science, VII (1977), 129–90.CrossRefGoogle Scholar

³⁴ On the development of nationalism in Scotland see Miller, W. L., The End of British Politics? (Oxford: Clarendon Press, 1981)Google Scholar, and Miller, W., ‘The Connection between SNP Voting and the Demand for Scottish Self-Government’, European Journal of Political Research, V (1977), 83–102CrossRefGoogle Scholar. On the impact of the state's involvement in the economy on voting behaviour see Dunleavy, P. J., ‘The Urban Basis of Political Alignment: Social Class, Domestic Property Ownership, and State Intervention in Consumption Processes’, British Journal of Political Science, IX (1979), 409–43CrossRefGoogle Scholar, and Dunleavy, P. J., ‘The Political Impact of Sectoral Cleavages on the Growth of State Empoyment’, Political Studies, XXVII (1980), 364–83 and 527–49.CrossRefGoogle Scholar

³⁵ Miller, W., Electoral Dynamics (London: Macmillan, 1977)Google Scholar; Miller, W., ‘Social Class and Party Choice in England: A New Analysis’, British Journal of Poltical Science, VIII (1978), 257–84CrossRefGoogle Scholar; Miller, W., ‘Class, Region and Strata at the British General Election of 1979’, Parliamentary Affairs, XXXII (1979), 376–82CrossRefGoogle Scholar. Employers and managers are those economically active males employed in occupations in the Registrar General's socio-economic groups 1, 2 and 13.

³⁶ Corkindale, J. T., ‘Employment Trends in the Conurbations’, in Evans, A. and Eversley, D., eds., The Inner City: Employment and Industry (London: Heineman, 1980), pp. 157–8Google Scholar. The preliminary report of the 1981 Census shows that this pattern continued in the 1971–81 period, except that the highest rates of population growth were concentrated in the more distant rural areas rather than the semi-urban fringes of conurbations (See Census 1981: Preliminary Report, England and Wales (London: HMSO, 1981))Google Scholar. See also, Census Division, OPCS, ‘The First Results of the 1981 Census of England and Wales’, Population Trends, XXV (Autumn, 1981), 21–9Google Scholar. Movement out of the major cities in Scotland in the same period is charted in Census 1981 Scotland: Preliminary Report (Edinburgh: HMSO, 1981).Google Scholar

³⁷ McCallum, J. Douglas, ‘Statistical Trends of the British Conurbations’Google Scholar, in Cameron, G. C., ed., The Future of the British Conurbations: Policies and Prescriptions for Change (London: Longman, 1980), pp. 14–23.Google Scholar

³⁸ Corkindale, , ‘Employment Trends’, p. 171.Google Scholar

³⁹ Dugmore, K., ‘Migration and Social Change’, in Dugmore, , ed., The Migration and Distribution of Socio-Economic Groups in Greater London – Evidence from the 1961, 1966, 1971 Censuses (London: Greater London Council, 1975), pp. 4–32Google Scholar. If net emigration in 1965–66, as given in Table 1.1 (p. 7) of Dugmore's work, is expressed as a percentage of the resident population in 1966, the figures are: Professional and Managerial, 2·0; Skilled Manual, 1–5; Non-Manual, 1·0; Semi-skilled, 1·1 and Unskilled etc., 0·3.

⁴⁰ McCallum, , ‘Statistical Trends’, p. 27. McCallum's figures exclude socio-economic group 13. the smallest of the groups of employers and managers.Google Scholar

⁴¹ A comparison limited to constituencies with little or no boundary change shows that these figures could have been significantly affected by the boundary review.

⁴² Between 1974(F) and 1974(O) the mean swings in England and Wales (excluding three constituencies won by Plaid Cymru) within each of the categories used in Table 1 were: City, –3·6 (86); Very Urban, –3·3 (93); Mainly Urban, –2·8 (133); Mixed, –2·7 (141); Mainly Rural, –2·1 (66); Very Rural, –2·3 (27); All, –2·9 (546).

⁴³ See Miller, , Electoral DynamicsGoogle Scholar, and also ‘Social Class and Party Choice in England’.

⁴⁴ Corkindale, , ‘Employment Trends’, pp. 173–91.Google Scholar

⁴⁵ In ‘Planning in a Cold Climate: The Evolving Relationship between Planning and Market Forces in Britain in the 1970s’ (unpublished paper presented at the Annual Conference of the Political Studies Association, 1981)Google Scholar, Stephen Young argues that the interaction between planning policies and market forces has produced ‘two planning systems side by side’ (p. 12), thereby contributing to the existence of two political nations, which coincide closely with the areas of long-term swing to Conservative and to Labour.

⁴⁶ In this article, the convention adopted by F. W. S. Craig in his various Parliamentary Reference Services publications and by Butler, D. and Sloman, A. in their British Political Facts (London: Macmillan, 1979)Google Scholar of not regarding any Northern Ireland candidates fighting after 1970 as Conservative or Labour candidates is followed although some Northern Ireland Labour Party candidates (previously counted as Labour) fought in Northern Ireland in 1974 and 1979.

⁴⁷ Steed, , 1964, p. 348Google Scholar; Berrington, H., ‘The General Election of 1964 (with discussion)’, Journal of the Royal Statistical Society, Series A, CXXVIII (1965), 17–66CrossRefGoogle Scholar; Berrington, H., ‘The General Election of 1966: An Analysis of the Results’, Swinton Journal, XII (1966), 3–10Google Scholar; Berrington, H. and Bedeman, T., ‘The February Election’, Parliamentary Affairs, XXVII (1974), 326–32.Google Scholar

⁴⁸ Steed, , 1970, p. 389.Google Scholar

⁴⁹ Steed, , 1964, pp. 345–7Google Scholar; Steed, , 1966, pp. 286–7Google Scholar; Steed, , 1974 (F), pp. 317–23Google Scholar; Steed, , 1974(O), pp. 339–42. See also fn. 50.Google Scholar

⁵⁰ For a more detailed discussion see Curtice, and Steed, , 1979, pp. 405–7 and 414–16Google Scholar. It should be remembered that, as the Conservative-inclined seats where there had been a strong third party challenge were concentrated in the South & Midlands, part of the good performance in these seats in 1979 is to be accounted for by the high swing generally in the South & Midlands at that election.

⁵¹ Government statisticians have suggested that the overall pattern of change in the distribution of the population – a decline in the population of metropolitan areas and greater growth in the South & Midlands than in the North of England – will continue. See Social Trends (London: HMSO, 1979), p. 67.Google Scholar

⁵² In both the 1966 and 1979 elections, the two which departed most from the even split of the two-party vote, the actual outcome was rather closer than that projected from opinion polls at the beginning of the campaign. The electoral landslides before 1950 were all produced by an electorate which did not have the awareness of how it was intending to vote that opinion polls now provide.

⁵³ The distribution may also be non-normal because it is asymmetric, in which case electoral bias will occur. Electoral bias may also arise if constituencies are of unequal size. See also fn. 10 above. For further details on the impact of the kurtosis of the distribution of the two-party vote see Gudgin, and Taylor, , Spatial Organisation of Elections, pp. 71–3.Google Scholar

⁵⁴ Northern Ireland is excluded from this table and, unless the United Kingdom is stated, from the rest of this section. All twelve seats were safe Conservative seats (in two-party terms) from 1955 to 1970, whereafter they were not fought by either major party.

⁵⁵ It therefore follows that seats which are ‘marginal’ as between one of the two leading parties and a third party are classified as safe unless the other leading party is also in close contention.

⁵⁶ The total (United Kingdom) two-party vote is used rather than that in Great Britain only, or that in seats won by the two leading parties only (to which seats the cube law is more strictly meant to apply), on the grounds that it is the relationship between the division of the two-party vote and seats across the whole polity which should be used to assess the significance of the operation of the electoral system for democratic theory. When the cube law was originally used to defend the electoral system in the 1950s it was conceived of as operating across the whole of the United Kingdom, not just in Great Britain. In addition, our practice recognizes that, because of their loss of Northern Ireland seats, the Conservatives needed to win more seats in Great Britain in order to attain office, i.e. that the portion of the distribution of the two-party vote for which the two leading parties were effectively competing for national office was slightly shifted by this development. The apparent inconsistency of our practice arises from the fact that a behavioural phenomenon which occurred in only part (albeit a large part) of the country was the main cause of a change in a seats-to-votes relationship that was theoretically conceived of as operating across the country as a whole. The use of any of the mentioned alternatives slightly alters the number of marginal seats at any one election but not the trend of their decline.

⁵⁷ The figures in Table 14 are of the division of the two-party vote in Great Britain rather than in the United Kingdom, but the small adjustment that needs to be made to these figures to include Northern Ireland prior to 1974 (F) does not affect the truth of this assertion. See Craig, F. W. S., British Electoral Statistics 1885–1975 (London: Macmillan, 1976), p. 34.CrossRefGoogle Scholar

⁵⁸ It will be seen that the trend revealed by the number of marginal seats at each election differs slightly from that shown by the standard deviation and kurtosis. This is because those latter figures are also influenced by the shape of the distribution outside the range of marginal seats. Thus, although the number of marginal seats increased between 1974(O) and 1979, the standard deviation increased slightly and the kurtosis fell, reflecting a fall of twenty-three in the number of constituencies won by either leading party with a standardized two-party vote of between 55 per cent and 60 per cent.

⁵⁹ Strictly speaking, a slight negative correlation between swing and previous two-party strength is required to leave the standard deviation unaffected in the event of non-uniform swing. See Gudgin, and Taylor, , Spatial Organisation of Elections, pp. 61–4.Google Scholar

⁶⁰ Non-random swing may also affect the kurtosis, particularly if, for example, there is a strong positive correlation between swing and the two-party vote in marginal seats, in which case it will fall. The detailed analysis of movement of seats into and out of marginality below covers changes that are reflected both in the changing value of the standard deviation and of the kurtosis.

⁶¹ A comparison of mean swings in categories of constituencies with the overall swing for the whole country (i.e. one based on the total national vote), rather than with the mean of the individual swings in all constituencies, may appear inconsistent. If we were simply examining constituency behaviour it would be so. But we are analysing the effect of the behaviour of different types of constituency (best measured by the mean of those falling within defined categories) on the relationship between seats and votes across the whole system, which is an entity in its own right and not the sum of various categories of individual constituencies. (For the reasons set out in fn. 56 above, that whole is the United Kingdom, not just Great Britain.) The behaviour of the whole country is registered by the total votes cast in it. Table I gives the mean swings for all the constituencies (in Great Britain only) which are included in the table in each period; the overall swings in those constituencies were +0·15 (1955–70) and +3·06 (1970(NT)–79). Thus the effect of comparing the mean swing in each category of Table I with the overall rather than the mean of all the constituencies in the table (as opposed to the effect of the impact of those constituencies not included in Table 1 on the overall (United Kingdom) swing) is 1·13 in the first period and 0·57 in the second. These differences are explained by the fact that Labour's vote was increasingly concentrated in smaller-sized and lower-turnout constituencies, producing an electoral bias in their favour. The electoral bias to Labour that existed in 1979 is evident in Table 14.

⁶² The five Black Country constituencies in the category had a mean swing of +7·00 in 1955–70; without them the category would have had a mean swing of –0·55. In the second period the nine Black Country constituencies in the category had a mean swing of –4·73; without them the category would have had a mean swing of +2·57. The increased weight of those constituencies in the second period is a further complication; this problem is unique to the Black Country where redistribution (following a radical change in its local government structure in 1966) had a more disruptive effect than in the rest of the country.

⁶³ In the 1970(NT)–79 period, most Outer London constituencies had larger swings to the Conservatives than similarly urban constituencies elsewhere in the South & Midlands. This reflects two quite different local movements. Between 1974(F) and 1974(O), an outer suburban ring of Greater London had a distinctly low swing to Labour (see Steed, 1974(O), p. 337); between 1974(O) and 1979 an area of North-East London, extending from the inner city zone to Essex and Hertfordshire, had a distinctly high swing to the Conservatives (see Curtice and Steed, 1979, pp. 396–7). It is too soon to judge whether these are short-term deviations, which will therefore be reversed, or a clear variation in the long-term pattern that we have established.

⁶⁴ There were thirty-two Very Urban South & Midlands constituencies outside both the Black Country and Greater London. Their mean swings were –0·40 (1955–70) and +1·35 (1970(NT)–79), giving advantages to Labour of 0·49 and 1·09 respectively.

⁶⁵ Further support for this view can be found if one charts the movement of seats between 1955 and 1964 (at which elections the number of marginal seats was the same). Movement in line with the North–South and urban–rural variation in swing had produced a net fall of sixteen seats, but this was fully compensated for by other movements.

⁶⁶ It is possible to be more specific as to where the two were not in sufficient alignment. The only categories which saw the number of marginal seats significantly increased by congruent movements in 1955–70 were, in fact, the three most urban South & Midlands categories.

⁶⁷ Broadly speaking, one would anticipate that the rate of congruent movement to and from marginality would reflect the difference between the mean swing in the categories of a grouping and the overall (United Kingdom) swing. If one examines this, excluding those seats where there was a strong third party challenge (see Table 5), one finds that the difference was lower in the second period than in the first in the ‘Strong’ groupings, and higher in the ‘Moderate’ ones. On this logic the surprising finding is the fall in the rate of movement from incongruent safe to marginal in the two ‘Moderate’ groupings, especially the large fall which occurred in the ‘Moderately → Lab.’ grouping. We have attempted to understand this finding by undertaking a detailed analysis of the number of seats that would have moved to and from marginality in each period if all seats had experienced the mean swing for their category. This suggests that in the ‘Moderately → Lab.’ grouping the rate of movement from incongruent safe to marginal was higher than it should have been in the first period, while it was close to what would have been expected in the second. But it does not appear possible to explain the unexpectedly high rate of the first period by reference to any systematic factors.

⁶⁸ The boundary revision implemented at the 1974(F) election produced a similar effect, but this was outweighed by the polarization noted below.

⁶⁹ In the Conservative columns (b) is generally about three times the size of (a), in the Labour ones a little more so. This difference is accounted for by the fact that the Conservatives won the 1979 election: winning parties tend to win more seats in their weaker areas than do losing ones, and so their parliamentary party is somewhat more evenly distributed geographically. The extent to which the electoral system exaggerates the geographical cleavages is not a constant, but will depend on the shape of the distribution of the two-party vote within each category of seats (see Section 3). As the standard deviation of the two-party vote within each category of our North–South and urban–rural classification has tended to increase since 1970 (see p. 280), it is not surprising to discover that the ratio of column (b) to column (a) was generally higher in the equivalent table for 1955. Thus the tendency of the electoral system to accentuate these cleavages has been somewhat attenuated.

⁷⁰ Table 9(1) assumes votes would have been cast exactly as they were within the existing constituencies; (2) ignores votes cast for parties with less than 5 per cent within a regional area; (3) leaves the maldistribution of seats between regional areas exactly as it is; and (4) assigns seats proportionally by the d'Hondt (largest average) rule.

⁷¹ Recent tinkering with the rate support grant by the Labour party (in favour of urban areas) and by the Conservative party (in favour of rural areas) illustrates how the urban–rural cleavage has recently been reflected in the policy output of government. (See Bennett, R. J., The Geography of Public Finance (London: Methuen, 1980), pp. 355, 443Google Scholar and sources cited thereat.) A North–South cleavage in the relative impact of the June 1979 budget is shown in Johnston, R. J., ‘The Spatial Impact of Fiscal Changes in Britain: Regional Policy in Reverse?’, Environment and Planning A, IX (1979), 1439–44.CrossRefGoogle Scholar

⁷² Gudgin, and Taylor, , Spatial Organisation of Elections, pp. 74–5 and 116–9.Google Scholar They point out (p. 75) that ‘The Liberals are, in a sense, penalised for being a nationwide party’.

⁷³ In all cases shown the party concerned contested all, or nearly all, of the constituencies in the area concerned. In Scotland there were only thirty-four Liberal candidates in 1974(F) and forty-three in 1979 out of seventy-one seats, and these two cases are therefore excluded.

⁷⁴ The SNP representation in 1979 lies between the second and third type of case. At that election their vote was just insufficient for them to benefit as much as they did at the two previous elections from the moderate degree of positive skewness and variance that the distribution of their vote has. They were 5 per cent or less behind the winning party in six constituencies. For further discussion of the distribution of the SNP's vote see Miller, , End of British Politics?Google Scholar, Chap. 7.

⁷⁵ For further discussion of the statistical underpinnings to the allocation of seats and votes in three-party elections, see Gudgin, and Taylor, , Spatial Organisation of Elections, Chap. 5.Google Scholar

⁷⁶ Miller, , Electoral DynamicsGoogle Scholar, Chap. 3. The percentage of the variance explained by the percentage of employers and managers is much less in the case of the Liberals (30 per cent) than in the case of the Conservatives (62 per cent) or Labour (66 per cent). The even distribution of the Liberal vote is also to be explained by its failure to be strongly clustered by those other factors that systematically affect it (e.g., the degree of rurality of a constituency).

⁷⁷ Since 1922, the twelve have comprised nine safe Protestant constituencies, and three marginal Catholic ones which have periodically elected Unionist MPs. Out of the new seventeen, there are likely to be two safe Catholic constituencies and another three or four marginal ones. Thus we should not expect the seventeen Northern Irish MPs to be as coherent a group as the present twelve often have been.

⁷⁸ The assumption of a constant Liberal and Nationalist vote means that constituencies which are marginal between a major party and a minor one change hands as a result of uniform swings between the two major parties. Hence the total of Other seats in Table 14 varies.

⁷⁹ In each parliament lasting more than three years since 1955, the government has suffered a net loss of seats in by-elections, averaging just over seven seats (which loss would reduce an overall majority by fourteen). The 1966–70 Labour government lost fifteen MPs through by-elections or defection (i.e. a reduction of thirty in the overall majority over just four years) so this figure could well underestimate the initial majority needed to guarantee a five-year term.

⁸⁰ As defined in fn. 10.

⁸¹ See The Economist, 14 02 1981, pp. 72–3Google Scholar, which shows the political implications of shifts in the electorate since 1976.

⁸² This comment is partly based on Gudgin and Taylor's theoretical modelling of the likely consequences of the use of non-partisan districting commissioners (such as those used in the United Kingdom) in drawing up constituency boundaries. They view the commissioners' districting solution as a random solution within the constraints imposed upon them (such as keeping to county boundaries, contiguity, etc.); such a random solution, they argue, is most likely to result in the distribution of seats between the parties for which there is the largest number of permitted solutions. A new random solution is, therefore, likely to be similar to a previous solution in the way that it reflects the spatial division of voters. See Gudgin, and Taylor, , Spatial Organisation of Elections, pp. 140–58.Google Scholar We have also examined all the Commissioners' current proposals to abolish an existing seat or to create a new one. These appear to leave the number of marginals unchanged.

⁸³ See also fn. 52 above.

⁸⁴ This simulation assumes (i) that the overall swing would be the same as the mean constituency swing, and (ii) that the current seats won by minor parties would continue to be won by them, but all others would remain in the hands of the two leading parties. In addition, seats where a 1970(NT)–79 swing cannot be computed are excluded. As the 1970(NT)–79 swing contained some movements contrary to the main pattern, this exercise repeats those contrary swings. However, contrary movements between marginal and safe would, under these assumptions, only produce a net loss of six marginal seats. A further loss of one marginal seat would be accounted for by the Inconsistent categories. A normal distribution with a standard deviation of approximately 20·0 roughly fulfils the preconditions for a square law. As, however, its kurtosis would be less than that of a normal distribution, our hypothetical distribution would have an exaggerative quality even less powerful than that of a square law.

⁸⁵ Both the Nationalists' and the Unionists' support was acquired through the granting of concessions specific to the interests of their area, such as the pursuit of devolution for Scotland and Wales, and the enactment of the increase in the number of Northern Ireland seats noted in the text. In addition, during the last few months of that parliament, Ulster Unionists also, for example, attempted to persuade the government to provide a natural gas pipeline to Northern Ireland and succeeded in dissuading it from enacting homosexual law reform in the province.

⁸⁶ Some examples of the 1979 result under alternative electoral systems are given in Curtice and Steed, , 1979, p. 430.Google Scholar