Measuring Electoral Change in Three-Party Systems: an Alternative to Swing

Measuring Electoral Change

Measuring Electoral Change in Three-Party Systems: An Alternative to Swing

D. F. L. Dorling, University of Newcastle upon Tyne C. J. Pattie, University of Nottingham R. J. Johnston, University of Essex

Ina recent paper in this journal, Thus analyses of spatial (i.e., inter- pattern varied, this would be indica- Butler and Van Peek (1990) advo- constituency) variations in electoral tive of regional or other differences cated analyzing patterns of electoral change usually look at the ups and in the relative performance of the change in the USA with the swing downs of individual parties, as three parties. statistic-the average change in the recommended by Rose (see Johnston In this introductory note we move share of the vote won by two parties and Pattie 1992a, 1992b). In this the use of triangular graphs beyond contesting successive elections. The note, we suggest the use of two the visual to the analytic. We derive of their case was countered statistics which summarize change two statistics summarizing change in by Rose (1991), who showed that in the three-party situation. three-party systems, and briefly most liberal democracies do not have illustrate their use in analyzing elec- two-party systems; thus the swing toral change in Great Britain between statistic, which involves comparing The Electoral Triangle 1987 and 1992. the performance of two parties only, conceals more than it reveals of the It has long been recognized that Measuring Electoral Change pattern of electoral change in most the distribution of constituencies in Three-Party Systems situations. His preference was for the according to the percentage of votes separate study of the "ups and among three parties can be depicted Figure 1 is a triangular graph in downs" of each party. using triangular graphs (see Gudgin which the axes represent the per- In a riposte to Rose, Gibson (1992) and Taylor 1979; Miller 1977; Upton centages of the votes cast for the argued for the superiority of swing 1976; and Stray and Upton 1989). three parties together which were over the single party measures. His These have been used in a number of won by the Conservative (C), Labour case was built on a curious argu- presentations of the English three- (L) and Liberal Democrat Parties ment, however. On the basis of party system during the 1970s, 1980s (D). For the triangular graph to be goodness-of-fit statistics, he showed and 1990s. (Throughout that period used, the three percentages must sum that a combination of independent the Conservative and Labour parties to 100; other parties and abstainers variables relating to the characteris- dominated the electoral system. Up must be omitted from the calcula- tics of constituencies in Greater to and including the 1979 general tions. London predicted variations in swing election, the Liberal party was the Nationally, the percentages for the better than they predicted variations third. In 1983 and 1987, the third three parties at two elections (1 and in the performance of individual par- "party" was the Alliance of the 2) were ties. Such analyses in no way indicate Liberals with the newly-formed the superiority of swing as a measure Social Democratic Party. In 1992, C L D of electoral change, however; they the third party was the Liberal Election l 40 40 20 merely demonstrate that swing is Democrats. For examples of the use Election 2 46 37 17 more closely correlated to some of the triangle, see Johnston, Pattie independent variables than is another and Allsopp 1988.) There was a movement away from measure of change. Gibson's argu- More recently, triangular graphs both Labour and the Democrats, ment is a case of a spurious have been used to portray changes in with the Conservative party the net correlation. the three-party distribution of the gainer. This is shown by the arrow 41analysts of British elections vote, using arrows to depict the shift for the national shift on Figure 1, since the 1970s have recognized that from one election to the next. Both which is oriented to the "southeast." the two-party system assumed by the Dorling (1992) and Upton (1989, Also shown on Figure 1 are the swing statistic no longer exists, and 1991) have placed these arrows on shifts for two constituencies (a and that study of changes in the propor- cartograms, thereby illustrating the b). The relevant figures are: tion of that part of the electorate geography of variations in electoral which supports one of the two par- change. If the pattern were uniform C L D ties Constituency a only (almost invariably the Con- across the country, then all arrows Election I 3 5 30 35 servative and Labour parties) is not would point in the same direction Election 2 40 33 27 revealing. England now has a and be of the same length (this Constituency b three-party system, and Scotland and would be the equivalent of Butler's Election 1 30 55 15 wales each has a four-party system. concept of "uniform swing"); if the Election 2 3 5 45 20

kernber 1993 Features

FIGURE 1 three-party systems, using trigonom- etry based on the triangular graph:

(1) The directional angle (Ad), which summarizes the net direction of change in a constituency, relative to the national pattern; and (2) The length of the arro W (Ld), which indicates the magnitude of change. To provide a brief illustration of these two, we have analyzed Great Britain between the general elections of 1987 and 1992, when there were 633 separate constituencies.' For this, we use the percentage of the votes cast for the three main parties only, which nationally were:

Values of Ad and Ld were calculated for each constituency. Figure 2 shows the national arrow, pointing "south south west" (because the Conservative percentage of the votes cast remained virtually Conservative (C) b constant, whereas Labour's percentage increased and that of the Liberal These two shifts are in different The Appendix gives the formulae for Democrats fell). It also provides a directions from the national pattern. computing these angles. template for interpreting the values That for constituency a is oriented On Figure 1 there is a second dif- of Ad. Thus, for example, an angle almost "due south," because Labour ference between the national change of between - 63" and - 3" indicates as well as Conservative was a net and that in each of the two constitu- a greater than average loss of votes gainer. That for constituency b is encies-the latter two arrows are for Conservatives and a loss for the oriented "east-north-east," reflecting longer than that for the country as a Democrats, countered by an increase gains by both Conservative and whole. This is because the latter had for Labour, whereas one between Democrats. greater net change in the pattern of + 57" and + 117" indicates a Con- Different shifts are represented by votes than was the case nationally: servative gain and a loss for each of arrows at different angles. In trig- for constituency a the net change in the other two; in the latter segment, onometry, those angles would nor- the distribution of votes (the sum of the larger the angle the smaller the mally be measured relative to a the absolute differences divided by Democrat loss and the larger the notional base. Rather than compare two) was 8 and for constituency b it Labour decline. patterns of change with a rather was 10: the national net shift was Frequency distributions and sum- meaningless datum, however, we only 6. Thus the greater the volume mary statistics for the two variables have developed a measure of the of movement the longer the arrow, are given in Table 1. The data for angular difference between the arrow which gives us a second measure of Ad indicate substantial variability for each constituency and that for electoral change. (The absolute dif- around the national figure, with only the national pattern. In this, positive ferences just described are equal to just over half of the constituencies angles represent arrows to the the length on the graph divided by within 25" of it; relatively few are "north" of the national arrow (l.(;., the square root of 3.0.) The Appen- more than 90" from the national moving in an anti-clockwise direction dix also gives the formula for deriv- trend, however, indicating that most from it); negative angles represent ing the length of each arrow. constituencies fell within the "south- arrows to the "south" (moving western" third of the template. These clockwise from the national arrow). indicate, just as the swing statistics Thus the larger the angle (the maxi- An Application: for earlier two-party contests illus- mum value is + 180") the greater the Great Britain, 1987-1992 trated (Johnson 1983), that there was deviation from the national trend, little uniformity of electoral change whereas the sign of the angle indi- We have derived two measures of across the country's constituencies. cates the direction of that deviation. electoral change in constituencies in Most swung towards Labour-any

PS: Political Science & Politics Measuring Electoral Change angle between - 123" and + 57"- and few shifted towards the Liberal Democrats (an angle either > - 63" or > + 117"). There were fewer large positive angles (substantial shifts to the Conservative party) than there were large negative ones (substantial shifts away from the party of government).

TABLE 1 Summary Statistics for the Measures of Angle and Length (Shifts between the 1987 and 1992 General Elections in Great Britain: 633 Constituencies)

Angle Number Length Number -180:-135 14 0: 1 16 -134: -90 34 1 :2 38 -89: -60 22 2:3 43 -59: -45 15 3:4 58 -44. -40 8 4:5 75 -39: -35 15 5:6 52 -34: -30 26 6:7 68 -29: -25 26 7:s 42 -24: -20 36 8:9 39 -19: -15 33 9:lO 43 -14: 210 53 10:ll 24 -9: -5 54 11:12 32 4. -0 54 12:13 16 0: 4 49 1394 16 P 5: 9 39 14:15 12 Conservative (C) b 10:14 27 1916 9 15: 19 19 16:17 13 U): 24 20 17:18 9 25:29 17 18:19 4 30: 34 I5 19< 24 Regional Differences around the national mean of 35: 39 10 - 4.23", the large positive values- 40: .44 S Much has been written about the 45: 59 18 which indicate little growth in the 60: 89 14 increased regionaI polarization in the Labour vote-are recorded for the 90;' 134 4 British electorate since the 1960s Scottish regions; the largest negative 135: 1.80 6 (e.g., Johnston, Pattie and Russell deviations, which indicate substantial 1993). To enquire whether there were Meana 30.74 7.82 Labour growth and relative stability regional variations between 1987 and in the Liberal Democrat perform- . - Standard Deviation 35.57 5.91 1992 we used analyses of variance ance, are for the more rural regions together with multiple classification of the south. aThe mean angle is calculated irrespective of analysis (ANOVA with MCA) to Variations in the volume of sign. investigate differences between 22 change, as indicated by arrow regions in both angle and length of lengths, showed less change than the . The data for length show that arrow. (The regions are those used in national figure throughout northern although most shifts were less than 8 all of our recent analyses: see England, and also in London's outer units long-a relatively small net Johnston, Pattie and Allsopp 1988 zones (where it is widely believed that movement-there was a considerable for a map. They comprise the coun- the Conservative party "saved" its positive skewness, with some very try's Standard Statistical Regions, majority). substantial shifts indeed. subdivided into the major conurba- More detailed analyses of these Inter-constituency variations in tions and the rest.) variations are called for, but are electoral change within Great Britain The results are given in Table 2, beyond the scope of this introductory have been a research focus of geog- which shows the results of the analy- note. For the present purposes, the raphers and others in recent years ses of variance (the F values) and of results in Table 2 indicate that we (e.g., Johnston, Pattie and Allsopp the MCA (the difference between have derived measures which reso- 1988). Here, by way o'f illustration of each region's average and the grand nate with our general appreciation of the use of our new statistical mea- mean). They indicate significant the regional variations in British elec- sures, we present the results of two inter-regional variations on both vari- toral behavior between the 1987 and analyses of such variations. ables. In terms of angular variations 1992 general elections.

December 1993 Features I TABLE 2 3 percentage points) the Conservative Results of the Analyses of Variance with Multiple Classification Analysis: percentage actually increased: where Regional Variations in Angle and Length, Great Britain, 1987-1992 Labour was in second place, it too won an increased share of the vote i Analysis of Variance whereas the Liberal Democrat percentage fell; in the five seats where Angle Length the Liberal Democrats were the main 1 F value 8.79 3.78 challengers on average the Labour 0.24 0.12 - Multiple Classification Analysis TABLE 3 Average Regional Deviation from Marginality and Angle: Grand Mean of Conservative-Held Seats, 1992 Angle Length Analysis of Variance Region -4.23 7.82 43.02 -0.34 Second Strathclyde Margin Place Interaction East Central Scotland 49.06 0.91 Rural Scotland 34.81 4.54 F value 7.91 3.97 3.03 Rural North -6.85 0.54 Beta 0.28 0.14 Industrial North East 22.64 -1.73 Merseyside 1.69 -1.31 Average Value = - 15.89 Greater Manchester 2.65 -1.94 Second-Placed Party Rest of North West -0.03 -2.18 West Yorkshire 10.68 -0.66 Liberal South Yorkshire 13.99 -3.03 Conservative Lead Labour Democrat Rural Wales- 9.68 1.03 0.0-2.9 percent 33.83 58.97 Industrial South Wales -4.81 -0.92 (7) (5) West Midlands Conurbation 5.47 -1.46 3.0-5.9 percent 17.77 22.94 Rest of West Midlands -1 .n -0.25 (6) (4) -11.22 0.94 East Midlands 6.0-8.9 percent 11.10 -95.59 East Anglia -6.32 1.g4 Devon and Cornwall -38.23 7.98 (8) (2) Wessex -51.93 1 .88 9.0-1 1.9 percent 0.57 -48.07 Inner London 7.82 1.54 (1 1) (6) Outer London -4.31 -0.21 12.0 c percent -7.52 -34.81 Outer Metropolitan -1.95 -1.51 (155) (128) Outer South East -26.36 -0.50 The numbers in parentheses refer to the number of constituencies in each category. Marginality and Tactical Voting Democrats were second in 1987,' the increase was much less, as was the relative shift would be towards them decline in the ~ib~~~lD~~~~~~~vote. Another topic of considerable (i.e., a large positive angle). (An average angle of 59" puts the psephological interest at recent To test this hypothesis, we split the trend in those seats almost exactly or British general elections has been tac constituencies into five bands the margin between a Labour gain tical (or "strategic") voting. The depending on their degree of mar- and a Labour loss, according to the focus of opposition has been on ginality (the Conservative lead over template in Figure 2.) defeating the incumbent Conservative the second-placed party in 1987, In constituencies where Labour party and as a consequence it has expressed as a Percentage of the total in second place, as the margin been suggested that the more mar- poll then), as shown in Table 3. For between it and the Conservative ginal the Conservative party's hold each band, we further classified the incumbent increases so the average on a seat, the greater the likelihood constituencies into those in which angular value falls. In the relatively that opponents will concentrate their Labour came second in 1987 and safe seats with the Liberal Democra votes on the party in second place those where the Democrats occupied in second place, the large negative after the previous election (Johnston that por ~tion. values indicate both Labour gains and Pattie 1991). An analysis of variance showed and Conservative losses. Overall, To test the validity of this argu- that there were significant differences therefore, the conservative party di ment as a potential explanation for in the average angle between both not suffer greatly from tactical vot- the inter-constituency variations in categories, as there was (slightly) for ing in its marginal seats, though electoral change between 1987 and the interaction between the two there was a shift to Labour in the (Table 3). The average value for 1 1992, we look at those seats held by most marginal where it was in sec0 the Conservative party only. We Conservative-held seats of - 15.89" place. expected to find that in the more indicates that in those seats as a i! marginal seats, where Labour was whole there was a slight shift towards **** t . second in 1987 the direction of Labour and away from the other two change would be towards it (i.e., a parties. In the most marginal seats This section gives two very brief negative angle) whereas where the (with a Conservative lead of less than examples only of the types of PS: Polifical Science & P01 740 Measuring Electoral Change

analysis possible with these new IF A, > ?r then A, = A, - (2*r) Rose, R. 1991. "The Ups and Downs of measures of electoral change in IF Ad < -a then A, = Ad + (2*r) Elections, or Look Before You Swing." Britain's three-party system. They PS: Political Science & Politics 24: 29-33. illustrate the potential for analytical To convert that angle from radians into Stray, S. and G. J. G. Upton. 1989. "Tri- degrees angles and Triads." Journal of the Opera- work which the use of swing denies tional Research Society 40: 83-92. and which investigation of the move- Ad = Ad * (180/r) Upton, G. J. G. 1976. "The Diagrammatic ment for each party separately would TO compute the length of the line Representation of Three-Party Contests." ignore. Political Studies 24: 448-54. Ld = J((Xc - Xn)' + (Yc - Yn)3. Upton, G. J. G. 1989. "The Components of Voting Change in England 1983-1987." Electoral Studies 8: 59-74. Conclusion Upton, G. J. G. 1991. "Displaying Election Notes Results." Political Geography Quarterly With Rose, we contend that the 10: 200-20. two-party swing statistic popularized 1. In fact there were 633 in 1987 and 634 by Butler and promoted by Gibson is in 1992. The constituency for Milton Keynes not a sensible measure of electoral was divided in 1991, because its electorate change in three-party systems. Rather had become very large (there were some slight than adopt the procedure of looking alterations to adjacent constituencies too). at each party separately as suggested For our purposes, we have combined the two 1992 Milton Keynes constituencies. by Rose, however, we have derived 2. In 1987. seats were fought by the Alli- About the Authors two new measures of shifts in three- ance, to which the Liberal Democrats were party systems which are based on use the 1992 successor in most constituencies. Daniel Doding of the triangular graph. Those mea- Daniel Dorling sures are presented and briefly illus- completed his Ph.D. thesis on Viiualiza- trated here, as potentially useful References tion of Spatial Social indices which can be employed in Structure at the Uni- further work, on Britain and else- Butler, D. E. and S. D. van Beek. 1990. versity of Newcastle where. "Why Not Swing? Measuring Electoral upon Tyne in 1991. Change." PS: Political Science & Politics This was followed by 23: 178-83. a two-year Joseph Appendix Dorling. D. F. L. 1992. "Stretching Space Rowntree Foundation and Splicing Time: From Cartographic Fellowship studying housing in Britain. He is To compute the relative angles, which are Animation to Interactive Visualization. " currently a James Knott Fellow at the Univer- calculated in radians, for shifts from elec- Cartography and Geographic Information sity of Newcastle upon Tyne. His research tion a to election b. Systems 19: 215-27. 267-70. interests focus on the analysis of society Gibson. J. G. 1992. "Measuring Electoral through the use of large data sets. D, = Vote for Democrats at Change: Look Before You Abandon election b in constituency i Swing." PS: Political Science & Politics Charles Pattie D,, = Vote for Democrats at 25: 195-98. Charles Pattie is a election b nationally Gudgin, G. and P. J. Taylor. J979. Seats. lecturer in the depart- Votes and the Spatial Organization of ment of geography at D, and D, = the same variables Elections. London: Pion. the University of for election a Johnston, R. J. 1983. "Spatial Continuity Nottingham. His and Individual Variability." Electoral main research inter- L~,L,, Lbi, L,, = the same variables Studies 2: 53-68. ests include electoral for votes for Labour, and Johnston, R. J. and C. J. Pattie. 1991. geography, and he is C,, C,, Cbi,C,, = the same variables "Tactical Voting in Great Britain in 1983 the author of a large for votes for Conservative and 1987: An Alternative Approach." number of studies of British Journal of Political Science 2 1: spatial aspects of voting in Britain, including Then 95-108. (with R. J. Johnston and J. G. Allsopp) A Johnston. R. J. and C. J. Pattie. 1992a. Nation Dividing? The Electoral Map of Great Yi = (Dbi - Dai)*J3 "Unemployment, the Poll Tax, and the Britain 1979-1987 (Longman). Y, = (Dbn - Dar3*J3 British General Election of 1992." Xi = (Cbi + Lai - Lbi - C,) Environment and Planning C: Govern- Ron Johnston X, = (Cbn + L, - L,, - Can) ment and Policy 10: 467-84. Ron Johnston has For the constituency (i) the angle (Ai) is Johnston, R. J. and C. J. Pattie. 1992b. "Is been Vice-Chancellor the See-Saw Tipping Back? The End of then of the University of Thatcherism and Changing Voting Pat- Essex since 1922; If Xi < > 0.0 then Ai = arctan terns in Great Britain 1979-92." Environ- before that he spent (Yi/Xi) else Ai = r and if Xi < 0.0 ment and Planning A 24: 1491-1506. 18 years as professor then Ai = Ai + r Johnston, R. J.. C. J. Pattie and J. G. of geography at the Allsopp. 1988. A Nation Dividing? University of Shef- For the national angle (A,) London: Longman. field. His main If X, < > 0.0 then A, = arctan Johnston, R. J., C. J. Pattie and A. T. research interests Russell. 1993. "Dealignment, Spatial are in political and electoral geography and in (Y ,/X,) else A, = r and if Polarisation and Economic Voting: An the history of geography. He is author of The X, < O.OAn = A, + r Exploration of Recent Trends in British Geography of English Politics: The I983 To compare the constituency and the Voting Behaviour." European Journal of General Election (Croorn Helm) and Money national angles Political Research 23: 67-90. and Votes (Croom Helm) and co-author (with Miller, W. L. 1977. Electoral Dynamics in P. J. Taylor) of Geography of Elections A, = Ai - A, Britain since 1921. London: Macmillan. (Penguin).

December 1993